Science in Christian Perspective

EXPLANATION IN THE PHYSICAL SCIENCES
FREDERICK H. GILES, JR.*

From: JASA 17 (September 1965): 79-86.

By noting a series of answers to a simple question regarding a common physical event, some of the properties of explanation in the Physical Sciences are illustrated. The importance of the empirical, the logical, and the psychological aspects of scientific theories are noted: the ultimate acceptance of a particular explanatory framework appears to depend upon all three of these aspects.

A one-hour discussion of "Explanation in the Physical Sciences" is a task fraught with difficulties. The subject is as broad as science itself, and the literature is extensive. It is nearly impossible for a professional philosopher of science to keep abreast of the field. It is impossible for the non-professional.

The subject is deep and formidable. In a blurb advertising a recent publication dealing with scientific explanation, the following quote appears: "It is not, I think, anything other than another graphic characterization of the existing state of affairs to say that no one today knows what a scientific explanation is . . . It is at this moment very much a mute question what general conditions an account of a fact must satisfy if it is to constitute 'scientific explanation."¹

Therefore, with a recognition of many limitations in understanding and insight, as well as in the necessary bounds of time and space, we will proceed into the subject much as an infant explores the ocean. We will wade in, splash around a bit, have fun, and then get out; with some on the inside, much more dripping off on the outside, perhaps a bit chilled, but with some feel for the subject none-the-less.

What is an explanation? Perhaps the most ready answer is "an explanation answers the question 'why?"'. Unfortunately, however, the word "why" carries a variety of meanings. In his book, The Structure of Science, Professor Ernest Nagel takes 10 different questions, and uses the word "why" in 10 different ways.² In a comparable sort of study, Aristotle discusses four causes which lend four distinct meanings to the question "why?".³ As an outline for this discussion, turn Doctor Nagel's scheme inside out and consider 10 answers to a single question.

A ball released from a man's hand is observed to drop. To the question "why did the object fall?" the following answers are possible:

2. That's the way "Nature" is, or "Providence" (God) has so ordained.

4. All objects, left to themselves, fall. 5. The ball is heavier than air.

7. There is a gravitational force pulling the ball to the earth.

8. The ball is in the gravitational field of the earth. 

9. Objects tend to a state of lowest potential energy. 10. Masses move along geodesics in space-time.

Here then are ten "explanations"; ten answers to a simple question concerning a very common observation, and the possibilities are still not exhausted.

Each answer makes a connection between the event to be explained and some broader, or more general, or more fundamental, or more immediate context.

*Frederick H. Giles is Associate Professor in the Department of Physics at the University of South Carolina. Paper presented at the Science Symposium, Wheaton College, Wheaton, Illinois, in February, 1964.

The event is related to some thought structure: a presumably mutually understood reference framework. A suitable explanation will fit the event smoothly into the framework, and the acceptability of the explanation will be determined by the smoothness of the fit. The appropriate framework will depend upon the context of the question, as well as upon the experience and sophistication of the question and the questioned. Hopefully, a sequential consideration of the above answers will give some feel for the type of reference frames which arise, how they arise, and the extent to which these frames may form a backdrop for explanation in the physical sciences.

1. The ball wanted to fall. This type of answer does not currently arise in the physical sciences. It seems to reflect an "animistic" view of things: a living breathing earth, on which objects are endowed with volitional capabilities. Today we presume that inanimate objects do not desire, and that the projection of this anthropormorphic activity on to such objects is naive and unnecessary. An answer of this sort may, however, be quite appropriate in some biographical or psychological context; for example, the falling object may be a human being who has dropped from a roof.

2. That's the way "Nature" is; or, "Providence" (God) has so ordained; or, that's as "Chance" would have it. Scientists sometimes use this sort of statement, but it would not be considered a "scientific explanation." It is beyond the province of the scientist to ask why "Nature" is as it is, yet the answer does presume that there exists some very broad, inclusive framework called Nature, God, Providence, even sometimes Evolution or Chance, in which all our experience occurs.

Such frames are much broader than "physical science". To use them as the immediate basis for scientific explanation is not considered fair. They purport to subsume all of experience: the events observed, as well as the explanations of the events. They are so inclusive that unique and testable deductions cannot be made from them: an event fits into such a framework simply because it occurred. Any explanation fits the event into the framework simply because the explainer wants it to.

These all-inclusive frames of reference may however become the final, fiat, court-of-appeal when honest ignorance disallows the use of a more immediate context. Unfortunately, resort is most often made to this sort of explanation only under conditions of exasperation, frustration, or laziness, and the situation is frequently further aggravated by the view that such appeals are unassailable.

3. The man let go of it. This reply is in direct contrast to the answer discussed in the immediately preceding paragraphs: whereas the former answer involved a frame of reference that was too broad, this explanation associates the observed event with no framework at all. The reference is only to a preceding event.

Now there are times when this type of reply may be exactly what is desired. A mother, upon hearing a crash in the next room, might well ask, "Junior, why did the vase fall?" She is not interested in being told that free objects move along geodesics in spacetime. Similarly, the falling of an apple would be "explained" by an orchard man in terms of "high winds" or "weak stems", but this would not satisfy Isaac Newton. Because it does not refer back to a framework, but only to a preceding event which, though perhaps more controllable, is really no broader a foundation for explanation than is the event in question, this sort of explanation would probably not be graced with the adjective "scientific".

First, answer number 3 assumes there is some sort of link between the event to be explained and the one explaining it. Whether there is a real or necessary connection between the events is a matter for later, deeper, and much more thought. Saying that one event "causes" a subsequent one is perhaps inaccurate, or even wrong, but the usage is certainly handy and common. For this discussion therefore, the "handy and common" has been chosen.

Secondly, the reply "The man let go of it" assumes one's knowledge that it is natural for unheld objects to fall. By "natural" one means that this is what an object does when it is left alone: a falling object is merely "doing what comes naturally". This assumption arises from observation, and it soon leads to the following generalization.

4. All objects left to themselves, fall. This answer arises from experience, and explains the event in question by putting it into a particular class of observed regularities. The answer exhibits the leap of faith which our minds make so naturally, and which undergirds modern science. Note the implicit assumption. In the past, objects when left to themselves, fell. This statement is then made to be more than a historical report: it is the foundation for predicting, for expecting, for "explaining" future similar events.

For this reason, it becomes one of the jobs of the scientist to catalog observed regularities. The statements of these regularities are the beginnings of scientific "laws", and an event is explained when it is properly related to such a statement. It is a "law" that when objects are left to themselves, they fall.

Using a mutually familiar regularity as an explanatory framework is often sufficient to quiet a questioner, but it is recognizably very incomplete. Like folders in a file cabinet, or like pigeon holes in a desk, rudimentary laws of this sort collect our immediate observations into handy regions, but as experience extends the number of folders, a more sophisticated and inclusive filing system becomes essential. More about this later.

5. The ball is heavier than air. Whenever a regularity has been uncovered, everyone is properly pleased. Now, suppose one uses previous experience and the generalization expressed in answer number 4 to predict what will happen when he releases, not a ball, but a helium-filled balloon. Instead of falling down, the balloon falls up! Such experiences make it obvious that one must have some sort of warning "footnote" addended to the law that "all objects, when left to themselves, fall." Other footnotes will also come to mind: for example, a cork will fall down in air, but it will fall up if it is released under water.

Unfortunately, footnotes of this sort are unpredictable. They are found only by extended experiment and observation. They are the result of trial and error, and they normally come as a shock. The danger of further observations upsetting an empirical rule must always be recognized. It thus becomes the job of a scientist not only to catalog regularities, but also to catalog any known exceptions. Answer 5 derives from the existence of a known footnote, and presupposes a previous knowledge of the rule which was the basis of answer number ⁴.

6. The object has a downward acceleration of 32 ft./ sec.². Though still essentially only a description of an observed regularity, this reply has that expected scientific "ring" to it. Two features have been introduced: the first is the use of a technical term requiring a precise definition, and the second is a quantitative element indicating a measurement has accompanied the observation. Both of these qualities are usually present or implied in the statement of a "law". The first feature assures ungarbled communication and transfer of information, while the second feature leaves the law open to unequivocal tests for exceptions or necessary extensions in its applicability.

The two features go hand in hand. In the Physical Sciences at least, it is difficult to imagine a definition which doesn't allow or imply a means of measuring the quantity or quality defined. There is however considerable disagreement regarding the inverse, i.e., does the measurement of a quantity necessarily allow or imply a definition of it? Consider the case in point. A quantity, "acceleration," is defined in terms of a particular relation between lengths in space and durations of time. The idea of acceleration was used by Galileo, and it was found to be very convenient in the description of motion. It is easily amenable to measurement: one measures intervals of space (lengths or distances), along with the intervals of time needed to traverse the distances, and then relates the measured quantities according to the definition.

But what of the concepts of "space" and "time" themselves? At the outset, these fundamental concepts will be considered intuitive. Further experience and theorizing may, and will, modify one's ideas as to the properties of space and time: whether or not they are structured, whether or not they are both manifestations of the same basic manifold, whether or not they are reversible or essentially right-handed, etc. Yet, through it all, the essential concepts of "space" and "time" are assumed understood. Intervals of space and time are measurable. Whether or not the concepts themselves are thus defined is left an open question.

A measurement is essentially a comparison according to certain rules, between the quantity in question and an arbitrarily agreed-upon standard of the same quantity. There are strikingly few quantities that are directly measured. Space (i.e., lengths, areas, and volumes) and time, along with at most two or three others (perhaps number, mass, or electric charge) complete the list. In the physical sciences, a measurement of a defined quantity, e.g. acceleration, involves a relationship between measurements of the fundamental few.

These relationships are generally expressable in "equation" form, and are amenable to mathematical manipulation. This makes mathematical shorthand available for description, and the observed regularities may be presented as laws, couched in the language of the mathematician. One has "a formula for it.

Kepler's three laws of planetary motion are somewhat more sophisticated examples of this point. The Danish astronomer Tycho Brahe made very accurate observations of the position of the planets in the skies: he catalogued these observations, and recorded all the appropriate measurements. Johannes Kepler, convinced along with Copernicus that the solar system was centered at the sun, manipulated the geometric picture suggested by Copernicus and found that this model did not exactly fit the data which had been collected. The fact that Kepler trusted the data rather than the original model is what makes him a central figure in the development of science. Rather than trying to torture the data to make it fit his picture, Kepler set out to find the particular geometric picture that the data fit. As is well known, he was successful and he was able to reduce the reams of data to three simple rules which today bear his name. These simple rules, these "empirical" laws, these statements of observed regularities, were quantitatively accurate and could be expressed in mathematical form. This was a tremendous step forward: all the data was subsumed under one formula-a formula which could be readily manipulated and used for predictive as well as explanatory purposes-and the motion of a single planet could be "explained" in terms of the motion of others.

Recourse to these rudimentary laws is probably the lowest level of explanation in the physical sciences. Though rudimentary, these laws are however fundamental. They describe what is observed, and are subject to the dictates of immediate measurement. Galileo reported, as an observed regularity, that all objects fall toward the surface of the earth with the same acceleration. This report came in the face of Aristotle's dictum, deduced from a postulated explanatory pattern of much wider compass, that bodies fall toward the earth with speeds that increase with their weight. The experiments of Galileo became the authority. Therefore, as broader and broader explanatory frames are invented to include more and more experience in a single thought structure, the deductions from the inclusive "laws" that characterize such frames must logically lead to expressions of the simple empirical laws. Using the analogy of the filing cabinet, one may devise better and broader systems for categorizing more and more material, but he still must properly file the individual folders.

7. There is a gravitational force pulling the ball to the earth. One is immediately struck with the fact that this answer is not a bald description of the sort previously considered. Indeed, the concept "force pulling" is related to the observation "ball falling" by recourse to the theory of motion invented by Isaac Newton. Admittedly borrowing and building upon the ideas and observations of his predecessors, the broad explanatory framework developed by Newton has been one of the most successful in the history of science.

Before going further, it is necessary to introduce another fundamental concept which is very familiar to the physicist-in fact, it is very familiar to every one yet which is extremely slippery when one tries to define it. The concept is that of an object; better still, that of "mass". Here again, as in the case of space and time, one has one of those concepts which appear to be intuitive. The mass of one object may be compared with the mass of another, so that "mass" may be measured, but just what mass itself is, is not defined in terms of more fundamental quantities. Newton himself suggested, in a recognizably circular definition, that the mass of an object is the amount of matter it contains. Perhaps the way to leave the subject for now is to state that the mass of an object is that property that makes an object an object.

As far back as Aristotle, the idea of a "force" being a push or a pull was common. Furthermore, experience indicates that in the horizontal direction at least, it takes a push or a pull to start or stop a moving object. Newton generalized this experience and stated that forces cause masses to change their motion, i.e., to accelerate. A measure of a force becomes the amount of acceleration it imparts to a given mass. Thus forces may be defined and measured in terms of mass, distance, and time; the three basic concepts. 

What now, if an object is not acted upon by any force? Sharpening a conjecture of Galileo's, Newton stated his famous law of inertia: an object tends to remain at rest, or in a state of constant motion in a straight line unless acted upon by some external force. A free object therefore does not accelerate! A freely falling object is therefore not "doing what comes naturally": it is not "free". The idea of "natural" has changed. It is a mark of Newton's genius that he recognized at the outset what was to be meant by the "natural" or unperturbed state of a mass, even though in bur experience no completely free object has ever been observed.

The finding and defining of a "natural" state seems to be imperative if one is to develop a broad framework for use in description and explanation. Note, however, that this "natural" state is not necessarily the one that is most obvious at the outset. Consider the "natural" taste of water. Most folk would describe or think of it in terms of the fluid that comes from the faucet. Upon tasting pure water, the reaction is that it has a rather queer flavor. The "natural" state of water is really a most uncommon state. Might I be so bold as to suggest that perhaps one of the reasons that no broad underlying framework has as yet been developed in such areas as psychology, sociology, and even perhaps biology, is because no agreed upon "natural" state has been defined.

Now, using Newton's laws of motion, the effects of forces upon the motion and trajectories of objects could be predicted and described. The inverse was also true; given the observations of the positions and velocities of an object, one can deduce just how it is being acted upon by forces. So, since objects accelerate only when acted upon by forces, and since unhindered objects accelerate toward the surface of the earth when they are released, these objects must be acted upon by a force. We call this force "weight". The source of this force, though not defined and still only vaguely understood, is labeled "gravity". Thus the answer: "There is a gravitational force pulling the ball to the earth."

An elucidation of the behavior of the gravitational force was another of the fundamental contributions of Newton. He recognized that the falling of an object (an apple in the familiar story) was due to a gravitational force drawing the object to the earth. He further recognized that because the moon went round the earth, and because the moon is a mass which "tends to travel at constant speed in a straight line unless acted upon by some external force", there must be a force pulling the moon toward the earth. He then conjectured that the same force that pulls an object to the ground at the earth's surface might very well be the one that reaches out and pulls the moon. By thus extending the concept of gravitational force, Newton formulated a rule which described a general attraction between masses. The rule was amenable to mathematical manipulation, and could be written as an equation. Predictions based on it could be checked in the laboratory as well as by astronomical observations.

The success of this "law of universal gravitation" is well known: the scope and number of experimentally verified results deduced from this law are amazing. Using the rules of algebra, Kepler's three laws of planetary motion could be deduced. The spherical shape of the earth could be predicted, as well as the probability of the existence of an equitorial bulge.

The motion of the moon could be described and its future motion predicted. The existence of, the tides is an expected result, deduced directly from the rule. A variation in weight with altitude was predicted and verified. A direct consequence of the law states the observation that at the surface of the earth, all objects fall with the same acceleration.

This law of universal gravitation is of a sort which is more general than the simple, direct, emperical laws of which Kepler's rules were an example. A unifying concept-in this case the concept of gravity has been extended to provide a theoretical basis, a framework if you please, for description, prediction, and explanation. Gravity itself is not defined; the rule describes the action of gravitational forces.

Notice a particular element of faith in the foregoing discussion. Newton assumed that the laws of motion which were validated by observations and experiments on the earth's surface, were applicable to the motion of the moon, an unreachable object far out in space. Not only was the idea of "gravity" extended, but the whole realm of the applicability of laboratory based experiments was vastly broadened. Today, this attitude is taken for granted: the chemistry of the stars is the chemistry of the earth; the laws of physics are applicable in the outer galaxies. The assumption appears very general: even in science fiction, the intelligent entities from other worlds are generally pictured as being the same sort of stinkers that we humans are.

The law of universal gravitation is an example of a good scientific theory. It correlates much data and experience. It relates hitherto unconnected events: the idea of the tides and the moon, the idea of the shape of the earth and the fact that it is revolving, the idea of weight varying with altitude. Its predictions, when they could be quantitatively checked, were found to be verified precisely. The law could be used to predict hitherto unknown phenomena.

Some one hundred years after the death of Newton, astronomers discovered a discrepancy between the predicted orbit of the planet and the actually observed orbit. Their discrepancy was small, but very definite. Either Newton's law of universal gravitation did not hold exactly for masses as far away as Uranus, or, there existed some hitherto unobserved mass out in the solar system, whose effect and presence had not been considered. Working backward from the observed effect, mathematicians in both England and France used Newton's law to calculate where in the sky this extra object must be. Astronomers looked, and the planet Neptune was found at the predicted location. The planet was discovered on paper before it was discovered in the heavens! Is it any wonder that the thinking of the world was shaken: one could presumably sit in an office, mentally juggle some numbers, and then tell an astronomer what he will see when he looks millions of miles out into space.

Other sources of forces were elucidated. Taking those into account, the past as well as the future behavior of a particle could be described and predicted in terms of a knowledge of its present position and velocity. With the rise of the atomic theory of chemistry, the Newtonian synthesis was made even broader. Everything is made up of tiny particles, and in the kinetic theory of gases, Newton's laws of motion were successfully applied to the individual atoms in order to predict the bulk behavior of gaseous materials. So far reaching was the success of Newton's ideas that to "explain" came to mean the giving or the describing of a mechanism: "giving a mechanism" meaning to describe in terms of particles obeying Newton's laws.

8. The object is in the gravitational field of the earth. The Newtonian framework was mathematically refined under men like Hamilton, Jacobi and others, and in time, it was also found that certain conceptual refinements were useful. Answers (8) and (9) illustrate a couple of these refinements.

The idea of a force acting across empty space is a bothersome one. To picture the transmission of a force, one needs some sort of "material" contact or connection. For example, just how does the earth reach out and hold the moon; how does the earth contact and twist a compass in order to make the needle line up north and south; how does a magnet reach out and pull a nail to itself? The idea of a force reaching out through space-action at a distance, as the physicists have called it-was repugnant even to Newton.

To circumvent this problem, a new concept was invented: the idea of a field. In the case of a magnet, the magnet is assumed to influence all of the space around it, and this region of influenced space is by definition the region in which the magnetic field exists. Any other magnet or explanatory piece of iron brought into this region is influenced by the field; the stronger the field, the greater the influence. In a similar way, the earth is assumed to influence the region around itself, and to set up a gravitational field. Another mass in this region is attracted toward the earth by virtue of the presence of the field. It is convenient to picture these fields in terms of lines along which an exploring object will spontaneously move. In the case of the earth, the gravitational field would be pictured as lines extending directly out from the surface and a falling object comes in along one of these lines. The further out the lines go, the further apart they become, and therefore the weaker the field is pictured to be.

In physics today the concept of a field is considered more basic than the idea of a force although in the laboratory one still thinks in terms of forces and still measures intervals of space and time. The concept which was invented to make the explanation of a phenomena more compatible with one's feel for things, has become more basic than the original and perhaps more obvious concept that called it into existence. To a physicist, answer (8) is a simple, concise reply to the original question. To the ordinary layman, it is probably unintelligible.

9. Objects tend to a position of lowest potential energy. Within the explanatory framework, certain combinations have been named. One of these is "energy".

The energy concept has proved to be tremendously useful in relating a number of previously disconnected observations. Heat, light, sound, motion, electrical currents, chemical bonding, etc., may all be correlated by the use of this concept. "Energy" is probably the most fundamental and most widely used concept in physics today: physics has sometimes been defined as the study of energy and its transformations.

The reason for the importance of this concept is that throughout every process which has so far been amenable to physical description, the amount of energy involved has been found to remain unchanged. That is, if one begins a process with a certain amount of energy, one finds that the same amount remains at the end of the process, although it may appear in a somewhat different guise. This particular observation is the basis of a different sort of law-a principle if you like-called the law (or principle) of conservation of energy.

There are several such conservation laws in use in the physical sciences. Throughout a chemical process, the amount of material involved at the beginning is the same as that at the end, although the properties of the materials may be considerably altered. This is the law of conservation of mass. The principle of conservation of heat is basic in the study of calorimetry. In modern science, conservation of mass and conservation of heat have been subsumed as merely special cases of the principle of conservation of energy. However, there are some other conservation laws: the law of conservation of linear momentum, the principle of conservation of angular momentum, the principle of conservation of electric charge, which are independent examples of this sort of rule. They are extremely convenient and in modern physics they are basic in their application.

Another principle, which to our knowledge has never been violated, states that when left to itself, a physical system tends to a condition such that its energy output possibilities are a minimum. Don't give up-this short statement is a succinct way of describing a variety of observations. Moving objects tend to slow down due to friction; hot objects tend to cool off; no engine is 100% efficient; water flows from a leak in a boiler; and of course, an object falls down when it is released near the earth's surface. This is the essence of answer (9).

By the year 1900 a language and a structure-called classical physics-based on Newton's mechanics and upon the theories of electricity and magnetism which had been developed in the nineteenth century had become the "common sense of the physicist." In fact, it was (and still is) the "common sense" of most people in the west. Space and time were fixed and absolute. They were continuous, and time flowed uniformly in one direction. In space, the shortest distance between two points was a straight line, and space was pictured somewhat like a big cupboard in which the galaxies, the solar system, as well as the atoms are situated, and in which all motions take place.

The universe was generally pictured as rather machinelike. Determinism in varied degrees became the rule of the day. Classical Physics was, a closed system. All physical phenomena could presumably be explained within this one framework. Many philosophers and sociologists took a step further, and felt that the framework subsumed all of knowledge. Knowledge was limited; there was only a certain amount to learn because once learned, Newton's laws described the past and the future. Man was boundless; he was on his way to knowing everything. Although hindsight makes us feel that the folk at the turn of the century should have been much more suspicious, it is certainly true that a tremendous number of deductions which had been made on the basis of classical physics, did lead to descriptions and predictions which were experimentally verified.

10. Masses move along geodesics in space time. As new and more accurate experiments were performed, it became apparent that "common sense" was insufficient to explain all the observations. Internal inconsistencies arose: new deductions were not validated by experiment. Predictions as to the exact orbit of the planet Mercury could not be made without an uncomfortable stretching of the Newtonian framework. It could be deduced that one should be able to see a kettle of boiling water in a dark room, and this is just plain not the case. One should have different results if he performs electrical experiments on a moving train or if he performs them in a train station-a most discomforting prediction. Light falling upon certain metals was observed to release electric charges, and this fact could not be deduced in terms of the classical theories.

As in the case of all extensive explanatory frameworks, classical physics was very flexible. The "closed" system which is necessary for exact description and prediction was stretched and twisted in order to contain new information. However, it soon became apparent that the old system could not be reliably extended to explain an increasing number of new observations. The "closed system" had to be punctured. It still surrounded vast areas of knowledge, but it couldn't encompass all known physical phenomena. In the analogy of the filing cabinet: the old system had no room for a new set of folders.

New frameworks of thought have been invented and devised: quantum mechanics to describe events which occur in the realm of the extremely small, and relativity theory to explain events which occur in the realm of the extremely large or extremely fast. These new frameworks are far removed from "immediate experience." They picture a universe which has lost its machine-like qualities, but still is amenable to mathematical description. Relativity theory in particular has necessitated a change in our view of what space and time are like. Three-dimensional space and time have been combined in such a way as to form a four-dimensional manifold in which the concept of mass looses its substance and becomes a manifestation of distortion in the new space-time. These distortions then tend to coalesce in the shortest way possible. This is effectively what is meant by the statement that "masses move along geodesics in space-time."

Currently, the picture is by no means complete. It is true that classical physics is insufficient to explain all of the phenomena that has been observed, yet it is still the most complete and the broadest framework within which physicists may operate. In the past twenty years, ". . . the discrepancy between the classical mechanical thinking and the formal development of physics has further increased. At the same time there is no decisive advance in the emergence of a new comprehensive foundation that can be accepted with assurance."⁴

Conclusion. Explanation in the physical sciences means the logical (either inductive or deductive) fitting of an observation into an acceptable framework. Although perhaps implicit in the foregoing discussion, a final few paragraphs regarding the acceptability of a framework are necessary.

At least since the. time of Galileo, a first (but perhaps not necessarily the first) criteria requires that predictions based upon deductions from the framework be experimentally verified. The verification must be quantitative and exact. In many of the newer theories, it is not required that the outcome of individual events be predictable, but statistical relations between these outcomes are to be exactly verified.

A second reason for the acceptance of a framework is its simplicity and mathematical beauty. In the rebellion which many feel heralded the dawn of modern science, Copernicus decried the cumbersome mathematical machinery necessitated in the Ptolmaic description of a geocentric solar system. The much simpler mathematics occasioned by the heliocentric picture was the only virtue of such a description: the predictions based upon deductions from the Copernican framework were no better than those deduced from the Ptolemaic. In more modern times, Dr. P. A. M. Dirac makes the following claim: "Relativity . . . was soon generally accepted by physicists. There are two reasons for this: (a) It is in agreement wtih experiment and (b) there is a beautiful mathematical theory underlying it, which gives it strong emotional appeal. The second reason is not so much talked about, but in my own opinion it is the stronger one ... There is just one rock which weathers every storm . . . the assumption that the fundamental laws of nature correspond to a beautiful mathematical theory."⁵

Note that the mathematics may change. In the machine-like framework of classical physics the development of continuous connections between past, present, and future is describable in terms of continuous mathematics; the mathematics of the calculus and differential equations. In the newer theories, the beauty of the framework shows itself in a mathematics which deals more primarily with symmetries, with the mathematics of property, groups and classes of similarity. In any case, the beauty of the mathematics is a deciding characteristic of the accepted theories.

A third reason for the acceptance of an explanatory framework, a reason which might possibly be considered a subheading of the previous one, but which needs special emphasis, is noted in the following quotation from John Dewey. Concerning the acceptance of the theory of evolution, Dr. Dewey writes "If one . . . finds that some concensus of judgment has finally been reached, he discovers that this has come about not so much through exhaustive logical discussion as through a change in men's point of view. The solution is psychologically rather than logically justified."⁶ Dr. Dewey is right. The theory or framework by which an event is explained must lead to verifiable predictions, yes; it must have a simplicity and a mathematical beauty, yes; but with it all, the scientists must like it.

EPILOGUE:

When initially presented, the ideas suggested in the above paper were made open for oral discussion and application. Since that is impossible here, the following short epilogue seems appropriate. Three points at which the foregoing material bears upon Christian thought and witness are noted, and are briefly presented as seed thoughts for further development and for grist in later discussions.

First, the tentativeness of physical theories-even the broadest and most widely accepted of them-has been stressed. Using pictures from the physical sciences as theological proofs or as foundations of faith is therefore both risky and suspect. The distinction must be clear: as theological analogies these laws and theories may be very helpful, but not as proofs. This statement is equally true for those who use the pictures of physical science as "anti-theological" proofs, and thus again just as truly, as foundations of faith.

Secondly, the movement in physics away from immediate experiment, the concomitant development of "axiomatic" formulations -of historically empirically based theories, and the realization that these beautiful formalisms are the foundations of further thought has helped remove some of the so-called "scientific" bias against the "believing is seeing" emphasis in the message of JESUS.

Finally, in contrast with their counterparts in other disciplines, the physical scientists seem to worry less about attacks upon, or the demise of some well established theory. Physical scientists are also much less prone to grace a mere guess with the description "theory": a tentative suggestion should be empirically, logically, and psychologically well established to merit that appellation. Thus, when a theory is found to be wrong or wanting, the reaction is often one of welcome excitement. (Witness the "overthrow of parity" in 1957.) The upshot is a frame of mind which is generally quite open--often quite open therefore, to a hearing of the message of the Gospel. At the same time however, the upshot is a frame of mind that eschews commitment-including commitment to JESUS, the CHRIST.

1. Blurb from "Interscience Publishers", advertising the book "Philosophy of Science; Volume H", containing this quote from Nicholas Rescher, University of Pittsburgh.

2. Nagel, Ernest. The Structure of Science, Harcourt, Brace and World, Inc. (1961), chapter 2.

3. Aristotle. Physics. Book 2.3: see also Metaphysics, Book Delta 2.

4. Tisza, L. "The Conceptual Structure of Physics", in the Reviews of Modern Physics, Vol. 35, No. 1 (January 1963), p. 151.

5. Dirac, P. A. M. "Quantum Mechanics and the Aether", In the Scientific Monthly, Vol. 78, No. 3 (March 1954), p. 142.

6. Dewey, John. "Evolution and Ethics", In the Scientific Monthly, Vol. 78, No. 2 (February 1954), p. 57.

7. Ideas from so many books have been borrowed and presented in this discussion that it is Impossible to note them an. Particular indebtedness, however, to the book "Introduction to Concepts and Theories in Physical Science" by Dr. G. Holton, and to the books "Concepts of Space" and "Concepts of Force" by Dr. Max Jammer, must be acknowledged.