Science in Christian Perspective

Newton's Laws as Allegory
VERN SHERIDAN POYTHRESS
Westminster Theological Seminary
Chestnut Hill, Philadelphia
Pennsylvania 19118

From: JASA 35 September 1983): 156-161.

Fresh insight into scientific laws can be gained by viewing them as "allegories within the universe as God's choral poem. Newton's laws serve as a principal example.

In an earlier article (Poythress 1983) 1 argued that the universe can be viewed as God's choral poem. Within that poem are many analogies and multi-dimensional relationships. In particular, the world "as poem" is (1) personally structured, (2) linguistically structured, (3) shot-through with metaphor and analogy, (4) utterly dependent on God, (5) undergoing development, (6) surprising in showing a triumph over chaos.

Since science can be viewed as a special system of allegories ("models") within the poem, the above features should at least at times characterize scientific laws. Let us see how Newton's laws in particular look from this type of perspective. As summarized by the Encyclopedia Britannica (1974: vol. 13, p. 19) Newton's three laws of motion are

(1) that a body remains in its state of rest unless it is compelled to change that state by a force impressed on it;

(2) that the change of motion (the change of velocity times the mass of the body) is proportional to the force impressed;

(3) that to every action there is an equal and opposite reaction.

Newton's Laws as Surprising

Consider first the motif of triumph over chaos: regularity in the universe constitutes triumph of order over chaos. Newton's laws are an example of this. The physicist and the engineer typically take for granted Newton's laws (or subtle modifications of them). The laws are "obvious," part of the texture of our thoughts. It is practically necessary to jump out of one's skin to go back to the 16th and 17th centuries. Before Newton "took over" the world, such things were not at all obvious. As long as people were still groping towards a solution, there seemed to be many possible answers. Only when one possible answer demonstrated its superior simplicity, accuracy, and efficacy did it manage to eliminate the others. Before Newton there were those who tried to account for motion in terms of an Aristotelian framework that invoked purposes and potentials. Others, including the early Newton himself, were attracted to Cartesian mechanism; they tried to account for all observable motions and changes in terms of underlying invisible mechanical linkages, involving no action at a distance. Moreover, Galileo's concept of inertia, further developed by Newton, had to triumph over the "obvious." It was an "obvious" fact in those days that some substances (such as fire and smoke) had an innate tendency to move upwards, others to move downwards. All motions on earth had an "innate" tendency to stop (because of friction, we would now say).

I want to reintroduce-the surprise and wonder into Newton's laws. It is surprising, not "obvious," that they are fruitful and illuminating. Why should God have created a world in which everything (not just a few things for which it might be convenient) has the constancy in rest or motion indicated by the first law? Some philosophers of science have argued that the first law boils down to a stipulative definition of "rest." But the fact is that (1) such a "definition" does have some relation to our prescientific starting point in a vague, intuitive concept of rest; (2) this definition happens to be a tremendously fruitful generality. Why should it be possible to generalize so effectively?

Similarly, the second law of motion can be construed as a stipulative definition of "force." It gives a recipe for calculating net force on a material body. But again, (a) such a definition does have some relation to our intuitive starting point in kinesthetic sense of muscle tension and exertion; (b) the vector law for addition of forces, the linear force law for springs, and the inverse square law for gravitation, all have a surprising simplicity, showing the "unreasonable" fruitfulness of the definition. God has chosen, in these cases, a world of extraordinarily simple order, order adapted to the mind of man. To use Chesterton's language, the train has arrived at Victoria.

Newton's Laws as Metaphor

It is easy to see that Newton's laws are a kind of "allegory. 11 With the help of certain further contextual explanations, the laws jointly set up a detailed mapping or correlation between positions, velocities, forces, and masses on the one hand, and mathematical equations on the other. The correlation links one aspect of the universe to another, just as John Bunyan's allegory links the experiences of growth, temptation, and sin in the Christian life to the story of a pilgrimage.

Consider next the personal character of God's poem. Can Newton's laws be seen as "personal" in some sense? If so, how? Of course, the laws are not about persons. But neither is all poetry. To say that poetry is personal is to suggest that poetry has authors and interpreters who are persons. It is, perhaps, also to suggest that poetic meaning itself is intelligible only in the context of persons, and that personal engagement is necessary on the part of the interpreter in order to discern, appreciate, and unfold the meaning.

To say, then, that Newton's laws are personal is, first of all, to say that the formulators and interpreters of these laws are persons. On one level, this is trivial. Within the history of human science, human persons are indeed the formulators and interpreters of scientific laws. But many people think that the laws existed, even without being formulated, prior to the existence of any particular person. So the laws themselves, prior to human formulation, would not be in any sense personal.

As a biblical theist, I do not agree with this point of view. "Law" may indeed exist before there are created persons. But to have a "law," to have something that 11 holds," one must have a law-giver. God as a person must order the world, must triumph over chaos, must hold it to a pattern, if we are to say that a law holds. Of course, philosophers and others have denied that the analogy between God and a human law-giver, or between God and a human designer, artist, or creator, holds up this far. I cannot at this time follow the argument down to its roots (but cf. Stanley Jaki 1980). So I will content myself with saying that, through the Bible, God has opened my eyes to see that the kind of "law" and the kind of conformity to law that this world displays clearly reveal a personal, omnipotent, eternal creator (Rom 1:19-20).

There is, then, a law-giver. But we must distinguish between what God ordains on the one hand and what man as scientist guesses that he ordains on the other. Newton's laws, uttered by man, are not the law . They are an analogical imitation or replication of an aspect of God's law for the world.

Many scientists proceed about their business quite competently, of course, without believing in God or invoking him (Laplace, I have no need of that hypothesis"). Superficially, in the short run, they succeed. But they succeed because they live on borrowed capital. They know of God, as Rom. 1: 18-20 points out, but hide the fact from themselves to save themselves from its psychic costs. They are like the hippy on an airplane ride who tells you that he doesn't trust anyone straight or anyone over thirty. He conceals from himself his reliance on the pilot. Likewise, scientists covertly rely on their knowledge that the universe-airplane is in good hands. In fact, if the universe is not governed by a person, there is simply no intelligible reason why persons can say anything intelligible about how it is governed.

Second, poetry is personal in that it demands personal involvement for its interpretation and appreciation. Are Newton's laws analogous? It might seem that science in general and Newton's laws in particular are in this respect at the opposite pole from poetry. Much poetry talks directly about persons and much science talks in mechanistic metaphors. Hence the one demands a kind of personal involvement not characteristic of the other. But even within the sphere of poetry, the mode of personal involvement and commitment depends on the particular poetic subgenre in question. And poetry is not without demands for "objectivity. " One does not simply pour into a poem one's own views and one's own emotions. Moreover, precisely in the context of philosophy of science, Michael Polanyi (1958, 1969) argues that all human knowledge whatsoever is "personal." There is no knowledge without commitment, without interests motivating the search and the learning, and without a tacit background of contexts of life making each particular statement meaningful.

These are the principal ways in which Newton's laws are

Vern Sheridan Poythress is presently Associate Professor of New Testament at Westminster Theological Seminary. He has a particular interest in interpretive principles, based on his background in linguistics and apologetics. He holds six earned degrees, including a Ph.D. in mathematics from Harvard University, a Th.D. in New Testament from the University of Stellenbosch (South Africa), and masters degrees in biblical studies from the University of Cambridge and Westminster Theological Seminary. He has also taught linguistics at the University of Oklahoma. He has published a book on Christian philosophy of science, and articles in the areas of mathematics, philosophy of science, linguistics, hermeneutics, and biblical studies. Dr. Poythress is a minister in the Presbyterian Church in America.

personal. But I will risk going a bit farther, even though my arguments become more tenuous. Even the specific content of Newton's laws includes or at least suggests some quasipersonalistic overtones. A person's initial understanding of these laws is mediated by the use of analogy with each person I s broad personal experience as an individual in the world.

The use of "body" in Newton's laws to designate inanimate material things is much older than Newton. Yet even that use of "body" is not without its quasipersonal overtones. Newton's laws would be impossible without a key assumption. That assumption is that for many practical purposes entities like planets, bullets, balls, and rocks can be treated as wholes, with an integrity of their own. And the sense that we have of the integrity of an inanimate thing is analogically related to the experience that we have of the integrity of our own body. The Oxford English Dictionary rightly designates this use of "body" as "transferred from the material part of man to matter generally. . . . "

I want to reintroduce the surprise and wonder into Newton's laws. It is surprising, not "obvious," that they are fruitful and illuminating.

But the quasipersonification of "body" is more obvious when one looks at the rest of the language of Newton's laws. The body remains at "rest," analogous to a human being's experience of resting. Then it is "compelled," analogous to compulsion on a human being. It is compelled by a "force," analogous to kinesthetic force of man's band on someone else. In the second law, the concept of "mass" appeals to kinesthetic sense of heft. In the third law, the concept of action and reaction appeals at least vaguely to the analogy of reciprocity and interchangeability in the activity of two human beings.

What we are encountering here is the fact that the subhuman and even inanimate world has been created by God so that it is intelligible to us. As human beings we have access to the inanimate world. Of course, this inanimate world is not something equal to us. it is not something actually, literally human, or animistic. But neither is it something alien to us, something that we cannot identify with. We are made "of the dust of the ground. " That is an observation not only, not even primarily, about atoms and molecules of our body, but about a kind of "kinship." It is Dot a mistake to quasipersonify material bodies. Rather it is good and true, provided we realize, as Newton did, the limited scope of the personification. At some level it is necessary to do something like this, because only so can we make anything intelligible to us. That which is absolutely alien has, by definition, no point of contact with us. Hence there can be no point of access to knowledge of it.

The combination of quasipersonification and quantification is what gave Newton's laws a kind of symbiotic power. The quantification reins in the flight of imagination involved in personification. Conversely the quasipersonification provides a poetic picture and framework to guide the interpretation of and organization of the calculations, as well as their application to new types of phenomena.

One of the aspects of quasipersonification operates in a noteworthy way in the third law, namely the idea of transformation of point of view. One of our human abilities is the ability to step into someone else's shoes. We can imagine what it is like living and seeing the world from another person's standpoint. This represents a deeply personal and in fact interpersonal capacity. As single individuals we are able to harbor, in our minds and lives, shadows or projections of the views of other persons, and this is an important and necessary foundation for understanding of and participation in social (interpersonal) life.

Newton's third law requires a structured transformation between two viewpoints, both distinct from the starting ego-viewpoint of the scientist-observer. As with the other two laws, the observer must be able to transfer the quasipersonal language of rest, force, and impulsion from himself to inanimate bodies. He must know what it is consistently to adopt a single "body's" viewpoint. That is, be must be able to bold in his intellectual grasp simultaneously all forces, velocities, and the mass of a single body. He must be able to distinguish them from other forces of other bodies. They are forces, velocities, and mass from the perspective or viewpoint of that body.

But now in the third law the observer is required in addition to become conscious explicitly of a transformation from one body's viewpoint to the viewpoint of another. Only if he knows how properly to make this shift will he be able intelligibly and correctly to use the third law as intended. The third law does not make proper sense if "action" and "reaction" are interpreted as two forces or impulsions acting simultaneously on a single body, or acting successively on a single body, or acting on two bodies successively, or acting on two bodies simultaneously, without the one body being the "source" for the force acting on the other. The two forces must, in a sense, be manifestations of the same structured phenomenon, but viewed from the perspective first of body, "feeling" the "compulsion" "exerted by" body,, second of body, "feeling" the "compulsion" "exerted by" body,. The model being used here is definitely the model familiar to everyone from his experience of shifting in his mind from the viewpoint and actions of one personal participant to the viewpoint and actions of the other.

Thus the formulation of Newton's laws appeals to personal experience and our personal ability to adopt others' viewpoints. The formulation itself depends on ultimately personal metaphors more than one might first expect. Of course, growing familiarity with and continued use of the laws .. purifies" one's understanding of them. The individual words come to have technicized meanings under the constraints of quantifiability. The development of habit and routine makes consciousness of any quasipersonal connotations unnecessary or even counterproductive. But the quasipersonal aspects are, I believe, capable of being reactivated when one tries to apply and extend the theory beyond the area of the routine.

There are two phases of scientific activity involved here. During the creative, imaginative, path-breaking phase, quasipersonal analogies operate. Then this phase is followed by a phase of increasing rigor and quantification. The vocabulary is technicized and loses its suggestiveness. Both phases, together with their mutual dynamic interaction, are necessary for the healthy growth of a science. The rigorous laws due to controlled models are the more familiar side of scientific enterprise. But how do we arrive at that final rigor? The pathway there is not itself "rigorous." Einstein (1934:4) puts it thus:

The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. [rigorous stage] There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them. (creative stage)

The two stages must in a sense be recapitulated in the experience of the learner of science. He learns the meaning of technical terms like "mass" and "force" by starting from more intuitive, quasipersonal senses of the terms, and gradually technicizing them in his mind.

Newton's laws are far from being the only instance, or even the most obvious instance, where quasipersonal associations f rorn the imaginative, creative phase of science are buried beneath the surface. One can detect quasipersonal connotations in many other places in scientific literature simply by focusing on the verbs and words semantically derived from verbs. The verbs often connote personal activity.

Listen, for instance, to Edward 0. Wilson describe visual processing, using language not too remote from the industrial assembly line:

Vision, for example, begins its journey when the radiant energy of light triggers electrical activity in the approximately one hundred million primary light receptor cells that comprise the retina. Each cell records the level of brightness (or color) that touches it in each instant of time; the image transmitted through the lens is thus picked up as a pattern of electrical signals in the manner of a television camera. Behind the retina a million or so ganglion cells receive the signals and process them by a form of abstraction. Each cell receives information from a circular cluster of primary receptors in the retina. When a ligbt-dark contrast of sufficient intensity divides the retinal cluster, the ganglion cell is activated. This information is then passed on to a region of the cerebral cortex low in the back of the head, where special cortical nerve cells reinterpret it.... (1978:74).

Or Feldman-Sears (1981:104) on wheat genetics:

Hybridizations of this type are facilitated by the shared genorne, which acts as a buier, ensuring some fertility in the resulting hybrids. In such cases the different genomes, which are brought together from different parenK can exchange genetic material and form a new, mixed genome.

Or Rose (1981) on autoimmune diseases: Those that invade the body are usually held at bay by the body's immune defenses, an elaborate system that stands guard to intercept and destroy foreign cells. (p. 80)

Instead of damaging the thyroid cells these antibodies stimulate them, spurring the thyroid to make more hormones. The overproduction of thyroid hormones causes symptoms of restlessness, weight loss and palpitations. (p. 82)

They include macrophages, which take up antigens and present them to the lymphocytes in an appropriate way in order to initiate the immune response. The macrophages are also important phagocytic (scavenger) cells, engulfing and digesting invading microorganisms and other antigenic particles. (p. 82) (Italics are mine.) Language with quasipersonal connotations is widespread in contemporary science.

Let us now return to Newton's laws and consider another possible aspect of the analogy with poetry. Can Newton's laws be considered as linguistic in structure? It is obvious that Newton's laws are in one sense a piece of language. Yet it is not the usual practice to consider them as at toot linguistic in nature. They can be paraphrased in many ways in English, French, or some other language, as well as represented by mathematical formulas. Therefore, being able to identify them as Newton's laws does not depend on the specific form or mode of linguistic expression. Nevertheless, it ought to be possible to obtain insight into these or other laws by reflection on language, since God's speech lies behind any human attempt to express the regularities of God's "poem."

I will here adopt tagmemic theory (cf. Pike 1967, 1976, 1977) as a linguistic approach convenient for analyzing Newton's laws. There are several competing linguistic theories in the academic marketplace today, and tagmemic theory is not by any means the most popular. However, in addition to other strengths, it has the advantage of presupposing a personal world in which persons are irreducible participants (Pike 1976:108). This fits in with my earlier concerns for the personal character of the world.

Another emphasis of tagmernic theory is that of multiple perspectives. Persons are capable of a multiplicity of perspectives (Pike 1976:122-123). Using various perspectives or frameworks as starting points, they are capable of producing more than one theory accounting for the same data. This immediately explains many otherwise very frustrating facts about the clash of different theories in the social sciences. For instance, it explains the apparent inability of the academic linguistic community as a whole to finally settle on a single theory as the "best. " Sociology, anthropology, economics, and psychology are similarly beset with a plurality of competing theories, no one of which, in modern times, has been able to drive the others totally from the field. As Kuhn (1970) observes, competing models for understanding a given scientific domain may both be able to explain a large number of facts. Moreover, by sufficient "enrichment" and ad hoc means, they can account even for anomalies.

Our first reaction may be to give thanks that the natural sciences do not produce the same kind of apparently permanent pluralism as exists in the social sciences. Except for times of "scientific revolution" studied by Kuhn, natural sciences tend to operate within the bounds of a single dominant model. Yet when we look more closely, we must admit that natural sciences also offer us at least some examples of multiple-perspective theories. Newtonian mechanics offers us the multiple perspectives in time and space defined by Galilean relativity. Special relativity offers us the perspectives defined by Lorentz relativity. Quantum mechanics offers us the wave perspective and particle perspective, transformable into one another by means of the duality of the uncertainty relations and commutation relations. The theory of gases offers us the perspectives of thermodynamics and statistical kinetic theory. And mathematics? Well, that is for my next paper, but there are often choices between a more geometric or more algebraic approach.

the reality of the knowledge embodied in a law, Tagmemic theory recognizes that there are units in language of various sizes and types. There are alphabetical letters, words, phrases, sentences, and so on. Each unit has a unity, integrity, and organization of its own, but it is also related to other units. According to tagmemics, our knowledge of a unit can be characterized by the intersection and interaction of three perspectives on the unit. These three are labeled the contrast, the variation, and the distribution of a unit (cf. Pike 1976:109, 112-113; 1977:2).

The contrast of a unit is its distinctiveness: what separates it from all other units. The variation of a unit is the range within which it may vary and still remain that unit. The distribution of a unit is the context or range of contexts in which it may occur. Thus, for the word "horse," its contrast is its distinctiveness over against other words, especially other nouns like

Newton's laws are far from being the only instance, or even the most obvious instance, where quasipersonal associations from the imaginative, creative phase of science are buried beneath the surface.

Tagmemic theory, then, would ask whether the phenomena treated by Newton's laws could not also be treated some other way. Can we, say, reformulate Newton's laws? Can we reformulate them slightly by changing our coordinate system by a Galilean transformation? Can we reformulate them more radically by introducing generalized coordinates? Only many years after Newton did Lagrange determine a generalized formulation of the laws. For a system with n degrees of freedom measured by generalized coordinates q_1......q_n,  Newton's laws can be formulated

d/dt ( L_i/q_i^{) - L}_i^/q_i ^{= 0.}

Contrast, Variation, and Distribution of a "Law"

I now return to tagmemic theory in order to derive a second too] for analyzing scientific laws. This second too] can give us a means of dealing with the limited nature as well as cow, house, man, mountain. Its variation includes variation in pronunciation (sometimes "hoss") and variation in application (referring to various types of horses from time to time). Its distribution is like that of many nouns, though we do not expect to see it as the subject or a verb like "speak," "sell," etc. (For further exposition of contrast, variation, and distribution, see Poythress 1976:123-124, Pike 1977:1-3, 1980.)

Now let us look at Newton's laws in terms of their contrast, variation, and distribution. Newton's laws contrast with other possible laws (such as the Aristotelian theory of innate potentials). They are meaningful, intelligible, testable partly in terms of such contrast. The most stringent tests involve more precise formulations like the inverse square law of gravitation, because this clearly contrasts with many other possible formulas for force, and with formulas that might relate the various other properties and spatial relationships between two (or more) bodies. Newton's three laws, by themselves, are not open to such stringent tests because they are quasidefinitional in nature.

Newton's laws also have variation. That is, they apply to a large number of different particular cases. just to what extent they apply to the very large, the very small, the very distant, etc., is not exactly known when they are first formulated. Hence the fact of variation expresses a limitation on the knowledge embodied in the laws. The laws are a "mere" generality (they do not give us the details of each system). And we do not know exactly how sweeping this generality will prove to be.

Finally, Newton's laws have distribution. They are distributed in many contexts. The context of ordinary language and ordinary experience is the tacit background from which the particular words and over-all model involved in the laws gain their meaning, Moreover, the laws are also distributed in the context of one another. Each has the meaning that it does only when they operate together. Moreover, they have this particular meaning only as long as people are able to grasp what it means to go about measuring or calculating force, mass, velocity, and so on. The laws are dependent on a system of correlations between mathematics and standardized apparatuses for measurements of various kinds. Yet the apparatuses may change, be replaced, be restructured (replacing a spring clock with a pendulum clock or with a piezo-electric clock) without radical alteration of the purport of the laws.

We may say, then, that Newton's laws can be thought of as a particular piece of human language (more specifically allegory). These laws are a stanza of poetry interpreting an aspect of God's universe-poem. But on close inspection, it appears that this piece of poetry gains its significance from its interconnections with and interweavings with a larger and richer context of language. The stanza achieves its power as part of a group of stanzas. It is, moreover, one perspective out of many. We are able to adopt this single perspective, and simultaneously able tacitly to utilize a rich surrounding context defining its terms. By so doing we put Newton's laws effectively to work. Such is the unique gift of persons, of " poet-interpreters."

Encyclopedia Britannica. 1974. 15th ed. Macropedia Vol. 13 (Chicago: Benton).

Feldman, Moshe, and Sears, Ernest R. 1981. "The Wild Gene Resources of Wheat," Scientific American 244 no. I (January) 102-112.

Jaki, Stanley L. 1980. The Road of Science & the Ways of God. Chicago: University of Chicago.

Kuhn, Thomas S. 1970. The Structure of Scientific Revolutions. 2ed. Chicago: University of Chicago.

Pike, Kenneth L. 1967. Language in Relation to a Unified Theory of the Structure of Human Behavior. 2d ed. The Hague-Paris: Mouton.

---. 1976. "Toward the Development of Tagmemic Postulates," Tagmemics. Volume 2: Theoretical Discussion. Ed. Ruth M. Brend and Kenneth L. Pike. The Hague-Paris: Mouton. Pp. 91-127,

1980. "Here We Stand-Creative Observers of Language, 'Approches du langage: colloque interdisciplmaire. Publications de la Sorbonne. Serie " Etudes" 16:9-45.

Pike, Kenneth L. and Evelyn G. Pike. 1977. Grammatical Analysis. Dallas: Summer Institute of Linguistics.

Polanyi, Michael. 1958. Personal Knowledge., Towards a Post-Critical Philosophy' Chicago: University of Chicago.

Poythress, Vern Sheridan. 1976. Philosophy, Science and the Sovereignty of God. Philadelphia: Presbyterian and Reformed.

Wilson, Edward 0. 1978. On Human Nature. Cambridge: Harvard University.