Whitehead's Philosophy of Science

Perhaps the best way into his mature cosmological vision is to begin with his earlier philosophy of science (or natural philosophy) as developed in 'The Concept of Nature' (1920)

According to Susanne Langer, who was one of Whitehead’s students at Radcliff in the 1920s, every great philosophical scheme “must, in its original form, be regarded as a myth^[1], which sets forth freshly and naively some new point of view [and] reveals new opportunities for rational construction” (The Practice of Philosophy, p. 178). Whitehead understood philosophy as the search, as mystical as it is logical, for “direct insight into depths as yet unspoken” (MT, p. 174). When developing a novel philosophical scheme of thought, the philosopher must refer to forms or patterns in experience for which words do not yet exist. For this reason, according to Langer, new schemes initially come to us “clothed in an extravagant metaphorical form.” Or, as Whitehead put it, as “metaphor mutely appealing for an imaginative leap” (PR, p. 4). In Langer’s view, while we may feel such schemes are fantastical and, literally speaking, incredible, we may still be left with a sense of their profound importance due to “the presence of some buried meaning” that while perhaps not worthy of literal belief nonetheless provokes deep contemplation (PP, p. 220). Langer no doubt related to her teacher and “great inspirer” (Mind I, p. 336) Whitehead’s “Philosophy of Organism” as a kind of elaborate myth, an extended biological metaphor helpful for reframing our understanding of the basis of mind in the active dynamism of life.

In an unpublished manuscript (quoted by Dryden, “Whitehead’s Influence on Susanne Langer’s Conception of Living Form,” in Process Studies, 26:1-2, 1997, p. 62-85), Langer refers to Whitehead’s metaphysics as “a strange creation by a great scientist,” which, like most great metaphysical systems,

“goes beyond the inventor’s literal conception; it is a genuine philosophic myth—not an allegory or consciously poetic statement, but a living myth…a cosmological myth of a divine universe striving for self-realization and enjoying its existence.”

She adds that

“even a person who finds his metaphysical use of these ideas fantastic may have recourse to his books again and again for the ideas themselves, because of their applicability within biological and psychological contexts.”

Langer herself made tremendous use of Whitehead’s abstractions in biological, psychological, and aesthetic contexts. Whitehead, himself a mathematician and physicist before becoming a philosopher, argued forcefully for their application in the physical sciences, as well. Just as Langer suggests we ought not to take Whitehead’s metaphysical scheme literally, perhaps we ought not take her own seeming reduction of the Philosophy of Organism to myth quite literally. Whitehead certainly understood himself to have articulated a realistic process-relational ontology better suited to the findings of post-classical physics and evolutionary biology than the defunct dualist or materialist metaphysics assumed by science since the 17^th century. Still, his repeated emphasis on the importance of imagination in metaphysics suggests he also recognized its non-rational role:

“The useful function of philosophy is to promote the most general systematization of civilized thought. There is a constant reaction between specialism and common sense. It is the part of the special sciences to modify common sense. Philosophy is the welding of imagination and com­mon sense into a restraint upon specialists, and also into an enlargement of their imaginations. By providing the generic notions philosophy should make it easier to conceive the infinite variety of specific instances which rest unrealized in the womb of nature.” (PR, p. 17)

In further defense of Langer’s point, there is also Whitehead’s repeated praise of Plato’s unsystematic but highly suggestive dialogues, which almost always end in intellectual aporia with a mythic illustration of the deeper meanings as yet ungraspable in the precisely articulated form of scientific propositions. In his magnum opus, Process and Reality, Whitehead took himself to be generalizing from the findings of the special sciences including quantum and relativity physics, physiology and evolutionary biology, and psychology (including the psychology of religion). He ends up with an elaborate list of entirely novel categories, which is off-putting to those who, having decided to undertake a reading of one of the most difficult texts in all of the Western canon, arrive at Process and Reality basecamp for the first time expecting an expansive and welcoming vista. Instead we are greeted with a bramble of initially incomprehensible existents, explanations, obligations, and derivative notions. Whitehead makes us work for the new worldview he is offering. He assures us in chapter one laying out his speculative method that he is not producing a deductive system capable of computing the world from clearly demonstrable premises. Philosophy is not primarily about deduction but rather a search for premises. He pretends to no certainty or completion. He’s offered a matrix of general propositions which he hopes, in addition to being logically consistent and coherent, applies to and elucidates all our experience, physical and mental, sensory and emotional, empirical and moral, scientific, artistic and spiritual, such that the ancient and modern problems of space, time, causality, the mind/body problem, etc., no longer arise.

But rather than here attempting to begin the ascent toward understanding the payoff of his mature metaphysical scheme, I believe it is more instructive, as an introduction to his thought, to begin with an earlier, explicitly non-metaphysical work: The Concept of Nature (1920).

In this book, Whitehead examines the philosophical underpinnings that unify scientific thought. It is thus best understood as falling in the genre of philosophy of science, or perhaps philosophy of nature. The philosophy of a particular special science assumes and aims to articulate the unifying characteristics that make it a coherent discipline. Extending this, the philosophy of all natural sciences endeavors to unify them into a single, cohesive science (or, failing this, to demonstrate why such unification is impossible). Here is an excerpt from Whitehead that lays out what is at stake in his philosophy of science, and why for the purposes of natural science, he finds it necessary to put to the side (without thereby dismissing!) many important metaphysical questions:

“The recourse to metaphysics is like throwing a match into the powder magazine. It blows up the whole arena. This is exactly what scientific philosophers do when they are driven into a corner and convicted of incoherence. They at once drag in the mind and talk of entities in the mind or out of the mind as the case may be. For natural philosophy everything perceived is in nature. We may not pick and choose. For us the red glow of the sunset should be as much part of nature as are the molecules and electric waves by which men of science would explain the phenomenon. It is for natural philosophy to analyse how these various elements of nature are connected. In making this demand I conceive myself as adopting our immediate instinctive attitude towards perceptual knowledge which is only abandoned under the influence of theory. We are instinctively willing to believe that by due attention, more can be found in nature than that which is observed at first sight. But we will not be content with less. What we ask from the philosophy of science is some account of the coherence of things perceptively known.” (CN, p. 29)

Whitehead begins by asserting that nature is what we are aware of in perception; it is the immediate content of sense-awareness that exists independently of thought while remaining accessible to thought. In this context, he claims that nature is “closed to mind,” meaning that entities and relations we become aware of in perception can be analyzed without necessarily referencing the role of the mind or perceiver. In claiming such a closure, he does not mean to imply any metaphysical separation between mind and nature. He means only to underscore that the relations within nature are self-contained and objectively analyzable. He thus refers to natural science as “homogeneous” thought about nature, opposing it to “heterogeneous” thought that would drag in metaphysical questions about the relation of knower to known, or about the relation of thinking to sense-awareness. As natural science is concerned with “homogenous” thought about nature, it excludes moral and aesthetic values from its analysis. This despite the fact that such values are deeply intertwined with our self-conscious agency as scientists and philosophers. For a comprehensive cosmology, including an understanding of the conditions making possible the emergence of conscious scientists, we cannot ignore the metaphysical significance of such values. But for the purposes of natural scientific research (and natural science is, it must be emphasized, a purposive activity!), values are not part of the homogeneous thought required for scientific generalizations derived from what we are aware of in perception.

Whitehead introduces three components in our knowledge of nature-as-perceived:

1. Fact: The undifferentiated totality presented to sense-awareness.

2. Factors: Differentiated elements within this totality, identified through sense-awareness.

3. Entities: Factors considered in their role as objects of thought, necessary for forming finite, expressible propositions and for filtering out irrelevant infinities from our reasoning.

Thus nature is described as a network of concrete events characterized by abstract entities, with the latter providing the propositions formed by our homogenous thoughts about the events of nature with objective referents that remain recognizable across the passage of events. Whitehead’s account of nature in terms of events and entities (or objects) is his alternative to the traditional doctrine of matter, which was derived from Greek philosophy and particularly from Aristotelian logic. Under the mostly unconscious influence of Aristotelean subject-predicate logic, modern science came to postulate matter as a metaphysical substratum underlying its observable attributes. This perspective erroneously separates entities from the factors disclosed in sense-awareness, treating entities as substances with attributes rather than as integral elements of what we are aware of in perception. 

“The unquestioned acceptance of the Aristotelian logic has led to an ingrained tendency to postulate a substratum for whatever is disclosed in sense-awareness, namely, to look below what we are aware of for the substance in the sense of the ‘concrete thing.’ This is the origin of the modern scientific concept of matter and of ether, namely they are the outcome of this insistent habit of postulation.” (CN, p. 18)

Whitehead argues that this bifurcation of nature into an insensible substance underlying its sensible properties is a misconception resulting not only from an uncritical acceptance of Aristotelean logic but from a classical conception of space and time as the external conditions in which nature is set. Whitehead accepted the new relativistic idea of space-time but disagreed with the then current formulation that used bits of matter as the relata for spatiotemporal relations. Instead, he argues that the true relata are events. In other words, space-time is a geometric abstraction derived from the interrelations of events, a way of characterizing the complex passage of these events, rather than a subtle material substratum or fabric within which material bodies are situated.

I can now unpack Whitehead’s criticisms of the still prevalent scientistic notion of the “bifurcation of nature”—the division of nature into two distinct realms: the apparent (what we directly perceive, including the red hue and warmth of the sunset or the pleasing interplay of notes in a melody) and the causal (the underlying reality of material particles and forces that is conjectured to cause our perceptions). On the bifurcation theory, the apparent world of colors and sounds could only be a kind of dream illusion, reducible in the terms of contemporary cognitive neuroscience to a kind of “controlled hallucination” somehow conjured in the skull (as “predictive processing” or “Bayesian brain” approaches argue; see, eg, Anil Seth’s book Being You). Whitehead rejects this bifurcated view as a complete muddle. He remarks elsewhere of such views, already on offer a century or more ago, that “Some people express themselves as though bodies, brains, and nerves were the only real things in an entirely imaginary world” (Science and the Modern World, p. 91).

Whitehead reminds us that “science is not a fairy tale” (CN, p. 40). We can make no sense of its great successes if we remain saddled with the bad metaphysics of the bifurcation theory. Scientific knowledge cannot be understood as the creation of fanciful mathematical properties of unknowable entities. Nature is not a bloodless ballet of numbers. Real events are occurring. Instead of seeking for hidden causes—hidden from our perception in principle, since conscious awareness of nature is on this theory a mere dream—Whitehead refocuses natural scientific investigation on what we are aware of in perception, which includes colors and warmth as much as electromagnetic waves. He construes the aim of science as the determination of the character of the things we know—that is, the nature that presents itself in our perceptual experiences. There is then only one nature: the one we perceive directly through our senses and tentative inferences therefrom. By dropping the term “apparent,” he underscores that all of nature is, in principle a least, accessible through perception and its technological extensions. There may of course be more to nature than what at first meets the eye. But there cannot be less!

It follows that a natural science that has overcome bifurcation would concern itself with the coherence of knowledge rather than the causes of knowledge. To illustrate this point, Whitehead uses the example of seeing a red coal in a fire. A post-bifurcation science would explain this phenomenon not by detailing how the mind perceives redness but by describing the physical processes—such as radiant energy entering the eyes and being transmitted through the optic nerve into the brain—that accompany the perception of red in nature. The chain of causation described by science need not involve the perceiving mind; instead, it focuses on the objects and events, and the relations between them, within perceivable nature itself. This does not mean that “mind” or “consciousness” are non-existent or of no philosophical interest. On the contrary! Whitehead’s underlying point is that the reality of the conscious mind and the possibility of knowledge are presupposed by natural science, and so themselves remain beyond its explanatory purview. Natural science is the study of the systematic relations evident in the passage of nature as we perceive it. This means that the so-called “hard problem of consciousness” is unsolvable precisely because it cannot even be properly formulated in natural scientific terms. Understanding the relationship between conscious minds and the natural world, and what the existence of such minds means about the deeper nature of our universe, would require going beyond natural science into metaphysics. But at this stage, Whitehead wanted to refrain from striking the match that would ignite the powder magazine and blow up the whole arena.

Whitehead acknowledges that he has been discussing an extreme form of bifurcation but notes that even the more moderate form, such as Locke’s theory of primary and secondary qualities (or “psychic additions”) remains problematic. This theory suggests that while we perceive objects in their proper time, place, and motion—with attributes like hardness and inertia—so-called subjective qualities like color, warmth, and sound are mere psychic additions and not truly part of nature. Whitehead challenges this theory by pointing out that perceptions of touch (e.g., the sensation of pressure or inertia) are just as much a result of transmission through the nervous system as perceptions of color or sound.

“This distinction is the product of an epoch in which physical science has got ahead of medical pathology and of physiology. Perceptions of push are just as much the outcome of transmission as are perceptions of colour. When colour is perceived the nerves of the body are excited in one way and transmit their message towards the brain, and when push is perceived other nerves of the body are excited in another way and transmit their message towards the brain. The message of the one set is not the conveyance of colour, and the message of the other set is not the conveyance of push. But in one case colour is perceived and in the other case the push due to the object. If you snip certain nerves, there is an end to the perception of colour; and if you snip certain other nerves, there is an end to the perception of push. It would appear therefore that any reasons which should remove colour from the reality of nature should also operate to remove inertia.” (CN, p. 43-44)

In both cases, nerves are excited and transmit their feelings to the brain, eventuating in perception. Therefore, any argument that removes color from the reality of nature on the grounds that it is a psychic addition should also remove inertia. There is no fundamental distinction between our ways of knowing different parts of nature; all sense-perceptions are on equal footing.

For Whitehead, reflecting upon the arena of natural science, what can be said is that the nature evident to us in our perceptual experiences is a complex of passing events. In this perceptual field we discern in addition to events definite mutual relations between them establishing their relative positions in the nexus of space and time. In addition to its spatiotemporal position relative to other events, each event exhibits a unique character. Characteristics, which can be recognized across multiple events, Whitehead also calls “objects.” This scientific distinction between events and objects anticipates his later metaphysical distinction between actual occasions and eternal objects; but for now, for the purposes of natural science, he distinguishes three types of objects:

1. sense objects like colors and sounds,

2. physical objects like coffee mugs, trees, and monuments (e.g., Cleopatra’s Needle), and

3. scientific objects like electrons and photons.

Whitehead notes that when science has a good handle on the adventures amid events of physical objects and scientific objects, it gains much of the relevant information required to predict when and how sense objects will be perceived in specific situations. For example, if we know there is a blazing fire, a mirror placed opposite it, and a person gazing into the mirror, we can predict that she will perceive the redness of the flame situated in an event appearing behind the mirror. This illustrates how the appearance of sense objects is conditioned by the adventures of physical and scientific objects, and how our sense experience may be delusive. However, it is also important to note that on Whitehead’s definition of nature as what we are aware of in perception, color must also be part of the real physical facts and not a “psychic addition” or subjective projection. There is nothing in the laws of electromagnetism or the data of neurology that indicate why the glow of the fire should be red or its radiance perceived as warmth. Some broader system of relations remains to be discovered that would account for our perception of sky-blue and heat. To the extent that we lack such psychophysical links, our understanding of the events of nature remains incomplete.

Science often works with more abstract objects like photons and electrons, which are not unreal because of their abstract status, but must never be severed from their experiential contexts as ingredients characterizing concrete events. Events can be characterized as “fields of activity” that influence the characteristics of subsequent events. These fields of activity come in the form of forces including gravity, electromagnetism, and chemical attractions. The lawful behavior of these scientific objects can be invoked to predict and control the course of events, so long as it is remembered that they are themselves abstracted from our perception of events. Whitehead cautions science against the irrational and anti-empirical pursuit of hidden causes of phenomena that would remain themselves imperceivable in principle. He develops his theory of “extensive abstraction” to show how precisely defined scientific objects like particles and fields are ultimately traceable back to carefully discriminated factors in our perception of fact.

The concrete facts are the events themselves, not the objects (whether sensory, physical, or scientific) situated in them. Again, to call something an abstraction does not mean it is nothing, but rather that it exists as an entity only within the concrete passage of nature. For example, a single electron is an abstraction because it cannot exist without the entire history and structure of the field that defines it. Similarly, the electromagnetic field itself, like the space-time manifold, is an abstract and for that reason highly precise way of characterizing the concrete passage of nature from event to event. It allows scientists to describe the relational possibilities of certain factors within fact.

Whitehead argues that sciences like chemistry and physics cannot express their ultimate laws in terms of middle-sized physical objects like cricket balls or Cleopatra’s Needle. These objects may seem obvious enough to our common sense, but they are too vaguely defined for the precision of scientific laws. Where does Cleopatra’s Needle begin and end? Is the soot that collects on its surface part of it? Is it not changing daily as it loses molecules or when its surface interacts with the acid of a London fog or, as occurred on September 7, 1940, when a bomb dropped by a German Luftwaffe plane permanently scarred its pedestal? Scientific objects like molecules and electrons have more definite simplicity in their character, which is why science expresses its final laws in terms of them.

I quote Whitehead at length giving expression to the “event-particles” that his theory of extensive abstraction allows science to construct:

“Again when we seek definitely to express the relations of events which arise from their spatio-temporal structure, we approximate to simplicity by progressively diminishing the extent (both temporal and spatial) of the events considered. For example, the event which is the life of the chunk of nature which is [Cleopatra’s] Needle during one minute has to the life of nature within a passing barge during the same minute a very complex spatio-temporal relation. But suppose we progressively diminish the time considered to a second, to a hundredth of a second, to a thousandth of a second, and so on. As we pass along such a series we approximate to an ideal simplicity of structural relations of the pairs of events successively considered, which ideal we call the spatial relations of the Needle to the barge at some instant. Even these relations are too complicated for us, and we consider smaller and smaller bits of the Needle and of the barge. Thus we finally reach the ideal of an event so restricted in its extension as to be without extension in space or extension in time. Such an event is a mere spatial point-flash of instantaneous duration. I call such an ideal event an ‘event-particle.’ You must not think of the world as ultimately built up of event-particles. That is to put the cart before the horse. The world we know is a continuous stream of occurrence which we can discriminate into finite events forming by their overlappings and containings of each other and separations a spatio-temporal structure. We can express the properties of this structure in terms of the ideal limits to routes of approximation, which I have termed event-particles. Accordingly event-particles are abstractions in their relations to the more concrete events. But then by this time you will have comprehended that you cannot analyse concrete nature without abstracting. Also I repeat, the abstractions of science are entities which are truly in nature, though they have no meaning in isolation from nature.

The character of the spatio-temporal structure of events can be fully expressed in terms of relations between these more abstract event-particles. The advantage of dealing with event-particles is that though they are abstract and complex in respect to the finite events which we directly observe, they are simpler than finite events in respect to their mutual relations. Accordingly they express for us the demands of an ideal accuracy, and of an ideal simplicity in the exposition of relations. These event-particles are the ultimate elements of the four-dimensional space-time manifold which the theory of relativity presupposes. You will have observed that each event-particle is as much an instant of time as it is a point of space. I have called it an instantaneous point-flash. Thus in the structure of this space-time manifold space is not finally discriminated from time, and the possibility remains open for diverse modes of discrimination according to the diverse circumstances of observers. It is this possibility which makes the fundamental distinction between the new way of conceiving the universe and the old way. The secret of understanding relativity is to understand this. It is of no use rushing in with picturesque paradoxes, such as ‘Space caught bending,’ if you have not mastered this fundamental conception which underlies the whole theory. When I say that it underlies the whole theory, I mean that in my opinion it ought to underlie it, though I may confess some doubts as to how far all expositions of the theory have really understood its implications and its premises.” (CN, p. 172-4).

I share these paragraphs because I believe Whitehead has addressed and could help us resolve a century’s old debate between physicists and philosophers that rages to this very day. I mean the famous Bergson-Einstein debate in 1922 about the status of lived time or duration vis a vis the clock-time that features in Einstein’s relativity theory. The split between what Einstein called “psychological time” (misunderstanding what Bergson meant by duration) and the measured time of physics is a particularly spectacular instance of the bifurcation of nature. There are plenty of physicists who have taken Bergson’s side over the years (Lee Smolin might be the most prominent living example, but Ilya Prigogine should also be mentioned), and many contemporary philosophers who take Einstein’s (like Tim Maudlin has done here a few days ago in response to Evan Thompson’s article defending Bergson—though interestingly Maudlin also defends the irreversible flow of time). So this is not just a divide between physics and philosophy, but cuts across both disciplines in interesting ways. I believe an alternative self-understanding of science has been clearly and compellingly articulated by Whitehead and kindred organic thinkers, an approach freeing science from the dead end of seeking heroic feats of explaining away everything that matters to us while still granting it real purchase on the nature of things. “The bifurcation theory however dies hard” (CN, p. 44).

I will quote the remainder of Whitehead’s chapter 8 from Concept of Nature as it addresses the supposed paradoxes of relativity theory directly and shows how Whitehead honors Einstein’s discovery but diverges from his philosophical interpretation:

“These different measure-systems with their divergences of time-reckoning are puzzling, and to some extent affront our common sense. It is not the usual way in which we think of the Universe. We think of one necessary time-system and one necessary space. According to the new theory, there are an indefinite number of discordant time-series and an indefinite number of distinct spaces. Any correlated pair, a time-system and a space-system, will do in which to fit our description of the Universe. We find that under given conditions our measurements are necessarily made in some one pair which together form our natural measure-system. The difficulty as to discordant time-systems is partly solved by distinguishing between what I call the creative advance of nature, which is not properly serial at all, and any one time series. We habitually muddle together this creative advance, which we experience and know as the perpetual transition of nature into novelty, with the single-time series which we naturally employ for measurement. The various time-series each measure some aspect of the creative advance, and the whole bundle of them express all the properties of this advance which are measurable. The reason why we have not previously noted this difference of time-series is the very small difference of properties between any two such series. Any observable phenomena due to this cause depend on the square of the ratio of any velocity entering into the observation to the velocity of light. Now light takes about fifty minutes to get round the earth’s orbit; and the earth takes rather more than 17,531 half-hours to do the same. Hence all the effects due to this motion are of the order of the ratio of one to the square of 10,000. Accordingly an earth-man and a sun-man have only neglected effects whose quantitative magnitudes all contain the factor 1/10⁸. Evidently such effects can only be noted by means of the most refined observations. They have been observed however. Suppose we compare two observations on the velocity of light made with the same apparatus as we turn it through a right angle. The velocity of the earth relatively to the sun is in one direction, the velocity of light relatively to the ether should be the same in all directions. Hence if space when we take the ether as at rest means the same thing as space when we take the earth as at rest, we ought to find that the velocity of light relatively to the earth varies according to the direction from which it comes.

These observations on earth constitute the basic principle of the famous experiments designed to detect the motion of the earth through the ether. You all know that, quite unexpectedly, they gave a null result. This is completely explained by the fact that, the space-system and the time-system which we are using are in certain minute ways different from the space and the time relatively to the sun or relatively to any other body with respect to which it is moving.

All this discussion as to the nature of time and space has lifted above our horizon a great difficulty which affects the formulation of all the ultimate laws of physics—for example, the laws of the electromagnetic field, and the law of gravitation. Let us take the law of gravitation as an example. Its formulation is as follows: Two material bodies attract each other with a force proportional to the product of their masses and universally proportional to the square of their distances. In this statement the bodies are supposed to be small enough to be treated as material particles in relation to their distances; and we need not bother further about that minor point. The difficulty to which I want to draw your attention is this: In the formulation of the law one definite time and one definite space are presupposed. The two masses are assumed to be in simultaneous positions.

But what is simultaneous in one time-system may not be simultaneous in another time-system. So according to our new views the law is in this respect not formulated so as to have any exact meaning. Furthermore an analogous difficulty arises over the question of distance. The distance between two instantaneous positions, i.e. between two event-particles, is different in different space-systems. What space is to be chosen? Thus again the law lacks precise formulation, if relativity is accepted. Our problem is to seek a fresh interpretation of the law of gravity in which these difficulties are evaded. In the first place we must avoid the abstractions of space and time in the formulation of our fundamental ideas and must recur to the ultimate facts of nature, namely to events. Also in order to find the ideal simplicity of expressions of the relations between events, we restrict ourselves to event-particles. Thus the life of a material particle is its adventure amid a track of event-particles strung out as a continuous series or path in the four-dimensional space-time manifold. These event-particles are the various situations of the material particle. We usually express this fact by adopting our natural space-time system and by talking of the path in space of the material particle as it exists at successive instants of time.

We have to ask ourselves what are the laws of nature which lead the material particle to adopt just this path among event-particles and no other. Think of the path as a whole. What characteristic has that path got which would not be shared by any other slightly varied path? We are asking for more than a law of gravity. We want laws of motion and a general idea of the way to formulate the effects of physical forces.

In order to answer our question we put the idea of the attracting masses in the background and concentrate attention on the field of activity of the events in the neighbourhood of the path. In so doing we are acting in conformity with the whole trend of scientific thought during the last hundred years, which has more and more concentrated attention on the field of force as the immediate agent in directing motion, to the exclusion of the consideration of the immediate mutual influence between two distant bodies. We have got to find the way of expressing the field of activity of events in the neighbourhood of some definite event-particle E of the four-dimensional manifold. I bring in a fundamental physical idea which I call the ‘impetus’ to express this physical field. The event-particle E is related to any neighbouring event-particle P by an element of impetus. The assemblage of all the elements of impetus relating E to the assemblage of event-particles in the neighbourhood of E expresses the character of the field of activity in the neighbourhood of E. Where I differ from Einstein is that he conceives this quantity which I call the impetus as merely expressing the characters of the space and time to be adopted and thus ends by talking of the gravitational field expressing a curvature in the space-time manifold. I cannot attach any clear conception to his interpretation of space and time. My formulae differ slightly from his, though they agree in those instances where his results have been verified. I need hardly say that in this particular of the formulation of the law of gravitation I have drawn on the general method of procedure which constitutes his great discovery.

Einstein showed how to express the characters of the assemblage of elements of impetus of the field surrounding an event-particle E in terms of ten quantities which I will call J₁₁, J₁₂, (= J₂₁), J₂₂, J₂₃ (=J₃₂), etc. It will be noted that there are four spatio-temporal measurements relating E to its neighbour P, and that there are ten pairs of such measurements if we are allowed to take any one measurement twice over to make one such pair. The ten J’s depend merely on the position of E in the four-dimensional manifold, and the element of impetus between E and P can be expressed in terms of the ten J’s and the ten pairs of the four spatio-temporal measurements relating E and P. The numerical values of the J’s will depend on the system of measurement adopted, but are so adjusted to each particular system that the same value is obtained for the element of impetus between E and P, whatever be the system of measurement adopted. This fact is expressed by saying that the ten J’s form a ‘tensor.’ It is not going too far to say that the announcement that physicists would have in future to study the theory of tensors created a veritable panic among them when the verification of Einstein’s predictions was first announced.

The ten J’s at any event-particle E can be expressed in terms of two functions which I call the potential and the ‘associate-potential’ at E. The potential is practically what is meant by the ordinary gravitation potential, when we express ourselves in terms of the Euclidean space in reference to which the attracting mass is at rest. The associate-potential is defined by the modification of substituting the direct distance for the inverse distance in the definition of the potential, and its calculation can easily be made to depend on that of the old-fashioned potential. Thus the calculation of the J’s—the coefficients of impetus, as I will call them—does not involve anything very revolutionary in the mathematical knowledge of physicists. We now return to the path of the attracted particle. We add up all the elements of impetus in the whole path, and obtain thereby what I call the ‘integral impetus.’ The characteristic of the actual path as compared with neighbouring alternative paths is that in the actual paths the integral impetus would neither gain nor lose, if the particle wobbled out of it into a small extremely near alternative path. Mathematicians would express this by saying, that the integral impetus is stationary for an infinitesimal displacement. In this statement of the law of motion I have neglected the existence of other forces. But that would lead me too far afield.

The electromagnetic theory has to be modified to allow for the presence of a gravitational field. Thus Einstein’s investigations lead to the first discovery of any relation between gravity and other physical phenomena. In the form in which I have put this modification, we deduce Einstein’s fundamental principle, as to the motion of light along its rays, as a first approximation which is absolutely true for infinitely short waves. Einstein’s principle, thus partially verified, stated in my language is that a ray of light always follows a path such that the integral impetus along it is zero. This involves that every element of impetus along it is zero.

In conclusion, I must apologise. In the first place I have considerably toned down the various exciting peculiarities of the original theory and have reduced it to a greater conformity with the older physics. I do not allow that physical phenomena are due to oddities of space. Also I have added to the dullness of the lecture by my respect for the audience. You would have enjoyed a more popular lecture with illustrations of delightful paradoxes. But I know also that you are serious students who are here because you really want to know how the new theories may affect your scientific researches.” (CN, p. 179-84).

Whitehead accepts the new requirements of relativity theory that there is no single space or time in which the universe operates. He explains that the new theory introduces an indefinite number of time- and space-systems that can describe the universe, depending on the conditions of measurement. This divergence between space- and time-systems, which affronts common sense, is partly resolved by recognizing our immersion in the “creative advance of nature” as an ongoing process of novelty, and distinguishing this from the single serial clock-time that we wrongly imagine fully captures this advance. It turns out that the creative advance is not a single universal timeline but contains an indefinite number of more or less overlapping space-time systems.

Whitehead further elaborates on the implications of relativity for formulating physical laws like gravity. Newton’s law of gravity, which assume a single time and space, are no longer adequate under the new views of relativity. Simultaneity and measurements of distance differ between space-time systems, meaning that the laws must be reformulated based on events and their interrelations in the four-dimensional space-time manifold, rather than fixed points in absolute space and time. But in opposition to the Einsteinian idea of gravity as a consequence of the warping of space-time, Whitehead introduces the concept of “impetus,” a physical field that governs the gravitational relationships between events. In Principle of Relativity a few years later, Whitehead would develop his own tensor equations that for many decades were considered empirically equivalent to Einstein’s. As Whitehead insisted in the preface:

“It is inherent in my theory to maintain the old division between physics and geometry. Physics is the science of the contingent relations of nature and geometry expresses its uniform relatedness.”

Einstein, on the other hand, had collapsed geometry into physics, thus forfeiting geometry’s uniformity by allowing contingently arrayed masses to deform space-time itself. This makes no sense from Whitehead’s perspective, since space-time is an abstract way of measuring the relations between events and not an actual physical substratum. Measurement requires the assumption of uniform relatedness, i.e., that we can determine that our rulers remain rigid across any stretch of space. Einstein’s interpretation of relativity leads to the epistemological quandary of having to know where all the mass of the universe is arrayed before we can accurately measure distances. This is, of course, impossible, since we would already need to know our measurement is accurate to determine where the masses are.

Some have dismissed Whitehead’s amendments to the theory of relativity since his linear formulation turns out to diverge empirically from Einstein’s, and for the worse. But just as physicists were happy to adjust the free parameters of Einstein's equations by adding a bunch of “dark matter” to bring their predictions back into alignment with observations of galactic rotation, Whitehead’s theory of gravity could also be adjusted in light of new observations (though I would suggest this adjustment would be minor relative to that required for Einstein’s—not requiring inventing a huge amount of invisible mass). Whitehead really proposed a whole new genus of gravitational theories modeled on Maxwell's field equations, and if his unbifurcated philosophy of nature had found a foothold among professional physicists, could easily enough have been brought back into alignment with new observations.

Langer’s characterization of Whitehead’s Philosophy of Organism as a living myth—a cosmological metaphor—is both a tribute to its imaginative scope and an acknowledgment of the limitations of literal interpretation of metaphysical systems. While Whitehead’s ideas may at first appear fantastical and difficult to grasp, their power lies in their ability to restore our appreciation for the deliverances of direct experience, not in opposition to scientific abstractions, but as a more coherent and adequate basis for understanding their meaning. Philosophy operates in the liminal space between science, imagination, and common sense. Whitehead’s philosophy of science and mature process-relational ontology are not simply fictional stories or cosmic novels but serious attempts to overcome the bifurcation of nature, refute outdated materialist metaphysics, and construct a scheme of thought that does justice to modern science while at the same time upholding our concrete experience as the final arbiter of reality.

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^[1] Due to the influence of Ernst Cassirer’s philosophy of symbolic forms, it must be remembered that Langer does not mean “lie” when she says “myth,” but something more like a form of symbolic expression through which human beings participate in a unified, concrete imagination of reality, blending subjective experience and objective phenomena into a cohesive, emotionally charged cosmovision.