Whitehead’s Radically Empirical Theory of General Relativity

“The doctrine of relativity affects every branch of natural science, not excluding the biological sciences. . . . Relativity, in the form of novel formulae relating time and space, first developed in connection with electromagnetism. . . . Einstein then proceeded to show its bearing on the formulae for gravitation. It so happens therefore that owing to the circumstances of its origin a very general doctrine is linked with two special applications.”
–Whitehead (The Principle of Relativity, 3).

One of the biggest surprises for me upon reading Auxier and Herstein’s book The Quantum of Explanation was learning that Whitehead’s theory of extension (or “mereotopology” as it has come to be called) has been taken up by computer scientists working in the field of robotic vision (see for example the work of Ian Pratt-Hartmann).

“It is a widely acknowledged fact in this sub-discipline that Alfred North Whitehead’s work on extension is foundational for their enterprise. Our experience has been that Whitehead scholars are simply astounded to learn of this fact. Yet we should have expected and even predicted such a connection” (QE 90).

Guilty as charged. While I think I got things mostly right in section 3.2 of my dissertation (“From Geometric Conditions of Possibility to Genetic Conditions of Actuality”), the promising application of Whitehead’s topological scheme to robotic vision certainly brings this aspect of his project into sharper focus for me. As a radical empiricist, Whitehead was searching for a formal account of our concrete experience of projectively related extensa. We are finite creatures with limited sensory organs and processing capacity. We do not experience the world of spatial relations in terms of infinitesimal points or the geometrical schemes built up from such points. Rather, what we encounter in our immediate experiential field are the intuitive whole-part relational structures formalized by non-metrical projective geometry.

Following Einstein’s articulation of the special and general theories of relativity (in 1905 and 1916, respectively), and his problematic “mono-metric” identification of a 4-D geometrical model with physical space-time*, Whitehead pursued his theory of extension with renewed urgency. Somehow, the uniformity of spatial geometry had to be preserved, else scientific measurement would become impossible. Einstein did not appear to realize that allowing the contingent warping of space by massive objects undermined the fundamental logical requirements of measurement: that space have a necessary and universal structure (or, as Auxier and Herstein put it, “we must have a standard unit of spatial comparison for conjugacy…and standard(s) of spatial projection” so as to bring this unit into comparison with whatever we are trying to measure [QE 102]). By collapsing the difference between physical space and his favored geometrical scheme, Einstein made the structure of spatial geometry contingent upon randomly arrayed masses.

“We must know the complete distribution of matter and energy in the universe prior to knowing its geometry. But we must have a comprehensive grasp of this geometry in order to discover this distribution. As Whitehead pointed out, with General Relativity as our theory of space and gravity, we are saddled with a situation where we must first know everything before we can know anything” (QE 104).  

Einstein’s “mono-metric” model has been one of the most successful in the history of science. But because of the unexpected observations of the rotational velocity of galaxies and of cosmic inflation rates, its theoretical supremacy has begun to be seriously questioned. Some astrophysicists have attempted to save the theory by inventing “dark matter” and “dark energy” to explain the missing mass that would bring observations back into agreement with Einstein’s theory. Auxier and Herstein refer to these inventions as “an especially unhappy piece of nonsense” (QE 20). I’m sympathetic, but I wouldn’t go quite that far. To my mind, these invented entities are akin to the epicycles of Ptolemaic astronomy. In other words, these exotic and invisible forms of mass/energy (which supposedly compose ~96% of the universe) are postulated ad hoc in an attempt to “save the appearances” (as ancient astronomers used to say). Ancient astronomers were tasked by Plato with explaining the seemingly erratic motion of the planets in terms of a theoretical model composed only of uniform circular motions. When new planetary observations conflicted with the model, more circles were added (epicycles) to bring the model back into alignment with appearances. One view of science is that it is just about refining existing theoretical presuppositions to fit new observations, gradually approaching a perfect identity between model and reality. In this sense, the addition of epicycles to match observations could continue indefinitely. After all, Ptolemy’s geocentric model was more accurate than Copernicus’ heliocentric model (which itself still required epicycles until Kepler and Newton updated his math). The geocentric model is still accurate enough that modern planetarium projectors (invented in the 1920s by a company in Jena, Germany) continue to utilize it, reproducing Ptolemy’s deferents and epicycles with their internal gears and motors (see also).

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But as Karl Popper taught us, scientific theories must be subject to empirical falsification. The eternal circular orbits of Ptolemy’s model fall out of phase with the long-term evolution of planetary orbits, while the (updated) heliocentric model accommodates this evolution well. As Thomas Kuhn, another great philosopher of science, taught us, the history of science is not just about the gradual refinement of old theories to fit new observations in an asymptotic convergence of model to reality; rather, this history is also characterized by periods of revolutionary crisis as aging paradigms are supplanted by deeper, wider, more elegant and inclusive explanatory perspectives. Einstein’s genius was to bring the reigning Newtonian theory of gravity into alignment with Maxwell’s theory of electromagnetism. A deeper theory of space was born. But in a sense, despite many other successful observational predictions, empirical falsification is exactly what happened to Einstein’s gravitational theory when it failed to accurately predict the observed rotational velocity of galaxies. However, because this darling model had made a number of other accurate predictions, and because no widely accepted alternative paradigm was on hand, astrophysicists decided to fudge the numbers by inventing new free parameters, new epicycles, to bring the theory back into alignment with observations. Appearances were thereby saved, but at the cost of conjuring into existence an entire universe (or 96% of one, at least) of cold and dark, that is, unobservable, matter/energy.

Even though he did formulate a “bimetric” alternative in 1922 (QE 109), Whitehead’s problem is not with Einstein’s model. This isn’t a “scientists have been wrong before, so why should we trust them now?” argument. Science is about modeling. In some sense, scientific models are always wrong. That’s the name of the game, after all: build a model and throw it against reality until it breaks. Then study why it broke until you find a new model that doesn’t break as quickly. Gradually, more robust, inclusive models emerge. Rather, Whitehead’s problem is with the philosophically naive “model-centrism” that leads scientists to equate their favored model with reality in a dogmatically literalistic way. We should never assume the reigning physical models of the universe offer a final account of the way things are (especially when today’s two most successful models, relativity and quantum theory, remain irreconcilable). Science is not ontology: science is a method of inquiry involving the making and breaking of toy models.

The dogmatic equation of a favored geometrical model with physical reality not only undermined the logical basis of measurement, it led Einstein to dismiss our concrete experience of an irreversible flow of time as nothing more than a “stubbornly persistent illusion.” This is Whitehead’s famous “fallacy of misplaced concreteness” writ large. Einstein’s unquestioned commitment to the classical “spectator theory of knowledge” prevented him from grasping the profoundly relational implications of his new theory of space. He upheld the old Galilean-Cartesian view of a bifurcated Nature, construing our consciousness as somehow external to a cosmos that we can only ever confusedly experience. Whitehead offers an alternative, fully relational epistemology and ontology that re-embeds experience in the cosmos: we are creative participants in a cosmogenetic relational nexus.  

Instead of rushing to eliminate experience from our understanding of a relativistic (or relational) reality, Whitehead carefully examined the hidden epistemic presuppositions and metaphysical requirements of Einstein’s more specific application of relativity to the physics of light and gravitation. The result of his examination was eventually assembled in Process and Reality as the fourth category of explanation, a truly general principle of relativity: “it belongs to the nature of a ‘being’ that it is a potential for every ‘becoming'” (PR 22). Obviously, the importance of Whitehead’s fourth category of explanation (of which there are 26 others) can only be understood within the total gestalt of his categoreal scheme (which includes the category of the ultimate: Creativity; eight categories of existence, among which the most important are eternal objects and actual occasions; and nine categories of obligation). Whitehead’s categoreal scheme is laid out in Part I of Process and Reality as something like an opening credit roll listing the conceptual dramatis personae who, in Part II, will take the stage to exemplify their adequacy. But I’m not going to run through the whole dress rehearsal right now (for a helpful exegesis of Whitehead’s first four categories of explanation, see pgs. 108-110 of QE). Suffice it to say that Whitehead’s principle of relativity expresses the truth that everything co-exists in a web of relatedness, whether actually or potentially. 

Auxier and Herstein:

This is the principle that Einstein and his devotees have abandoned: not the mathematical expression of their physical model; that model is itself only an application of what has become the standard dogma of orthodox cosmology, with its narrowly defined approach to the interpretation of a truncated representation of experience. Rather, physical cosmology has left behind the full principle of relativity and its unqualified commitment to the incurable relatedness of the real. That abandonment comes in the truncation of experience at the root of their largely unexpressed theory of experience [i.e., the theory of the bifurcation of Nature]. For one cannot have a universal principle of relativity—applicable to all that is real—unless one takes experience in its real, relational totality. Experience—both actual and potential—is exactly the kind of reality that falls under the principle of relativity. One cannot take the metaphysical principle of relativity seriously unless one is a radical empiricist” (QE 110). 

In The Quantum of Explanation, Auxier and Herstein have brilliantly succeeded in elucidating the features of a radically empirical cosmology. As Whitehead reminds us early and often in Process and Reality, the purpose of philosophy is not to explain away the existence of the concrete by reduction to the abstract, but to explain the emergence of abstraction from concretion. The proper questions are: how does concrete fact participate in general form and how are general forms exemplified in concrete facts?

For a longer discussion of Whitehead’s radical empiricism a.k.a. relational realism, see my essay “Retrieving Realism: A Whiteheadian Wager.”


*It has been brought to my attention that the matter of whether Einstein thought the physics of gravitation is reducible to the geometry of space-time is not so clear cut. See for example: “Why Einstein did not believe that general relativity geometrizes gravity” by Lehmkuhl. The research continues… 

Searching for Stars: A Conversation with Alan Lightman

Pre-Defense Dissertation Draft Completed

My dissertation defense is on Monday morning. I’ve just finished the “pre-defense” draft. I have until April 11th to finalize the published version. Below are the abstract, table of contents, and acknowledgements. 

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  • Jacob Sherman, PhD, Chair
    Associate Professor, Philosophy and Religion Department, California Institute of Integral Studies

 

  • Sean Kelly, PhD
    Professor, Philosophy and Religion Department, California Institute of Integral Studies

 

 

  • Frederick Amrine, PhD
    Arthur F. Thurnau Professor, German Department, University of Michigan

 

COSMOTHEANTHROPIC IMAGINATION IN THE POST-KANTIAN PROCESS PHILOSOPHY OF SCHELLING AND WHITEHEAD

Abstract

In this dissertation, I lure the process philosophies of F.W.J Schelling and A.N. Whitehead into orbit together around the transcendental philosophy of Immanuel Kant. I argue that Schelling and Whitehead’s descendental aesthetic ontology provides a way across the epistemological chasm that Kant’s critiques opened up between experience and reality. While Kant’s problematic scission between phenomena and the thing-in-itself remains an essential phase in the maturation of the human mind, it need not be the full realization of mind’s potential in relation to Nature. I contrast Schelling and Whitehead’s descendental philosophy with Kant’s transcendentalism by showing how their inverted method bridges the chasm—not by resolving the structure of reality into clear and distinct concepts—but by replanting cognition in the aesthetic processes from which it arises. Hidden at the generative root of our seemingly separate human capacities for corporeal sensation and intellectual reflection is the same universally distributed creative power underlying star formation and blooming flowers. Human consciousness is not an anomaly but is a product of the Earth and wider universe, as natural as leaves on a tree. Through a creative interweaving of their process-relational orientations, I show how the power of imagination so evident in Schelling and Whitehead’s thought can provide philosophy with genuine experiential insight into cosmos, theos, and anthropos in the aftermath of the Kantian revolution. The two—anthropos and cosmos—are perceived as one by a common sense described in this dissertation as etheric imagination. This etheric sense puts us in touch with the divine life of Nature, which the ancients personified as the ψυχὴ του κόσμου or anima mundi.

Table of Contents

Abstract iv
Acknowledgements vii
Prologue — Imagining Cosmos, Theos, and Anthropos in Post-Kantian Process Philosophy 2
Chapter 1 — Kant as Guardian of the Threshold of Imagination 9
1.1 Whitehead, Schelling, and the Aftermath of Kant 16
1.2 The Kantian Mode of Thought 24
1.2.1 Thinking 27
1.2.2 Desiring 38
1.2.3 Feeling 42
Chapter 2 — Descendental Philosophy and Aesthetic Ontology: Reimagining the Kantian Mode of Thought 55
2.1 Aesthetic Ontology and Nietzsche’s Confrontation with Nihilism 70
2.2 Aesthetic Ontology in Sallis’ Elemental Phenomenology 95
2.3 Aesthetic Ontology in Deleuze’s Transcendental Empiricism 99
Chiasmus — Schelling and Whitehead’s Descendental Aesthetic: Crossing the Kantian Threshold 111
Chapter 3 — The Inversion of Kant: From a Mechanistic to an Organic Cosmology 132
3.1 The Refutation of Kant’s “Refutation of Idealism”: From Subject-Substance Correlation to Process-Relational Creativity 150
3.2 From Geometric Conditions of Possibility to Genetic Conditions of Actuality 167
Chapter 4 — Etheric Imagination in Naturphilosophie: Toward a Physics of the World-Soul 177
4.1 Traces of the Ether in Kant’s Opus Postumum 181
4.2 Etheric Imagination in Schelling and Whitehead 192
4.3 Nature Philosophy as “Spiritual Sensation” 201
4.4 Etheric Imagination and Vegetal Metaphysics 209
Epilogue — Incarnational Process Philosophy in the Worldly Religion of Schelling, Whitehead, and Deleuze 230
References 254

Acknowledgements

Without the intellectual encouragement and personal friendships of Jake Sherman, Sean Kelly, Fred Amrine, Brian Swimme, Robert McDermott, Eric Weiss, Elizabeth Allison, and Rick Tarnas, this dissertation could not have been written. Thanks to each of them, and also to the entire community of students in the Philosophy, Cosmology, and Consciousness Program for sharing their philosophical passion and for the conversations that helped spark many of the ideas expressed in what follows. Thank you, finally, to my fiancée Becca for her inspiring imagination, for her encouragement, and for her patience as I labored over drafts of this text for so many consecutive weeks.

The Politics of Renaissance Hermeticism, and the Magic of Science

I’ve been reading Frances Yates’ Giordano Bruno and the Hermetic Tradition (1964). Part of her project is to dispel the myth that Bruno was burnt at the stake primarily for his heliocentrism and generally scientific and materialist attitude. This was certainly one of the Roman Inquisitions many accusations, but the real reasons the Church lit his public pyre were political.

…the legend that Bruno was prosecuted as a philosophical thinker, was burned for his daring views on innumerable worlds or on the movement of the earth, can no longer stand…little attention was paid to philosophical or scientific questions in the interrogation…[instead, stress was laid] on Bruno’s religious mission. (p. 355)

His religious mission was to attend to the creation of the City of the Sun on Earth, which involved practicing the Hermetic arts of magic, astrology, and what after Jung we might call active imagination. This mission also had a political dimension, leading Bruno to ally with the likes of Henry of Navarro, who was to become King Henry IV of France. Bruno saw the potential for a universal reform of the Catholic religion in France, which was fresh off King Henry’s victory against the Spanish-backed Catholic League. Many heretical thinkers in 16th century Europe with more liberal views on religion were hoping Henry would bring peace to a continent ravaged by wars of intolerance. The Catholic Church, of course, had no interest in ceding its power to such a movement. The counter-Reformation was in full force.

Yates also tells the story of Tommaso Campanella, another Hermetic Magus who followed in Bruno’s footsteps by seeking to create the City of the Sun. Campanella lead a rebellion of Dominican monks against Catholic reformers in 1599.

But what did Bruno and Campanella’s religious mission have to do with new scientific ways of thinking and with the Copernican heliocentric theory? Campanella “praises Ptolemaeus and [admires] Copernicus, although Aristarchus and Philolaus were before him (in teaching heliocentricity)” (transl. Yates, p. 372). Both geocentric and heliocentric systems are upheld as worthy of study. Bruno’s primary reasons for holding to the heliocentric perspective were not mathematical or scientific (Ptolemy’s system was still more accurate than Copernicus’ at this point), but magico-symbolic and politico-religious. The return of the heliocentric theory was read by Bruno as an omen, a sign in the sky sent from God, prophesying the coming Golden Age when Europe would be ruled by Philosopher-Magi skilled in calling the winds of justice down to earth from the heavens.

What interests me in Yates’ historical account is the way Bruno was both modern and non-modern in his Hermetic religion: modern in that he affirmed the infinite reality of the universe; non-modern in that an infinite cosmos is the necessary counter-postulate to an infinitely real God. Modern in that he saw the moral necessity of religious freedom, but non-modern in that he felt the universe (or earth-heaven continuum) must be inter-woven throughout with astral spirits and permeated by an anima mundi (or world soul). All the beings in the universe are magically linked through the soul of the world to one another, and also to the One God, who is beyond being. The One beyond being, infinite in itself, is necessarily in relation to the beings of Being. This relation takes place through a series of revelations, beginning with the heavens. God’s infinite Speech/Word is “stepped-down” into the songs of the spiraling stars and dancing planets, which Plato identified with the Cosmic Intelligence of the World Soul. This revelation of the One through and to the many continues through every individual creature of earth, which in its individuality contains in hologrammatic form the entirety of the cosmos. As an earlier Hermetic thinker, Nicholas of Cusa, had intuited, the universe, as a reflection of God, “is a sphere of which the center is everywhere and the circumference nowhere.”

Yates ends her study on Renaissance magic by asking why it was that the scientific revolution of the 17th century began when it did. She speculates that the Renaissance Hermeticist’s new attitude concerning the place of the human being in the natural world re-directed the will, such that penetrating the secrets of the universe and coming to have mastery over nature no longer seemed so far fetched.

Behind the emergence of modern science there was a new direction of the will towards the world, its marvels, and mysterious workings, a new longing and determination to understand those workings and to operate with them. (Yates, p. 448)

Compare this attitude with that of the 3rd century Church father Tertulian, who argued that those interested in the workings of nature:

persist in applying their studies to a vain purpose, since they indulge their curiosity on natural objects, which they ought rather [direct] to their Creator and Governor.

There is a vast difference between the mechanism and mathematics of thinkers like Mersenne and Descartes and the animism and magic of thinkers like Bruno, Campanella, and Robert Fludd. But the transition between the two is not as clear cut as it would seem from our modern perspective. Like Bruno, many of the supposed fathers of the scientific revolution were deeply interested in occult knowledge. On Nov. 10th, 1619, while still a young man striving to discover a new foundation for knowledge, Descartes had a series of dreams and visions that he believed came from a higher source (Yates, p. 452). He began searching for the elusive Rosicrucian order (a Hermetic society) in Germany in the hope that they might help interpret his visions of a universal science of nature. He finally gave up in 1623 and returned to Paris, though some speculate that he actually did make contact with the secret society and had been initiated into the brotherhood. Kepler was also a rather transitional figure, having studied the Corpus Hermeticum quite closely alongside his astronomical research. Then there is the importance of alchemy to Isaac Newton, which is increasingly well-known: see especially Phillip Fanning’s recent book Isaac Newton and the Transmutation of Alchemy: An Alternative View of the Scientific Revolution (2009).

Yates points out that the early mechanists attempt to distance themselves from the magicians left them with a rather embarrassing problem: if nature was all mechanics, where did the knowing mind of the scientist fit in? The problem was especially pronounced and given its clearest formulation in Descartes infamous dualism between the res cogitans and the res extensa. “This bad start of the problem of knowledge,” writes Yates, “has never been quite made up” (p. 454).

Yates goes on:

[The mechanists] may have discarded notions on mind and matter which, however strangely formulated, may be in essence less remote than their own conceptions from some of the thought of today. (p. 455)

Writing in the early 60s, she was well-aware of the paradigm shift continuing to unfold as a result of the quantum revolution:

It may be illuminating to view the scientific revolution as in two phases, the first phase consisting of an animistic universe operated by magic, the second phase of a mathematical universe operated by mechanics. An enquiry into both phases, and their interactions, may be a more fruitful line of historical approach to the problems raised by the science of today than the line which concentrates only on the seventeenth-century triumph. Is not all science a gnosis, an insight into the nature of the All, which proceeds by successive revelations? (p. 452)

Might there be room in contemporary science for the return of the anima mundi?

The Poetics of Copernican Cosmology

Heliocentric universe, Harmonia Macrocosmica
Image via Wikipedia

In his cosmographic study of the Copernican Revolution,The Poetic Structure of the World (1987), Fernand Hallyn entirely re-envisions the foundations of modern science. Instead of reading Copernicus’ break with the geocentric scheme as a rejection of the enchanted cosmos of the ancient world, Hallyn makes clear that Copernicus himself believed he was only making ancient Platonic and Hermetic doctrines more plausible.

Copernicus writes:

“At rest…in the middle of everything is the sun. For in this most beautiful temple, who would place this lamp in another or better position than that from which it can light up the whole thing at the same time? For, the sun is not inappropriately called by some people the lantern of the universe, its mind by others, and its ruler by still others. The Thrice Greatest [Hermes Trismegistus] labels it a visible god, and Sophocles’ Electra, the all-seeing. Thus indeed, as though seated on a royal throne, the sun governs the family of planets revolving around it” (p. 22, On the Revolutions, 1978).

Quentin Meillassoux, in After Finitude, credits Copernicus with decentering earthly humanity in the universe; however, according to Hallyn, Copernicus also re-enacted the Platonic notion of astronomy as as divine science. In effect, through a rent in the imaginal fabric of the medieval sense of the sky, Copernicus caught a ray of light from a new heaven (or perhaps, in a gleam, saw heaven in a new way): he perceived the solution to the problem of the planets in the heliocentric theory; he stole fire from Zeus and elevated humanity to the status of the gods.

“It is highly unlikely,” he writes, “that anyone lacking the requisite knowledge of the sun, moon, and other heavenly bodies can become and be called godlike”  (p. 7, On the Revolutions).

Ptolemy, a more empirical and Aristotelean astronomer, humbly denied that the human mind could finally perceive the secret meaning of the planetary movements, since this secret was safely tucked away in the mind of an unmoved transcendent God existing above the vault of heaven. As far as Ptolemy was concerned,  hypotheses were all the human mind could hope for: we can but “save the appearance” by offering clumsy descriptions of the universe as if it were a mechanical gear-works originally rigged up by a now absent divine Architect. Perception of the inner truth of things was deemed forever beyond the capacity of the finite human being.

Copernicus’ intellect caught fire in his contemplation of the stars. His was the Hermeticist‘s method: to know through identity, to learn the song and dance of eternity’s moving image by becoming one with the everlasting Soul animating the whole. Half a century later, Kepler was able to simplify Copernicus’ geometry by allowing for elliptical orbits. He was also able to clarify the theological implications of heliocentrism by pointing out that a decentered earth is actually the perfect place for a contemplative creature such as ourselves to observe and come to understand the order of the universe.

Kepler writes:

“If the earth, our home, did not measure the annual orbit of the other planets –changing from place to place and station to station– human reason would never have arrived at knowledge of the precise intervals of the planets and other things that depend on those intervals; it would never have instituted astronomy” (p. 366, Selected Works, vol. 6, 1938).

In other words, Kepler analogizes the relationship between creature and Creator to that between an earth’s eye view of the solar system and a sun’s eye view. From the sun’s perspective, only a God with a priori knowledge of the spheres could understand their design, whereas on earth, a being capable of “the labor of reason” (p. 66, ibid.) could uncover their design in the course of time (a posteriori) as a result of the comparison of their relative motions. Man is like God, except man’s knowledge becomes in time, a moving image of God’s timeless wisdom.

[A variation on Whitehead’s theological scheme here occurs to me, wherein God’s primordial nature is equated with this timeless wisdom, while God’s consequent nature is equated with humanity’s gradual awakening to the divine meaning of the universe of appearances from within the limits of that very same universe. This is a Hermetic spin on Whitehead’s panentheistic cosmology, wherein God’s origin is the unconscious innocence of Nature and God’s end is the conscious responsibility of Man.]

The Copernican Revolution, according to Hallyn, was a victory for speculative organicism, for the idea that symmetry and systematicity are behind the appearances of nature, rather than the mechanical motion of separately and haphazardly arranged parts, as in Ptolemy’s model. But by the time of Newton, a conceptually degraded Copernicanism had provided the necessary conceptual foundation for the complete replacement of qualitatively differentiated, concrete space with the abstract, homogenous space of Euclidian geometry. As the Scientific Revolution marched onward, the enchanted and participatory cosmos of the Renaissance was forgotten in favor of an increasingly “objectified” universe devoid of “subjective” meaning.

It seems to me that another jolt of promethean imagination is necessary to complete the noösphere’s phase transition from the current, epicyclic materialistic paradigm –where subject and object remain sundered– into a more integrated vision of the cosmos as a living whole.