Wolfgang Smith and the Status of Geocentrism

Wolfgang Smith (born 1930) is a mathematician, physicist, philosopher of science, metaphysician, Roman Catholic and member of the Traditionalist School. He has written extensively in the field of differential geometry, as a critic of scientism and as a proponent of a new interpretation of quantum mechanics that draws heavily from medieval ontology and realism.

Smith graduated in 1948 from Cornell University with a B.A. in Philosophy, Physics and Mathematics. Two years later he obtained his M.S. in Physics from Purdue University and, some time later, a Ph.D in Mathematics from Columbia University.

He worked as a physicist in Bell Aircraft corporation, researching aerodynamics and the problem of atmospheric reentry.  He was a mathematics professor at MIT, UCLA and Oregon State University, doing research in the field of differential geometry and publishing in academic journals such as the Transactions of the American Mathematical Society, the Proceedings of the National Academy of Sciences, the American Journal of Mathematics, and others. He retired from academic life in 1992.

The following is an excerpt from The Wisdom of Ancient Cosmology: Contemporary Science in Light of Tradition. (2003), by Wolfgang Smith

The Status of Geocentrism

If there has been little debate in recent times on the subject of geocentrism, the reason is clear: almost everyone takes it for granted that the geocentrist claim is a dead issue, on a par, let us say, with the flat-Earth hypothesis. To be sure, the ancient doctrine has yet a few devoted advocates in Europe and America, whose arguments are neither trivial nor uninformed; the problem is that hardly anyone else seems to care, hardly anyone is listening. Even the biblically oriented creation-science movement, which of late has gained a certain prestige and influence, has for the most part disavowed geocentrism. The fact remains, however, that geocentrist cosmology constitutes not only an ancient, but indeed a traditional doctrine; should we not presume that as such it enshrines a perennial truth? To maintain, moreover, that this truth has nothing to say on a cosmographic plane- that the doctrine, in other words, is "merely symbolic or allegorical"- to think thus is to join the tribe of theologians who are ever willing to "demythologize" at the latest behest of the scientific establishment. It will not be without interest, therefore, to investigate whether the geocentrist claim- yes, understood cosmographically!-has indeed been ruled out of court. I shall argue that it has not. As regards the Galileo controversy, I propose to show that Galilean heliocentrism has proved to be scientifically untenable, and that in fact the palm of victory belongs to the wise and saintly CardinalBellarmine. I should add that the problematic of this article will lead us, in the final section, to elicit an interpretation of relativistic physics that accords with traditional doctrine.

Nothing perhaps is more impenetrable to the modern mind than the ancient cosmologies. Not only are these cosmologies inherently metaphysical, but what perhaps we find more puzzling still is the fact that they are also at the same time descriptive of the perceptible world, at least in a qualitative sense. When such cosmologies speak of the Sun, Moon, and stars, the reference is no doubt symbolic, but not "merely symbolic," which is to say that the cosmologies in question are not bereft of scientific content. It is this fusion of a "metaphysics" with a "physics," a natural science, that seems to baffle us the most. It needs of course to be understood that the kind of science to which I allude is worlds removed from the Baconian enterprise, both in points of method as well as in the end to be achieved. In particular, it appears that ancient cosmologists did not feel obliged to account for such things as retrograde planetary motions, or the precession of equinoxes; according to Thomas Kuhn, "Only in our own Western civilization has the explanation of such details been considered a function of cosmology. No other civilization, ancient or modern, has made a similar demand." Be that as it may, a shift from cosmology of the ancient kind to astronomy in the modern sense can be clearly discerned in Greece from the time of Pythagoras to Ptolemy. One has the impression that mythical and inherently metaphysical notions, such as that of the heavenly "spheres," were being gradually transformed into physical conceptions, destined to be scorned and discarded with the advent of modern times. Meanwhile, mathematical techniques of increasing complexity and sophistication were devised to attain ever greater accuracy in the description of observable phenomena.

The simplest part of Greek astronomy pertains to the stellar sphere. It turns out that stellar orbits could be described, with what seemed at the time to be perfect accuracy, on the assumption that the stars are fixed on the surface of an immense sphere concentric with the Earth, which rotates diurnally around an axis that could be identified within one degree by the position of the North Star, while the Earth remains stationary at the center of the universe. If it were not for the Sun and other "wanderers," the simple "two-sphere" model of ancient astronomy would have provided a seemingly perfect description of the relevant phenomena. But the orbits of the so-called planets proved to be complex and challenging in the extreme. Eventually Greek astronomers concluded that circular orbits concentric with the terrestrial sphere will not suffice for their description, and by the time of Hipparchus, whose active life can be dated between 160 and 127 B.C., the method of epicycles and deferents had come into use. The motion of a planet was now conceived as the sum of two circular motions: a small rotation, namely, around a center known as the deferent, which itself sweeps out a much larger circle centered upon the Earth. The epicycles were thus conceived as a small correction to the circular orbits of the older "spherical" astronomy. I would add that in addition to his work with epicycles, Hipparchus is said to have discovered the precession of the equinoxes, which he estimated at 36 seconds of arc per year (as compared to its actual value of some 50 seconds). He also estimated the distance to the Moon to be 33 times the diameter of the Earth, as compared to an actual value near 30.2. Following upon these discoveries, progress in planetary astronomy continued apace. It was not long before astronomers realized that orbits could be progressively corrected by adding epicycles to epicycles in an indefinite series. Moreover, they discovered that additional corrections could be introduced by displacing the center of a deferent. The resultant circles, known as eccentrics, could be adjusted to further improve the result. In addition, it was found that a higher degree of accuracy could also be achieved by taking the rate of rotation of a deferent or some other point in the geometric scheme to be uniform, not with respect to its actual center, but with respect to a displaced center known as the equant. The method of epicycles came thus to be supplemented by the use of eccentrics and equants. One can say in retrospect that Greek astronomy furnishes the first example of mathematical modeling on a serious scale. The development culminated in the work of Claudius Ptolemy, whose treatise known as the Almagest (circa 150 A.D.) dominated Western astronomy till at least 1543, when it began to be displaced by the Copernican theory.

What motivated Copernicus to reject the Ptolemaic theory in favor of a heliocentric astronomy? In his preface to the De Revolutionibus, Copernicus cites persistent inaccuracy and lack of coherence as his principal criticism of the prevailing astronomy. Some fourteen hundred years after the publication of the Almagest, the computational problems of planetary astronomy had not yet been solved with satisfactory precision. Worse still, there seemed to be no principle, no rhyme or reason, governing the proliferation of epicycles, eccentrics and equants. All these mathematical parts and pieces did not seem to fit together into a coherent whole. "It is as though an artist were to gather the hands, feet, head and other members for his images from diverse models," writes the Polish astronomer, "each part excellently drawn, but not related to a single body, and since they in no way match each other, the result would be monster rather than man." It has been pointed out that this perception reflects the Neoplatonist influences to which Copernicus was demonstrably exposed. In any case, what renders the expanded Ptolemaic model monstrous in the eyes of Copernicus is the ad hoc character of its multiple constructions, which is to say, its lack of mathematical intelligibility as a whole. By way of contrast, he maintains that the new heliocentric astronomy exhibits "an admirable symmetry" and "a clear bond of harmony in the motion and magnitude of the spheres." Consider, for example, the retrograde motion of planets: why should a planet reverse its normal eastward motion and retrogress for a time, till it resumes its eastward course? From the standpoint of Ptolemaic astronomy, this phenomenon presents itself as an inexplicable irregularity, which can indeed be accounted for through the introduction of appropriate epicycles, but can hardly be understood. From a heliocentric point of view, on the other hand, retrograde motion ceases to be an irregularity, and becomes simply a mathematical consequence of the fact that the Earth itself is in motion around the Sun. It is easy to see that this is the case. Simply draw three concentric circles representing the sphere of the stars, the orbit of the Earth, and the orbit of the planet. In the case of an inferior planet (Mercury or Venus), the latter circle will be the innermost, whereas, for a superior planet, the orbit of Earth will be contained within the other two. If now we mark successive positions of Earth and planet on their respective circles and connect corresponding points by a line to obtain "observed" planetary positions on the stellar sphere, we can readily see how the motion of the Earth gives rise to the phenomenon of retrogression. What is more, we discover that retrogression occurs when the planet is nearest to the Earth, which explains why retrogressing planets are observed to shine more brightly. Copernican astronomy, it appears, has provided the first scientific explanation of the fact that planets retrogress.

A second irregularity which the new theory explains beautifully is the observed variation in the periods of orbital planetary motion. Given that the Earth itself orbits around the Sun, the time it takes for a planet to return to its starting position, as observed from the Earth, is clearly not the same as the time it takes to complete an orbit. The observed variations in planetary orbital periods can therefore be explained, once again, by the postulated motion of the Earth. Copernicus cites many examples of this kind to document the explanatory power of the heliocentric hypothesis. I will mention one more: It is known that the planets Mercury and Venus can only be observed in the vicinity of the Sun. To account for this fact in Ptolemaic terms, it was necessary to introduce deferents and epicycles binding these planets to the Sun. Heliocentric astronomy, on the other hand, requires no such ad hoc constructs: the given phenomenon is an immediate consequence of the fact that the orbits of Mercury and Venus are contained within the orbit of the Earth.

This brings us to a major point of difference between Ptolemaic and Copernican astronomy: In the heliocentric scheme, the order of the planetary orbits can be determined from observational data. If the planets (including the Earth) revolve in circular orbits around the Sun, it is possible in fact to calculate the ratios of the planetary radii in terms of the angular distances from the Sun to the planets as measured from the Earth. Such is not the case in a geocentric system, where not even the order of the planets is determined by the appearances. In a word, the new astronomy is far more coherent than the old. It is this newly-discovered coherence that Copernicus is alluding to when he speaks of "a clear bond of harmony in the motion and magnitude of the spheres," and it is evident that he views this new "bond" as a powerful argument for the truth of his theory.

In actuality, however, the charge of incoherence applies to the new astronomy as  well. In practice Copernicus was forced to introduce epicycles and eccentrics of his own, and like Ptolemy himself, ended up with over thirty circles, without any appreciable gain in the degree of accuracy. Clearly, the problem of planetary astronomy had not yet found its solution.

It appears that the decades following publication of the De Revolutionibus witnessed few converts to the Copernican cause. To the general public the notion of an orbiting Earth seemed both absurd and impious, and even astronomers seem for the most part  have been wary of that hypothesis. The second half of  the century, moreover, was dominated by the imposing  figure of Tycho Brahe, a powerful opponent of heliocentrism. Brahe is known, first of all, for the uncanny accuracy his his astronomical measurements. His results are frequently precise to one minute of arc, an unrivaled achievement for naked-eye observation. What especially concerns us, however, is the fact that Brahe proposed a remarkable planetary theory of his own, which to this day finds partisans in Europe and America. Accepting the traditional notion of an immobile Earth and a stellar sphere engaged in diurnal geocentric rotation, he proposed that Mercury, Venus,  Mars, Jupiter, and Saturn circle the Sun, while the Sun and the Moon circle the Earth. It happens that this geocentric theory embodies all the advantages previously cited by Copernicus in behalf of his heliocentric model. It too explains such things as retrograde motion, the variation of planetary periods, and the binding of inferior planets to the Sun, without recourse to epicycles and other ad hoc constructions. In point of fact, it can be shown that the two planetary theories-the Tychonian and the Copernican-are mathematically equivalent, which is to say that they predict exactly the same apparent planetary trajectories.

It should however be noted that the two theories are not equivalent in regard to stellar astronomy, for it is evident that a displacement of the Earth would entail a corresponding parallactic shift in the apparent position of a star. Tycho Brahe himself had searched for such a shift, but found none. This means that stellar parallax, if it exists, must be of an order of magnitude less than a minute of arc, which would necessitate stellar distances far greater than astronomers were wont to assume. Copernicus himself had recognized that his hypothesis demands an enormous enlargement of the stellar sphere, and it may be worth noting that Tycho Brahe considered this fantastic multiplication of apparently empty space to be one of the most cogent reasons for rejecting the Copernican hypothesis. Yet, from a strictly scientific point of view, a decision between the two theories could not be made at the time.

Although the problem of planetary astronomy, as I have said, had not yet been solved, it turns out that both Copernicus and Tycho Brahe, each in his own way, had made decisive contributions which were soon to lead to a definitive solution. The breakthrough came in the first decade of the seventeenth century at the hands of Johannes Kepler. Availing himself of superior data supplied by Tycho Brahe, he proposed a new heliocentric theory which was destined to carry the field. After years of futile endeavor, Kepler abandoned the time-honored method of epicycles in favor of a radically new idea: he proposed that the planets revolve around the Sun in elliptical orbits with variable speed. His so-called First Law stipulates that the Sun is situated at one of the two foci of the planetary ellipse, while his Second Law states that the line segment from the Sun to the planet sweeps out equal areas within the ellipse in equal times. Qualitatively, this simply affirms that the planet moves faster the nearer it is to the Sun; in point of fact, however, Kepler's "law of equal areas" enables one to calculate the velocity of the planet at every position of its trajectory. In conjunction, the two laws lend themselves to a complete description of the planetary system. No need any longer for epicycles, eccentrics, equants, or other devices of the kind: it turns out that two simple and mathematically elegant laws 1 suffice to solve the age-old problem. As Thomas Kuhn points out: "For the first time a single uncompounded geometric curve and a single speed law are sufficient for predictions of planetary position, and for the first time the predictions are as accurate as the observations." It would take us too far afield to comment on the Neoplatonist basis of Kepler's conceptions; suffice it to say that he first recorded his new ideas in a treatise on the motion of Mars, the most challenging of the planets. It could well be said that the era of modern astronomy commences with the publication of this work, in the year 1609.

It was in the same year, 1609, that Galileo Galilei first turned his telescope to the sky, with startling results. In quick succession he discovered the Milky Way to be a sea of stars, detected mountains and craters on the Moon, the height and depth of which he could estimate from shadows, found dark spots on the Sun, showing that the Sun itself rotates around its own axis, and discovered that Jupiter has four moons. While none of these findings have a direct bearing on the Copernican question, they have had a decisive impact upon the European mentality in that they appeared to discredit the perennial distinction between the celestial spheres, which mankind had taken to be perfect and immutable, and the "sublunary'' world: this imperfect and ever-changing domain which constitutes our habitat. Peering through his telescope, Galileo seemed to behold one and the same kind of world wherever he looked: from the rugged landscape of the Moon to the moving spots on the Sun itself. It is hard for us to imagine the sensation in European circles stirred by reports of these new vistas. A widespread fascination with astronomical discoveries seems to have gripped European society, eliciting varied reactions. John Donne-to cite perhaps the most striking example-appears to have sensed the deeper significance of the Galilean "movement" almost immediately: "And new philosophy calls all in doubt," he penned back in 1611; "Tis all in pieces, all coherence gone." For the most part, to be sure, the response was less perceptive; as Kuhn points out on the lighter side, "The telescope became a popular toy." Yet far more than a toy! There can be no doubt that the new images gleaned through the telescope have contributed significantly to the demise of the ancient Weltanschauung.

One more Galilean discovery needs to be mentioned: the phases of Venus, namely, which seemed indeed to imply that Venus orbits around the Sun. But whereas Galileo exhibited this discovery as proof of the Copernican hypothesis, the fact remains that the phases of Venus are accounted for equally well on the basis of Tychonian astronomy. "It was not proof," writes Kuhn, "but propaganda."

Where, then, did the matter stand at the time of the Galileo controversy? One sees in retrospect that it stood very much as Cardinal Bellarmine had stated the case in his letter to Foscarini, in 1615: "To demonstrate that the appearances are saved by assuming the Sun at the center and the Earth in the heavens is not the same thing as to demonstrate that in fact the Sun is in the center and the Earth in the heavens," writes the Cardinal. "I believe the first demonstration may exist," he goes on to say,  "but I have very grave doubts about the second... " Yes, the work of Johannes Kepler does indeed clinch the first demonstration alluded to; as regards the second, the subsequent history of science has fully justified St. Bellarmine's "grave doubts." As I propose to show presently, the science of our day has in fact rendered the second demonstration unthinkable.

With the publication of Newton's Principia in the year 1687 the scientific triumph of Keplerian astronomy was complete. Kepler's First and Second Laws could now be derived theoretically on the basis of a brilliant new physics, a physics that could be tested and verified in a thousand ways. So far as the scientific community was concerned, geocentrism was now a dead issue. No one doubted any longer that the Earth does move; it only remained to design experiments that could detect and measure that motion. What were these experiments, and what did they prove?

One avenue of approach relates to the phenomenon of aberration. In 1676, a Danish astronomer named Olaus Roemer noted that the period between observed eclipses of one of Jupiter's moons varies by several minutes, depending upon the relative position of the Earth. He concluded that light propagates at a finite velocity, which he estimated to be 309,000 kilometers per second (a result, one might add, which is accurate to within 3%) Now if the Earth itself moves, that additional velocity will cause a shift in the apparent position of a celestial object. Think of a car driving through rain on a windless day. Relative to the car, the rain falls, not vertically, but at an angle, which depends upon the ratio of two velocities: the horizontal velocity of the car, namely, divided by the vertical velocity of the rain. From a measurement, therefore, of the so-called angle of aberration, one can determine the ratio of the velocities in question. This is the idea behind what appears to be the first experiment designed to demonstrate and measure the orbital velocity of the Earth. In 1724, James Bradley, the English Astronomer Royal, attached a telescope to the top of a chimney and began to observe the star Gamma Draconis, situated almost ninety

degrees above the horizon. As expected, he found that in the course of a year the apparent position of the star described a small circle, corresponding to an angle of aberration close to 20 seconds of arc. By simple trigonometry, that angle equals the arctangent of v/c, where v denotes the orbital velocity of the Earth and c the speed of light. It follows that an aberration of 20 seconds corresponds to an orbital velocity close to 30 kilometers per second, in good agreement with astronomical theory a la Kepler and Newton. By observing and measuring the aberration caused by the orbital velocity v, Bradley had apparently observed and measured the stipulated motion of the Earth. Galileo's celebrated Eppur Si Muove, so it seemed, had at last been confirmed, vindicated before the world.

The story, however, does not end at that point. In 1871, another British astronomer, named George Biddel Airy, conducted an experiment based upon an idea which had been proposed more than a century earlier by a Jesuit named Boscovich. The latter had pointed out that if the telescope in Bradley's experiment had been filled with water in place of air, the resultant angle of aberration would have been increased, due to the fact that the velocity of light in water is less than in air. However, when the experiment was finally carried out, it was found that the angle in question had not changed at all! On the face of it, this result disproves the claim that Bradley's shift of 20 seconds is caused by aberration. To everyone's amazement, the argument against the motion of the Earth seemed now to be logically compelling: Given that orbital motion implies aberration, it follows indeed that the absence of aberration implies the absence of orbital motion. Understandably, the failure of Airy's experiment sent shock waves through the scientific community. However, worse was yet to come. In 1887, Michelson and Morley conducted their now famous experiment, designed to detect and measure the orbital velocity of the Earth, not by way of aberration, but by comparing the observed velocity of light in the direction of that orbital motion with its velocity in the opposite direction. According to elementary considerations, the two velocities should differ by exactly 2v, where v again denotes the orbital velocity. But again, to everyone's consternation, it turned out that the two light velocities are exactly the same, which is to say that the experiment yielded a measured orbital velocity equal to zero. Two crucial experiments, based upon different physical principles, had now reached the same conclusion: the Earth does not in fact move.

At this juncture one has only two options: one can accept the verdict that the Earth does not move and opt for a duly refined Tychonian astronomy, or else one can search for a way of adjusting the laws of physics so as to render the Earth's orbital velocity to be in fact undetectable. History records that Albert Einstein opted for the second alternative, and in so doing, astonished the world with his theory of relativity. The special theory ingeniously "explains" the negative results of both the Airy and the Michelson-Morley experiments, while, at the same time, it leads to a host of other testable predictions which have since been verified. Without question, Einsteinian physics constitutes one of the most brilliant and successful ventures in the history of modern science. One must not however forget that it operates by the logic of "saving appearances," which is not the same thing, to paraphrase Cardinal Bellarmine, as demonstrating that what is claimed in theory is in fact the case. As Walter van der Kamp- that indefatigable champion of Tychonian astronomy- was fond of pointing out, the logic of relativity constitutes a ponendo ponens argument: from the premise "P implies Q," one falsely concludes "If Q  then P."

Getting back to Bradley's experiment, the question remains: If indeed the Earth does not move, and there is consequently no stellar aberration, how is the small circle described by Gamma Draconis to be explained? On a Ptolemaic or Tychonian basis, the answer is clear: the observed phenomenon is caused by an actual circular motion of Gamma Draconis relative to the Stellatum, the revolving sphere of the stars. A similar remark applies to the phenomenon of stellar parallax, which was finally detected by Henderson in 1832, and measured with greater accuracy in 1838 by Bessel and Struve. From a geocentric point of view there is obviously no such thing as stellar parallax, which is to say that the phenomenon in question must be caused, once again, by corresponding stellar motions. These motions, to be sure, are too small to be observable to the naked eye, and for this reason were not known in ancient times. My point is that Henderson's discovery, so far from proving stellar parallax, can be accounted for on a geocentric basis as well.

This does not however imply that it is a matter of indifference to stellar astronomy whether or not we adopt a geocentrist point of view: nothing could be further from the truth! The fact is that in contemporary astronomy the hypothesis of parallax plays a crucial role in the determination of stellar distance. This can already be seen from the circumstance that the standard unit of astronomic distance is the parsec, which is defined to be the distance at which a stellar object subtends an angle of 1 second relative to a baseline whose length equals the mean distance from the center of the Earth to the center of the Sun. Clearly, the parsec is a parallactic unit of length. It means, in effect, that a star situated 1 parsec from the Earth will have parallax on the order of 1 second. It is to be noted that the hypothesis of parallax imposes enormous dimensions upon the stellar universe: a single parsec turns out to be about 31 million million kilometers. Moreover, since most stars--all but a relative few- have no measurable parallax, their distance from the Earth must be at least 25 to 50 parsecs; and in point of fact, stellar astronomers are wont to employ the megaparsec as their preferred unit of distance. A Tychonian universe, by comparison, would still need considerable size: but nothing like the billions of light years to which contemporary astronomy lays claim. One sees that a geocentric interpretation of astronomical phenomena, by eliminating stellar parallax, would undercut our current picture of the stellar world. A Tychonian universe would differ radically, both in size and in architecture.

But whereas contemporary astronomy is thus implacably opposed to the geocentrist hypothesis, it happens that pure physics is not. According to general relativity, it is in fact permissible to regard the Earth as a body at rest: as Fred Hoyle has put it, the resultant theory "is as good as any other, but not better." Relativity implies that the hypothesis of a static Earth is not incompatible with the laws of physics and cannot be experimentally disproved. To be sure, physics as such cannot affirm that hypothesis; but neither can it deny its validity. Already in 1904, Henri Poincare had understood that "the laws of physical phenomena are such that we do not have and cannot have any means of discovering whether or not we are carried along in a uniform motion of translation" and by 1915, Einstein had concluded that the same applies to arbitrary motion. It appears that so far as physics is concerned, the geocentrist claim remains viable.

Given that the scientific challenge to geocentrism derives, not from physics, but from astronomy, we need to ask ourselves whether the latter science is in a position to prove its case. Our scientific knowledge concerning the stellar universe is of course based upon observations carried out either in terrestrial observatories or by means of instruments transported into outer space via satellites. It is crucial to note that the transition from observational data to claims concerning the stellar realms cannot be accomplished on the ground of physics alone, but requires additional hypotheses of an untestable kind. We have already encountered one such hypothesis in the assumption of stellar parallax, and the informed reader will likely recall the Doppler interpretation of stellar redshifts, as also the so-called cosmological principle, as further untestable assumptions basic to contemporary astronomy. The logic, here, is once again of the ponendo ponens variety, which is to say that the hypotheses in question are judged or validated by their success in "explaining" observable phenomena. But apart from the circumstance that such an argument is never compelling- as Cardinal Bellarmine pointed out long ago!- it happens that the prevailing astrophysical cosmology has so far flunked the empirical test: despite inflated reports, and decades of concerted effort, one finds that big bang theory does not square with the empirical data. Here too one has grounds to surmise, when the chips are down, that we are dealing, not indeed with "proof," but once again with "propaganda" of sorts. If the Airy or Michelson- Morley experiments had yielded their intended result, the scientific case against geocentrism, though still not compelling, would have been at least impressive; however, as the matter stands, the ancient doctrine has not even been rendered improbable, let alone has it been disqualified.

The late Walter van der Kamp has made an interesting point: "In truth," he said, "the choice is between Tycho Brahe and Einstein- Galileo et al are played out." Now, I certainly agree with the part about Galileo. To be precise, he is "played out," not because he affirmed the motion of the Earth, but because he staked the claim on ostensibly scientific grounds. One knows today on the basis of physics that Galileo's arguments are inconclusive, and that in

fact the stipulated motion cannot be proved at all. What I find misleading, on the other hand, is the notion of "choosing" between Tycho Brahe and Einstein. I reject the implication that Tychonian astronomy and Einsteinian physics are mutually exclusive alternatives. I shall argue not only that the two positions are compatible, but that each has its own validity. The key to the problem lies once again in the discernment of what may be termed levels of cosmic reality: though interrelated, these levels remain distinct and need to be distinguished.

To begin with the physical, let me recall that I use this term in a technical sense: it refers to the level or aspect of cosmic reality which answers to the modus operandi of physical science. The physical is thus defined and known through acts of measurement, which entails that it owns neither essence nor substance in the traditional ontologic sense. As Heisenberg observed with reference to quantum particles, physical objects constitute a strange new kind of entity "just in the middle between possibility and reality." Now, I will argue that on the level of these strange new entities, Einsteinian relativity has its place. It is by no means surprising, I say, that entities defined through acts of measurement should conform to principles of relativity: in the final analysis, are they not indeed relational by definition? Consider the case of velocity, the magnitude of motion: what else can it be, physically speaking, than a speed relative to this or that coordinate system, this or that frame of reference? On the physical plane there are indeed invariants- quantities, namely, which turn out to be the same relative to every coordinate system in some class- but no absolutes: nothing which is not inherently relational. For this one needs essence, something that answers to the question "What?". A stone, thus, or a cat is not relative, not simply relational, by virtue of the fact that it is something: a thing that is more than "midway between possibility and reality." A stone or a cat, therefore, is something which cannot be quantified, cannot be elicited by acts of measurement, and consequently does not pertain to the physical domain. As Eddington observed, "The concept of substance has disappeared from fundamental physics." Strictly speaking, physics does not deal with things. It is true that the notion of substance was retained in what is now called classical physics; that retention, however, was spurious, that is to say, inconsistent with the operational principles of physical science. As Eddington points out: "Relativity theory made the first serious attempt to insist on dealing with the facts themselves. Previously scientists professed profound respect for the 'hard facts of observation'; but it had not occurred to them to ascertain what they were." Albert Einstein was presumably the first physicist to arrive at a consistent theory based upon operational principles. It turns out that the tenets of relativity are not in fact ad hoc stipulations introduced to safeguard the Copernican hypothesis, as geocentrists are wont to claim, but respond to the  very principles upon  which physical science is based. It appears that in a world defined operationally- in what John Wheeler terms the participatory universe- Einsteinian relativity reigns supreme.

But how does the matter stand on the level of the corporeal world? Do the principles of relativity apply to a world that is to be known, not through acts of measurement but through acts of sense perception? Do Einsteinian principles still apply in a world where essences manifest in the form of sensible qualities, a world in which not only relations but actual substances are to be found? There is no reason to believe that this is the case. Nothing obliges us to suppose that in this corporeal domain, which is distinctly "more" than the physical, there can be no absolute rest and absolute motion, nor absolute simultaneity of events. If, on this higher level, stones and cats are real, why not also rest and motion, why not simultaneity of events as well? I have argued in The Quantum Enigma that it is the loss of essence, of substantial being, as one descends into the physical plane, that brings into play the quantum-mechanical superposition principle; I would like now to propose that the same loss, the same reduction, leads macroscopically to Einsteinian relativity. Where there is no substance to distinguish one reference frame from another, it is hardly surprising that the two are of equal weight. It is, as always, the loss of substance, of hierarchy in fact, that leads to the "democratization" of what remains.

One knows that the superposition principle is abrogated on the corporeal plane: one knows, for example, that a cat cannot be both dead and alive. It is this simple fact, as it turns out, that accounts for the so- called collapse of the state vector, which has mystified physicists since the advent of quantum theory in 1926. Is it not reasonable, then, to suppose that the principles of relativity are likewise abrogated on the corporeal plane? Now, this abrogation, which I take to be factual, has obviously immense implications. It suggests, for example, that Aristotelian physics may not, after all, be quite as chimerical as we generally assume. Furthermore, the aforesaid recognition evidently casts a new light on the geocentrist controversy. One sees, in particular, that Tychonian astronomy may be more than a merely "admissible" theory, as general relativity declares: more indeed than simply "as good as any other, but not better." The point is that the worth of geocentric astronomy can no longer be ascertained exclusively through acts of measurement. The question, one finds, cannot be resolved on purely physical grounds, but calls for considerations of a different order. The most that physics as such can say is that geocentric astronomy cannot be ruled out of court.

To summarize: Geocentrism is the cosmology at which one arrives by way of cognitive sense perception, whereas Einsteinian acentrism corresponds to the way of knowing native to the physical sciences. There can be no conflict, no contradiction between the two: the respective worldviews simply correspond to different perspectives, different darshanas, as the Hindus would say. However, geocentrism is the higher of the two, even as the corporeal plane is ontologically higher than the physical. Cognitive sense perception, moreover, having access to essence, is able in principle to transcend the corporeal plane: to pass, in the words of St. Paul, from "the things that are made" to the "invisible things of God" and beyond even these, to "His eternal power and Godhead." In a word, human perception opens in principle to the metacosmic realms (from whence it has descended), whereas the modus operandi of physical science confines us to a relational and indeed subcorporeal domain. Galilean heliocentrism, finally, is a bastard notion which spuriously confounds the two ways of knowing. One might add that there is also a traditional or authentic heliocentrism, which must not be confused with the Galilean; and this is what will mainly concern us in the following chapter.