REBUTTAL OF NORTH AND NIETOIn a surprising turn of events, Dr. Gary North hired Dr. Michael Martin Nieto, theoretical physicist at Los Alamos National Laboratory, to analyze alleged fatal flaws and defects in geocentric cosmology from the standpoint of an astrophysicist. Dr. North paid Dr. Nieto for the resulting essay, entitled "Testing Ideas on Geostationary Satellites," which is incorporated as the bulk of the publication bearing the superscription, "Geocentrism: An Astrophysicist's Comments." Dr. Nieto interacted with virtually no relevant geocentric material, although it was not only available to Dr. North, but actually forwarded to him in 1992. Dr. North saw fit to return the most technically-oriented and complete videotaped lecture on geocentricity available at that time, without having ever watched it. The video provided up-to-date technical references in answer to Dr. North's many challenges, but he refused to view it. He could have saved himself the money, and Dr. Nieto the trouble, had he not inflicted such blindness upon himself. The response to Dr. Nieto is contained in that video, and we need merely rehearse it here to refute Dr. Nieto's and Dr. North's papers. The fact that Dr. North held that very video in his hands and yet refused to view it, reflects a tragic breakdown of academic and intellectual integrity on his part. The great irony of Dr. Nieto's essay is his complete reliance on Einstein's General Theory of Relativity. The irony obtains from the fact that general relativity stipulates that any observer can consider himself to be at rest and that solving Einstein's field equations for his position will properly and satisfactorily describe all phenomena observed from that vantage point. When Drs. North Nieto assert that if the earth were at rest, geosynchronous satellites would necessarily fall down, they are asserting that general relativity is completely false. Since Dr. Nieto uses 2 of his 7 pages to air alleged experimental proof for general relativity, we observe that a kingdom divided against itself cannot stand, and that Dr. Nieto thereby destroys his own arguments. In fact, Dr. Nieto appears to be completely unaware of the well-documented key doctrines of general relativity, both as presented by Einstein and Mach, and developed subsequently into our own decade. This failure of scholarship (surprising, since the essentials are taught in freshman-level courses in physics) has led Nieto into multiple errors. North and Nieto are searching for the mystical geocentric force that holds up geosynchronous satellites, preventing them from falling to the earth given the geocentric hypothesis that they are not orbiting objects. "Where is this force?" they ask, for they have searched and found it not. So they appeal to their readers to search as well and see for themselves there is no such force, just as the Pharisees challenged, "Search, and look: for out of Galilee ariseth no prophet" (John 7:52). Had the Pharisees glanced at Isaiah 9, they could have spared themselves an embarrassing gaffe. Had Dr. Nieto reviewed Einstein first, he could have done likewise. The urge to hide the geocentric force acting on the geosynchronous satellite from his readership resulted in the following error by Nieto. Says he, "...one sees that there is no explicit mathematical theory as to why the satellite would stay up there if the universe were geocentric. The authors postulate that maybe there is a sphere of matter (no good, they realize, there is no force inside a sphere of matter), or then maybe there is a ring and maybe this could account for it. They speculate. But they do not show." Actually, we did show, but Dr. North didn't watch. Einstein taught that there is a force inside a sphere of matter that is in motion. He wrote plainly to Ernst Mach on June 25, 1913, "If one accelerates a heavy shell of matter S, then a mass enclosed by that shell experiences an accelerative force. If one rotates the shell relative to the fixed stars about an axis going through its center, a Coriolis force arises in the interior of the shell, that is, the plane of a Foucault pendulum is dragged around." Geocentrists have never denied the Gaussian proposition that there is no net force inside a stationary shell of matter but the distinguishing feature of geocentricity is the daily rotation of the universe around the earth. How did Nieto and North miss it? By using return mail. The magnitude of the force (usually discussed under the heading of "dragging of inertial frames") is cited in many references. Misner, Wheeler & Thorne, in their tome Gravitation, pp. 547, quantify the rotational drag by "simple dimensional considerations" and propose that Foucault must be identical with stars, or, namely, that the angular velocity of a Foucault pendulum equals the angular velocity (speed of rotation) of the stars (i.e., the rest of the universe) ibid, pg. 548. These well-respected authors (Kip S. Thorne is Cal Tech's black hole and general relativity expert; Wheeler & Misner taught at Princeton, Cal Tech and Oxford) approvingly cite the 1918 work of Thirring (pg. 547) in connection with this force and its computation. This last circumstance is doubly ironic, since Dr. Nieto's final footnote begins, "There is a gravimagneto effect related to the Earth's rotation, which amusingly draws upon the work by Thirring cited by [Dr. John] Byl." Dr. Nieto's faulty understanding of basic relativity theory could have been remedied by checking the work by Thirring. Hans Thirring begins by citing Einstein's 1914 paper. Einstein defines K as a Galilean-Newtonian coordinate system, and K1 as a coordinate system rotating uniformly relative to K. Since this directly represents the earth (K1) and the universe (K) in Dr. Nieto's antigeocentric cosmology, I will substitute these identifications for K and K1 in italics in Einstein's text to make Einstein's position clear to every reader: "Let the earth be a coordinate system rotating uniformly relative to the universe. Then centrifugal forces would be in effect for masses at rest in the universe's coordinate system, while no such forces would be present for objects at rest with respect to the earth. [The geosynchronous satellite is precisely such an object, at rest with respect to the earth, but viewed as having a centrifugal force acting on it with respect to the universe (MGS).] Already Newton viewed this as proof that the rotation of the earth had to be considered as 'absolute,' and that the earth could not then be treated as the 'resting' frame of the universe. Yet, as E. Mach has shown, this argument is not sound. One need not view the existence of such centrifugal forces as originating from the motion of the earth; one could just as well account for them as resulting from the average rotational effect of distant, detectable masses as evidenced in the vicinity of the earth, where the earth is treated as being at rest." In quite precise language, Einstein taught that the centrifugal force on an object in the earth's rest frame (the condition satisfied by the hovering geosynchronous satellite) is inadmissible as evidence of the rotation of the earth, for in the earth's frame that force arises from "the average rotational effect of distant, detectable masses." This 1914 teaching of Einstein is rather old news, and it remains inconceivable that Nieto would cite it, "amusingly enough," without reading it. Or is there a tragic pattern here? Thirring observed in his opening paragraphs that the complete equivalence between the reference frames, explaining such phenomena as the geosynchronous satellite or Foucault pendulum equally well in a geocentric reference frame, is secured by definition by Einstein's 1915 work: "the required equivalence appears to be guaranteed by the general co-variance of the field equations." This is what geocentrists mean when they assert (much to Dr. North's disdain) that the mathematics is the same for the heliocentric and geocentric models: Einstein's field equations are structured to supply the necessary upward force on the geosynchronous satellite in a geocentric as well as a heliocentric framework. In fact, the only reason Thirring wrote his paper was because the boundary conditions of Einstein's paper were geared for a finite universe, so that Thirring set forth, in his own words, "the mathematical development of a rotational field of distant masses for a specific, concrete example." After ten pages of tensor analysis, Thirring summarizes: "By means of a concrete example it has been shown that in an Einsteinian gravitational field, caused by distant rotating masses, forces appear which are analogous to the centrifugal and Coriolis forces." Hard again to imagine Dr. Nieto's amusement in citing in his favor a source, even second-hand, that negates his position. Harder yet to imagine Dr. Nieto rejecting Thirring's argument, since it simply (and ably) develops Einstein's own stated position. Einstein's position has not lacked for continued, and contemporary, treatment by the world's top relativity scholars. Another key (and, in fact, decisive) reference cited in the video North refused to view was taken from the journal, General Relativity and Gravitation, Volume 21, No. 2, 1989, pgs. 105-124. Professors Ø. Grøn and E. Eriksen, in the article Translational Inertial Dragging, take up, again, the issue of what forces arise within a spherical shell of matter. (Recall that Dr. Niento wrote, "there is no force inside a sphere of matter.") Grøn & Eriksen inform us that "The rotational inertial dragging effect, which was discovered by Lense and Thirring, was later investigated by Cohen and Brill and by Orwig. It was found that in the limit of a spherical shell with a radius equal to its Schwarzchild radius, the interior inertial frames are dragged around rigidly with the same angular velocity as that of the shell. In this case of "perfect dragging" the motion of the inertial frames is completely determined by the shell." (pg. 109-110). Intriguingly, the authors point out that "with reference to Newtonian mechanics we talk of inertial force fields in accelerated reference frames. However, according to the general principle of relativity, we may consider the laboratory as at rest. We then talk of gravitational dragging (acceleration) fields. The concept of 'inertial forces,' which may be regarded as a sort of trick in Newtonian mechanics, is thereby made superfluous." What is fascinating here is the recognition that the Newtonian centrifugal force due to inertia (of which Dr. North is so fond) is a fictitious force, and is "a sort of trick." One would have expected the geocentric model of the geosynchronous satellite to be the one filled with tricks and fictional forces, but such is not the case. (The authors intend no derogation of fictitious tricks in the Newtonian case, while buttressing the claim that geocentricity posits actual rather than fictitious forces to account for the behavior of objects such as geosynchronous satellites.) This is explicitly stated on page 113, where G&E cite C. Møller "in his standard [1952] textbook on general relativity", from chapter 8: "Einstein advocated a new interpretation of the fictitious forces in accelerated systems of reference. The 'fictitious' forces were treated as real forces on the same footing as any other force of nature. The reason for the occurrence in accelerated systems of reference of such peculiar forces should, according to this new idea, be sought in the circumstance that the distant masses of the fixed stars are accelerated relative to these systems of reference. The 'fictitious forces' are thus treated as a kind of gravitational force, the acceleration of the distant masses causing a 'field of gravitation' in the system of reference considered. Only when we work in special systems of reference, viz. systems of inertia, it is not necessary to include the distant masses in our considerations, and this is the only point which distinguishes the systems of inertia from other systems of reference. It can, however, be assumed that all systems of reference are equivalent with respect to the formulation of the fundamental laws of physics. This is the so-called general principle of relativity." This quote is important on two counts. (1) The italicized sentence (emphasis apparently in Møller's original textbook) is precisely what Dr. Nieto denies in his argumentation, namely, the general principle of relativity. But on what does Dr. Nieto base his arguments against geocentricity? General relativity! But count (2) is equally telling: Møller tells us that the only reference frame in which we can exclude consideration of the distant masses of the galaxies is in "systems of inertia," which G&E more carefully define as "frames of reference in which the cosmic mass has no observed rotation or translation acceleration." By this definition, the earth does not fulfill the requirement for being a system of inertia, since the heavens are observed to rotate around it. Therefore, Møller alerts us that we may NOT omit the rest of the universe in deriving the forces acting locally on the earth. Geocentrists assert as much, consistent relativists (e.g., Fred Hoyle) assert as much, but inconsistent or forgetful relativists (e.g. Nieto) fail to do their homework before taking up the issue. Grøn & Eriksen develop the consequences of Einstein's position to the hilt on pages 117-118 with an ironclad example: "As an illustration of the role of inertial dragging for the validity of the strong principle of relativity, we consider the Moon orbiting the Earth. As seen by an observer on the Moon both the Moon and the Earth are at rest. If the observer solves Einstein's field equations for the vacuum space-time outside the Earth, he might come up with the Schwarzchild solution and conclude that the Moon should fall toward the Earth, which it does not. So it seems impossible to consider the Moon as at rest, which would imply that the strong principle of relativity is not valid. "This problem has the following solution. As observed from the Moon the cosmic mass rotates. The rotating cosmic mass has to be included when the Moon observer solves Einstein's field equations. Doing this he finds that the rotating cosmic mass induces the rotational nontidal gravitational field which is interpreted as the centrifugal field in Newtonian theory. This field explains to him why the Moon does not fall toward the Earth." This is the decisive answer to Dr. North and Dr. Nieto. The Moon always shows the same face to the Earth, so that from the point of view of the Moon, the Earth is hovering 240,000 miles above it. In this picture, the Earth is to the Moon, what a geosynchronous satellite is to our Earth. The hypothetical Dr. North on the Moon solves his equations and wonders, "What holds the Earth up? Why doesn't it fall down here?" And Grøn and Eriksen have provided the answer, in complete consistency with the work of Einstein (1913, 1914, 1950), Thirring (1918, 1921), Møller (1952), Misner, Wheeler, Thorne (1973), Brill and Cohen (1966, 1968) and Orwig (1978). Which is only natural, since it is unthinkable that Einstein's disciples would break with him on the central tenet of his general theory. Whereas Dr. Nieto seems to recognize the element of curved spacetime in general relativity, he has failed to grasp the general principle of relativity itself, from which the subsequent geometric model flowed. In fact, he has (inadvertently, I would hope) lashed out at it. In passing, note that the plane of rotation of the cosmic mass in G&E's example is equatorial for the Moon general relativity provides for explaining such geosynchronous phenomena only for equatorial satellites. Dr. North wrongly assumes that in the geocentric model one can place geostationary satellites over North Dakota, whereas the geocentric literature has repeatedly taught that the field equations arising from cosmic rotation permit stable geostationary satellites only over the equator, and at the same prescribed height as that indicated by the Newtonian methods Dr. North favors. This has been asserted in books, in journals, on audiotapes, and videotapes. You'd have to try real hard to miss it. While on the subject of Einstein and Thirring, let us examine Dr. Nieto's final footnote: "There is a gravimagneto effect related to the Earth's rotation, which amusingly draws upon the work by Thirring cited by Byl. Attempts will be made to measure this effect with a gyroscope orbiting about a rotating earth (Schiff gyroscope experiment) and by two satellites (LAGEOS I and III) orbiting about a rotating Earth in complementary orbits. This is a prediction, whose test will hopefully come about this decade." Reading this somewhat flippant note, the certainty of the Earth's rotation is flatly assumed as proven, and about to undergo additional, if superfluous, proof. It is made to appear that Dr. John Byl erred by quoting from a source that is being used to develop an experimental proof of the earth's rotation! But all is not as it seems in footnote 13. The fundamental reference to experiments like this is found, again, in Misner, Wheeler & Thorne's Gravitation, pages 1117-1121, where the experiment alluding to Nieto's complementary satellite orbits (one polar, the other equatorial) is set forth in detail. MW&T tell us that "the Earth's rotation 'drags' the local inertial frames along with it. Notice that near the north and south poles the local inertial frames rotate in the same direction as the Earth does (W parallel to J), but near the equator they rotate in the opposite direction (W antiparallel to J; compare W with the magnetic field of the Earth!)" (page 1119). By sending satellites in orbits 90 degrees apart, scientists can maximize the effect they are trying to measure, which is very microscopic indeed (0.1 seconds of arc per year). But Nieto's use of this argument falls to the ground, since the physics being described here are those local to the gyroscope. Whether or not the earth is motionless, the experiment yields the same result. In fact, the very wording of the authors' argument deflates Dr. Nieto's point, since they specify that the motion is relative between the Earth and the distant galaxies. The force that the satellite experiment will be measuring is precisely the kind of force (inertial frame dragging) that general relativity scientists affirm holds up geosynchronous satellites when the earth is taken to be at rest. So, the amusing part of Dr. Nieto's footnote 13 is how badly it appears to have backfired. If it be objected that a 1973 book, definitive tome though it be, is somewhat dated in dealing with the 13th footnote, the literature is still rich in more recent references. In General Relativity and Gravitation, Vol. 20, No. 1, 1988, Cerdonio, Prodi and Vitale published an article entitled Dragging of Inertial Frames by the Rotating Earth: Proposal and Feasibility for a Ground-Based Detection, pgs. 83-87. The kind of hardware that Dr. Nieto has in mind is there described in depth, where "the effect of rotation results in a net magnetization of the [instrument's ferromagnetic] rod" (pg. 85). The resulting magnetic flux is measured by a device known as a SQUID. Yet, throughout the article, general relativity is assumed, and relative motion is affirmed. The very effect itself is described thus: "The Lense-Thirring field due to the rotating Earth is locally equivalent to a rotation in respect to distant stars..." Another expression is "the time average of the Earth's rotation with respect to distant stars." The choice of coordinate system is arbitrary, and the field mathematics follows after the preference of the physicist. Consult, by way of comparison, the citations of Thirring discussed earlier, on which this paper is dependent. In short, we have here Thirring cited against Thirring, Einstein cited against Einstein, and general relativity cited against general relativity. Dr. Nieto deliberately and directly undermines his own physics, and his arguments are manifestly self-contradictory. Consistent relativists have never been hostile to geocentricity. Dr. Fred Hoyle pointed out that had the trial of Galileo been held after Einstein published his general theory, it would have resulted in an even draw by mathematical and physical necessity. This is the legacy of general relativity: the overthrow of absolute reference frames, and the democratization of all coordinate systems. Let it be clearly understood that the presentation of general relativity's teaching on the geocentric model presented herein is central, not peripheral or obscure, in Einstein's theory. It was plainly presented to this author when he learned the fundamentals of general relativity and geometrodynamics at the California Institute of Technology at the age of 16 (as a research fellow for the 1973 California Junior Science & Humanities Symposium, under the supervision of Dr. Kip S. Thorne and his associates ‹ and often studying, in fact, from the galley proofs of Gravitation as it was being completed for publication). We can therefore safely rule out the idea that Dr. Nieto's training somehow glossed over this key proposition, in light of the fact that it is basic to Einstein's theory, and that Dr. Nieto freely cites references from general relativity's body of extant literature. He even indicates that he is actively seeking to improve upon Einstein, which would, presumably, imply some mastery and understanding of the theory one is attempting to supplant. Therefore, Dr. Nieto's multiple citations from the world of general relativity constitute academic suicide so far as this particular debate is concerned. A geocentrist could have easily quoted the selfsame references as Dr. Nieto did, but in so doing remained consistent with Einstein. (There are, in fact, a number of geocentrists who base their scientific understanding of the geocentric model directly upon general relativity, at least one of which has conveyed this clearly and concisely to Dr. North.) To summarize: it is impossible to launch an attack on geocentricity on the basis of general relativity, by definition. Proof of a moving earth is simultaneously proof that general relativity is a myth. This means that Dr. Nieto's analysis is shot through with factual errors in regard to the primary force of his presentation. Some of his errors are relatively innocuous, e.g., his description of Kepler's theory as involving concentric spheres "within which were inscribed regular polygons." (Kepler used Platonic solids and not flat polygons.) Unfortunately, most of the errors (factual, logical, and scientific) are simply fatal. Dr. Nieto, however, has also evidenced poor research in setting forth geocentricity's distinctives. He asserts at least six times that geocentricity has failed to predict certain phenomena that modern science has correctly predicted. These alleged failures earn geocentricity a demotion to the status of an antirational dogma. Through ignorance of geocentric physics, Dr. Nieto imposes a Procrustean bed on those he criticizes tantamount to stuffing words into the mouths of geocentrists. The predictive power of geocentricity, and its more comprehensive analytic range, will be addressed below. First, however, consider Dr. North's accusation that modern geocentricity has failed to produce fruitful results. Citing the parable of the fig tree, wherein "Jesus allowed it only four years of fruitlessness before cutting it down," North finds geocentricity long overdue for immediate termination. His arbitrary time-frame reveals a shallow view of modern physics. Galileo himself learned that merely setting forth a more elegant and attractive geometry for orbital kinematics was inadequate to prove his heliocentric model: he had to provide a complete, new theory of dynamics to support it. This work, undertaken by one of the great intellects of the period, was decades in the making. The formalism later received its capstone in the work of Newton. This development spanned more than a century of time. Dr. North's "fig tree" view finds its analogue in the vitriolic attacks launched against Galileo by his enemies, whose motivations were political and personal. The new dynamics of Einstein were born in the work of mathematician Georg Riemann, whose work on space curvature appeared so far removed from any known practical application that it was appeared completely useless. Yet, gravitation is now described using his tensor notation, which Einstein incorporated into the heart of his general theory. With Einstein came a new dynamical theory, geometrodynamics, with spacetime geodesics replacing outdated Newtonian trajectories. This revolution took the better part of a century, from the laying of the mathematical foundations in the mid-19th century to the completion of this towering edifice of 20th century physics. The case is no different with geocentric science: it, too, must develop a brand new dynamical theory to support its description of the behavior of the heavens. Unlike the peaceful development of Einstein's theory, the geocentric model's slow codification is being undertaken under tempestuous circumstances, in the face of ridicule, contempt, and self-indulgent scorn, yet propelled forward by laborers operating near their personal limits of physical stamina. Yet the work goes forward, and should be allowed the time that was accorded the preceding revolutions to bear their fruit. A preliminary overview of progress to date, giving a glimpse of the dynamical theory being presently developed by modern geocentric scientists, is herein set forth. Where the discussion touches on Dr. Nieto's concerns and challenges, the connection will be pointed out. (Keep in mind that not all geocentrists will agree with every detail of the following summary ‹ it only purports to be representative of the dominant strains of thought among top geocentric scholars.) GRAVITYOne would think that the only viable theories of gravitation worth considering were Newton's and Einstein's, given the substance of Dr. North's and Dr. Nieto's critiques. This gross oversimplification merely misleads the unwary reader, historically and scientifically. Newtonian gravity received competition from the LeSagean theory of gravity, and the LeSage hypothesis even received the theoretical attention of Lord Kelvin ("On the Ultramundane Corpuscules of LeSage," Royal Society of Edinburgh Proceedings, pgs. 577-589, 1871). The LeSage theory is a physical theory of gravitation, meaning there is an actual, understandable physical reason why gravitation exists and can be felt (unlike abstract notions such as action-at-a-distance and curved spacetime). The theory has undergone important revisions in the hands of geocentrists over the last decade, but the fundamental idea is retained. George-Louis Le Sage developed "his" theory in the late 1770's (the work was almost certainly plagiarized). He postulated that the universe is filled with countless infinitesimal particles, which he termed ultramundane corpuscles. These corpuscles are in extremely rapid motion, analogous to molecules in a gas, and are colliding continually with material objects from all directions, so that a net pressure is applied to all objects within this kinetic "ocean" of ultramundane corpuscles. In the case of a spherical mass in the middle of this corpuscular flux, the net force on the mass is zero, since the pressure is applied to it equally from all directions. However, in the case of two spherical objects near each other within this flux, the one sphere will block some of the corpuscles from colliding with the other, and vice versa. The objects shield one another from a portion of this flux, as determined by their mass and separation, such that there are more corpuscles pushing them together along the line joining their centers than there are keeping them apart. The closer they are, the greater the corpuscular pressure becomes. LeSage calculated the well-known inverse-square law from this shielding effect. In his theory, gravity is not a pull ‹ it is an external push. According to this view, a man's weight reflects the difference between how many corpuscles are hitting him from above, compared to how many are hitting him from below ‹ and is a function of the earth's mass attenuating the upward-directed flux. (In fact, the mathematics of LeSagean mechanics is the mathematics of attenuation.) It is easy to see why the LeSagean theory is termed a physical theory of gravitation: its fundamental principle is simple enough for a child to grasp, without metaphysical mumbo-jumbo. Advocacy for the theory declined after Lord Kelvin observed that the collisions between the hypothetical particles and normal matter would, over long periods of time, involve a heat transfer sufficient to melt planetary objects. (Subsequent physics showed how such particle collisions can be "elastic" and thus avoid any degradation of flux energy to heat ‹ but by then, LeSage had been forgotten in the stampede to canonize Einstein.) LeSagean gravitational theory is an important component in the dynamical thinking of most geocentrists, excepting those who prefer basing their position on general relativity. The theory has predictive power, for the equations of attenuation make it clear that the shape and orientation of an object determine the magnitude of force on it. In the LeSagean theory, a barbell held horizontally is heavier than one held vertically, and a feather will drop faster in a vacuum than a small ball of lead ‹ predictions that directly oppose the dynamics of Newton, Galileo, and Einstein. Until the last decade, the predictions of LeSage would have been laughed off the stage, until instruments sensitive enough to detect such anomalies were pressed into service. When these anomalies were discovered, modern science rushed in to herald the discovery of some fifth fundamental force, termed (erroneously) supergravity by some excited researchers. But they had been beaten to the theoretical punch by more than two centuries by the gravitational theory championed by the geocentrists. The peculiar behavior of pendulums just before and after an eclipse, and within deep mine shafts, has likewise been troubling to the standard gravitational theories, Einstein's included. Saxl and Allen's pendulum measurements during the solar eclipse March 7, 1970 were startling, and subsequent measurements by Kuusela (Finland: July 22, 1990 and Mexico: July 11, 1991) still reflected anomalous, though less severe, deviations. (Cf. Physical Review D3, 823 and General Relativity and Gravitation, Vol. 24, No. 5, 1992, pg. 543-550). Mineshaft measurements of the gravitational constant evaded conventional analysis (Cf. Holding & Tuck, "A New Mine Determination of the Newtonian Gravitational Constant," Nature, Vol. 307, Feb. 1984, pgs. 714-716). These anomalies were predicted by the LeSagean theory, not by Newton, not by Einstein. An ultrasensitive Cavendish torsion balance was pressed into service in the mid-1970's to determine experimentally how sound the inverse-square law of gravitation was (Long, "Experimental Examination of the Gravitational Inverse Square Law," Nature, April, 1976, Vol. 260, pgs. 417-418). The apparatus revealed systematic discrepancies of 0.37%. Considering how relativity theory makes much ado of infinitesimal anomalies it "predicts," this reported glitch is enormous ‹ and is predicted by the LeSagean model promoted by modern geocentrists. Here are several key experimental effects predicted and/or adequately explained only by geocentrists pursuing their theory of dynamics: one could legitimately turn the tables on Dr. Nieto and ask, "Where was modern physics? Its theories predicted something other than what was measured!" Modern physics tends to respond with a yawn to such challenges, and Dr. Nieto's view that the theories that fit the data best are the ones worthy of acceptance is, in fact, naïve. When comparisons between theories are made, the faithful will prove loyal to their theories, not the data. When confronted with evidence demonstrating the superiority of one theory over others (e.g., "A Comparison of Results of Various Theories for Four Fundamental Constants of Physics," International Journal of Theoretical Physics, Vol. 15, No. 4 (1976), pp. 265-270), the world of science merely shrugged, unmoved in its pre-existing biases. (In the example cited, the best theory, being anti-Einsteinian, gained no adherents for having met the experimental criteria better than did its cousins.) (This author, in phone conversation with a chief research scientist at the Laurence-Livermore Labs in 1992, pointed out that the electron diffraction effect had been again recently derived using classical physics. Quantum mechanics was developed in part because classical physics could not account for this effect, but now that this was no longer true, the scientist dismissed the news with an annoyed "So what?" His precommitment to modern QCD theory colored his scientific worldview completely.) The LeSage theory was developed mathematically, in painstakingly rigorous detail, and then underwent an important conceptual evolution in the mid-1980's. What if the ultramundane corpuscles were compressed to a greater density, so that more of them filled a smaller volume? In fact, what if they were squeezed shoulder to shoulder, so tightly packed that they could only jostle one another, but were no longer free to rocket through space like gas molecules do? Do the same rules of shadowing and attenuation apply now that the so-called LeSagean gas has become an ultradense mass? Would the pressure effects transmit in the same way as the original theory stipulated? Indeed, the same principles hold, except that acoustic pressure waves transmit the background gravitational pressure through this ultradense matrix. This ultradense medium of geocentric physics is identified as the Biblical firmament. It has a density so great that a teaspoon of the firmament would weigh more than a trillion universes combined. (The computed density is termed the Planck density, roughly 1094 g/cm3.) Such assertions seem to earn Dr. Nieto's label of being merely "ad hoc." But a little research (in contrast to cavalier dismissal) would reveal that the constituent elements of this geocentric postulate can be found in the most highly respected scientific journals and publications. In fact, the literature has been of inestimable help in obliterating objections to the geocentric notion of a physical, ultradense firmament. In The Very Early Universe (Gibbons, Hawking & Siklos, 1983 Cambridge University Press), M.A. Markov defines a "particle" termed a "maximon," possessing the 1094 g/cm3 density defined above, or more precisely, 3.6x1093 g/cm3 (pgs. 359, 361). He writes, "If a black hole has internal Planck dimensions and an external mass equal to the Planck mass, the matter density in it is quantum (rq). If it is not decaying, such a black hole represents some degenerate case: it can neither collapse, nor anticollapse if one assumes that the mass density cannot exceed rq. In other words, the requirement of a limiting density is very strong and leads to nontrivial consequences" (pgs. 366-367). Markov then explores the implications of a "liquid" made up of such maximons, and points out that from "a topological point of view the maximon liquid is a model of a quasi-isotropical space" (ibid). This citation is important, for geocentrists are often criticized for their description of "empty" space as a medium millions of times denser than lead, leading to the common objection that physical objects could never possibly move through so dense a medium. But the physics affirms the fact that such a medium can function as a space, through which other objects can freely pass. (A maximon is not necessarily a black hole, according to Markov, but "may be a particle of the same Planck dimensions, but with a structure essentially different from a black hole. Their gravitational radius coincides with their Compton length," ibid, pg. 365. This is pointed out here to cut short any critique that the firmament model clearly leans on general relativity by relying on the existence of microscopic black holes.) Note Markov's use of the word, "nontrivial." This word is the most appropriate term one could apply to the firmament of the geocentrists ‹ any object as stupendously massive as the firmament is asserted to be is to be taken very seriously, since it dwarfs the rest of the universe in comparison. It is ironic that geocentrists are routinely called upon to abandon this "quirky, inconsequential" notion, whereas secular science has continued to probe the idea theoretically and experimentally, while unaware of its ultimate implications. In short, "empty" space is not a vacuum; it is not a "nothing," it is a "something." Correspondingly, it has properties and attributes that "nothingness" cannot possess. Dr. Robert J. Moon, Professor Emeritus in Physics at the University of Chicago, published an article in 21st Century, May-June, 1988, pg. 26ff, entitled "Space Must Be Quantized," addressing precisely this issue. He points out that "according to accepted theory, free space is a vacuum. If this is so, how can it exhibit impedance? But it does. The answer, of course, is that there is no such thing as a vacuum, and what we call free space has a structure. ...[This impedance] equals 376+ ohms." This reactive, energy-storing impedance is a natural corollary of geocentric theory and its ultradense firmament; it has not been accounted for by conventional science, and is not contained within either Newton's dynamics or Einstein's gravitational field equations. Where was conventional science in accounting for this effect? The ultradense firmament of the geocentrists pops up in the literature in various guises, as theorists attempt to account for the experimental data flooding into the various centers of higher learning. Princeton's John A. Wheeler is credited with being the first to describe what is now called "spacetime foam," the notion that on ultramicroscopic scales empty space is filled with countless ultradense particles popping into existence and then becoming instantly extinct (1957). In 1968 he observed that "the central new concept is space resonating between one foamlike structure and another." Noted astronomer Stephen Hawking developed the implications of this "foam," which is distinctive in that on extremely small scales empty space is jampacked with violently random activity and enormous mass ("virtual" mass in the modern terminology). (Cf. MW&T, Gravitation, pgs. 10, 11, 1180.) The physics at this scale, and the mathematics used to describe it, are daunting even to the cognescenti. The geocentric firmament differs from the conventional understanding in affirming that the underlying particles are permanent and stable, whereas modern physics prefers to regard them as undergoing continuous and extremely rapid creation and annihilation, like an unstable foam. Both theories put the density of the particles at the Planck density. In Physical Review D, Third Series, Volume 47, Number 6, March 15, 1993, pg. R2166ff, Redmount and Suen explore the question, "Is Quantum Spacetime Foam Unstable?" Utilizing fluctuating black holes and wormholes as constituents of the structure of space is a serious liability, the physicists conclude, because the inherent instability of these structures makes them unsuitable candidates as components of the underlying structure of space. There must be, in fact, "strong constraints on the nature" of the structure of space at scales down to the so-called Planck length (about 10‹33 cm), the size of a maximon. This recent research points away from the Wheeler & Hawking models and toward the firmament of the geocentrists, which does not suffer from the stability problem associated with the hypothetical objects (wormholes, blackholes) populating the general relativity menagerie. In the geocentric hypothesis, the firmament particles, although unable to "break ranks" because their neighbors are too close, are yet in rapid motion, colliding rapidly and continuously with their neighbors. (The fact that they possess rotational spin, something first proposed by Maxwell, will be taken up a little later in connection with electromagnetic theory.) Their behavior has a somewhat stochastic, or random, nature ‹ as clearly taught as far back as LeSage in 1778. Their behavior is classical, but being as small as they are, they influence and induce other larger particles to behave in ways heretofore thought explicable only on quantum mechanical grounds. And, in point of fact, the tenets of the geocentrists' firmament theory have emerged in connection with quantum mechanics, going as far back as Louis De Broglie's work in the 1920's. An excellent discussion of this matter is set forth in J. P. Vigier's article, "De Broglie Waves on Dirac Aether: A Testable Experimental Assumption," Lettere Al Nuovo Cimento, Vol. 29, No. 14, Dec. 6, 1980, pg. 467f. Vigier wrote, "Since Dirac's pioneer work it has been known that Einstein's relativity theory (and Michelson's experiment) are perfectly compatible with an underlying relativistic stochastic «aether» model. Inherent to this model is Einstein's idea that quantum statistics reflects a real subquantal physical vacuum alive with fluctuations and randomness. This concept of a nonempty vacuum has been recently revived not only to yield a foundation to the stochastic interpretation of quantum mechanics but also to explain causally possible nonlocal superluminal interactions resulting from the Einstein-Podolsky-Rosen paradox. Indeed, if a forthcoming experiment of Aspect confirms their existence, the only way out of the resulting contradiction between relativity and the quantum theory of measurement seems to lie in the direction of an extension of the causal stochastic interpretation of quantum mechanics. This assumes the existence of causal subquantal random fluctuations induced by a stochastic «hidden» thermostat proposed by Bohm, Vigier and de Broglie." (pg. 467) Although to the layman the last citation might appear impenetrably dense, the main points can be made clear. There are two schools of thought in the world of quantum mechanics, termed the Copenhagen Interpretation, and the Stochastic Interpretation (sometimes called the Causal Interpretation). The Copenhagen Interpretation is rather counterintuitive and mystical sounding to the layman. One example will suffice: flip a coin and cover it up immediately before looking at it. Is it heads or tails? The Copenhagen Interpretation asserts that the coin is simultaneously heads AND tails while it is covered, but can be forced to fall back into either heads or tails once you take your hand off it and observe it. It then suddenly flips to a unique state by the mere act of observation. The Stochastic Interpretation, unsatisfied with this somewhat bizarre worldview, asserts that the various unusual quantum effects measured on subatomic scales have an actual physical cause (hence, Causal Interpretation). If there is difficulty in simultaneously measuring the momentum and position of a subatomic particle (the Heisenberg Uncertainty Principle), it may be due to actual background noise: this is the point of view of the Stochastic Interpretation. This source of noise is the "nonempty vacuum" Vigier refers to, a level of physical reality discernible on ultrasmall scales, and freighted with significance. Vigier's prologue used the word "superluminal," meaning any entities or interactions that travel faster than the speed of light. He pointed out that if Aspect's then-upcoming experiment measured any superluminal interactions, the contradiction between general relativity and the stochastic theory would have to be decided in favor of the stochastic theory. Translation: if Aspect's experimental result is positive, the consequences would be hostile to general relativity and favorable to the firmament model, the one stochastic model that satisfies the stability constraints stipulated by Redmount and Suen in March, 1993. Vigier reminds us "that Dirac «aether» rests on the idea that through any point O there passes a flow of stochastic particles and antiparticles" (pg. 468), reminiscent of the original LeSage theory. He then introduces spin to the stochastic particles making up what he calls a background sea of activity. He even prefers (pg. 470) that his stochastic particle undergo only short range motions: "contact particle-particle collision type interactions." This is the same restraint geocentrists place on their ultradense firmament model. Vigier, working with Petroni, published an important article a year earlier than the last reference, in Lettere Al Nuovo Cimento, Vol. 26, No. 5, Sept. 29, 1979, pg. 149, entitled "Causal Superluminal Interpretation of the Einstein-Podolsky-Rosen Paradox," wherein he demonstrates that his stochastic model does not encounter the same pitfalls that the competing tachyon theory of Sudarshan, Feinberg, & Recami encounters in explaining faster-than-light interactions and objects. Says he, "We show in particular that superluminal, phaselike, phononlike, collective motions of the quantum potential in Dirac's «aether» do not induce the well-known causal paradoxes of tachyon theory." At the conclusion of his exposition he points out, "It is interesting to note that this elimination of causal paradoxes is only possible in a subquantum model built on a Dirac's vacuum and cannot be applied to theories where superluminal signals are carried by tachyonic particles." He proposes allowing "superluminal signals to be «acoustical» waves with associated quantum potential..." in harmony with the better attested geocentric firmament model. (Geocentric astronomer Dr. Gerardus Bouw has performed some of the seminal computational work in this area of firmament dynamics in the early 1980's.) The experiment by Aspect that J. P. Vigier was anticipating was performed, and the results published in Physical Review Letters, Vol. 47, No. 7, August 17, 1981, pgs. 460-463. Aspect, with partners Grangier and Roger, introduces his results with a little history: "Since the development of quantum mechanics, there have been repeated suggestions that its statistical features possibly might be described by an underlying deterministic substructure." The apparatus, which performed polarization correlation on photon pairs, involves hitting an atomic beam of calcium with a krypton ion laser and a second, Rhodamine laser. The results confirm the existence of superluminal (faster-than-light) interactions, and served to further buttress the stochastic interpretation of quantum mechanics, which, as has been pointed out, has been evolving closer and closer to the geocentrist's firmament hypothesis. (The experiment was conducted again with greater precision, agreeing with the first experiment, and the new results published in Physical Review Letters Vol. 49, No. 2, July 12, 1982, again pointing to the geocentrist's firmament model by proving the existence of the quantum potential.) The issue of superluminal phenomena is significant in light of the common theoretical challenge to geocentric cosmologies that they require every object past Saturn to travel faster than the speed of light in order to complete a daily revolution around the earth. Just as most of the preceding technical citations were provided and explained in the famous videotape that fell on closed eyes, so too are the following references. In the February 1992 issue of the American Journal of Physics, W. M. Stuckey published an analysis titled, "Can galaxies exist within our particle horizon with Hubble recessional velocities greater than c?" (pgs. 142-146). Stuckey proposes to measure the speed at which galaxies are traveling away from us, utilizing their red shift. His test object, a quasar with a red shift of 4.73, is computed to be receding from us at 2.8 times the speed of light. So why is it a problem when geocentrists propose faster-than-light velocities for celestial bodies, and not a problem when mainstream scientists take such measurements in stride? Stuckey explains that the quasar is fleeing from us so rapidly (at what would at first glance appear to be a completely impossible velocity) due to a property of the space between here and there. The vacuum between us and the quasar is stretching and expanding, and thus carries the quasar away from us faster than the speed of light. When modern scientists inform us that objects can travel faster than light due to the expansion of space, we marvel at their wisdom and learning. When geocentrists inform us that objects can travel faster than light due to the rotation of space, we marvel at their insanity. Yet, both models stipulate the same origin of the superlight speed, namely, the intrinsic properties of the space in which the objects are placed. The idea of a rotating universe has been addressed in the secular literature on many occasions. Yu. N. Obukhov, in the recent study "Rotation in Cosmology" ( Dr. Nieto raises some observational challenges for geocentric cosmology, beginning with the parallax effect. There are two schools of thought among geocentrists as to how parallax arises (and if the quantum mechanicists can have two schools of thought, why not the geocentrists?). The "pure" form of geocentricity centers the stars on the earth, and describes the resulting annual stellar shifts by placing the Earth at one sink of a conformal mapping. This procedure has been worked out in rigorous detail for the two-dimensional case by James Hanson, and agrees with the observed phenomena. (This paper regards this model as "pure" inasmuch as it conforms to the original cosmology of Tycho Brahe without modification.) The "modified Tychonic model" centers the stars on the Sun, so that the stars participate in the Sun's annual migration, with the observed parallax being directly predicted by the subsequent geometry. This second model would satisfy the requirements that any consistent relativist would impose on a legitimate geocentric frame of reference, and may well even have direct and indirect Biblical support.
In the geocentric model, the firmament is in daily rotation around the earth, and undergoes annual oscillations as well. This motion of the firmament is evidenced in the Sagnac effect, the well-known Coriolis forces, and by geosynchronous satellites (or, in a more Tychonian vein, geostationary satellites). In the geocentric model, we agree that if the heavens ceased their rotation, the satellites would fall to the earth. But when the heavens are postulated to be in motion, it is Dr. Nieto's equations that are deficient, not ours.
There are four fascinating aspects of the geocentric model.
(1) The notion of a structured firmament analogous to a crystal lattice permits one to consider elementary particles (electrons, protons, neutrons, etc.) to be phonons (quantized vibrations) within that crystal. (Cf. P. J. Bussey, "The Phonon as a Model for Elementary Particles," Physics Letters A 176, 1993, pgs. 159-164.) Bussey shows how phonons exhibit all the experimentally measured properties of elementary particles, including particle splitting and wave collapse. The appeal of the theory is in its predictive power and correlation with reality. Its difficulty is that an appropriate medium must exist in which these vibrations are to propagate, namely, a medium having the properties of the geocentrist's firmament. Because the geocentric firmament's fundamental ultramassive particles are packed as tight as atoms within a crystal, it serves as the ideal lattice structure for a phonon-based theory of particle structure to succeed.
The notion of space being some kind of crystal (in harmony with the geocentric and Biblical views of the firmament) is a topic of serious discussion in modern physics. Holland and Philippidis have explored the idea in their article, "Anholonomic Deformations in the Ether: A Significance for the Electrodynamic Potentials," (Hiley & Peat, eds., Quantum implications, --1987 Routledge, pgs. 295ff). They write, "In attempting to discover the classical significance of the Am [electromagnetic potential & MGS] we have at our disposal several clues. Bohm has suggested an analogy between the Aharonov-Bohm effect and the dislocation of a crystal lattice... Dirac showed how an ether which at each point has a distribution of velocities which are all equally probable would be consistent with relativity, and alternative approaches to the quantum theory by Bohm and Vigier have indicated that a suitably fluctuating ether can contribute to an understanding of the microdomain. We recall that much effort was expended in the nineteenth century in trying to understand electromagnetic processes in terms of stresses set up in an ether treated as an elastic solid."
Philippidis, Dewdney and Hiley pointed out that "as far as the quantum domain is concerned, space cannot be thought of simply as a neutral back cloth. It appears to be structured in a way that exerts constraints on whatever processes are embedded in it. More surpisingly still, this structure arises out of the very objects on which it acts and the minutest change in any of the properties of the contributing objects may result in dramatic changes in the quantum potential... it is clear, therefore, that the quantum potential is unlike any other field employed in physics. Its globalness and homogeneity in the sense of not being separable into well-defined source and field points indicate that it calls for a different conceptual framework for its assimilation." ("Quantum Interference and the Quantum Potential," Il Nuovo Cimento, Vol. 52B, No. 1, July 11, 1979).
The firmament of the geocentrists is explored under the name of the quantum potential by some, and by different names by other researchers. G. Gaeta, writing in Physics Letters A 175 (1993), pgs. 267-268, wrote of an "unknown medium originating" the observed quantum Brownian noise. Says he, "If we accept this picture, the particles of the EPR experiment are in permanent contact with a NGV stochastic process." This functional synonym for the geocentrist's firmament is named after the scientists whose constraints color its characterization, Nelson, Garbaczewski and Vigier. Gaeta treats this medium as completely universal: "The universality of quantum mechanics corresponds to the universality of the NGV process: this means that no physical system or particle can be regarded as truly isolated, as every physical system or particle 'being subject to quantum mechanics' is at least in contact with the universal NGV process."
The concluding paragraph in the article, "Causal Particle Trajectories and the Interpretation of Quantum Mechanics" (Quantum Implications, pgs. 169-201) exposes the dilemma for modern physics in telling language: "The interpretation of Bohr and of de Broglie-Bohm-Vigier both emphasize that the fundamentally new feature exhibited by quantum phenomena is a kind of wholeness completely foreign to the post-Aristotelean reductionist mechanism in which all of nature in the final analysis consists simly of separate and independently existing parts whose motions, determined by a few fundamental forces of interaction, are sufficient to account for all phenomena. The difference arises in the methods for dealing with the situation. One thing however is clear; the organization of nature at the fundamental level is far more complex than mere mechanistic models can encompass. The ghost cannot be exorcised from the machine."
(2) The firmament itself provides for a complete gravitational theory based on the physics of shadowing and attenuation, yielding predictive results beyond those of conventional theory. By introducing the element of spin, and thus angular momentum, to the firmament subparticles, the antisymmetric properties of electromagnetic fields obtain, being construed as a transfer of angular momentum particle by particle and giving rise to the well-known perpendicularity of the electric and magnetic fields. In Dr. Bouw's model, the firmament even accounts for the strong nuclear force that holds protons and neutrons together in atomic nuclei: as two nucleons make actual contact, the shadowing effect goes asymptotic according to the known attentuation expression, and the total force is all inward, its magnitude characterized by the Yukawa potential. This model therefore is a nascent unified field theory, or what is now termed a GUT (Grand Unification Theory), that accounts for all available physical effects that can be measured by science, from gravitation, electromagnetism, strong nuclear force, the Uncertainty Principle, elementary particle structure, etc. In other words, the early work of developing a new dynamics is well underway, as propounded at the outset.
The third and fourth developments are recent, homespun insights not heretofore published, and therefore not yet subjected to peer review. Although potentially premature, the benefit from airing them outweighs the risk; I invite the reader to weigh the following notions carefully.
(3) It is often objected that if geocentricity were true, and the rotating heavens were dragging Foucault pendula and weather systems around, why doesn't that force pull on the earth itself and drag it along, causing it to eventually rotate in sync with the heavens? It appears that this straightforward application of torque to the earth should cause it to rotate in turn, but this turns out to be an oversimplification. As the heavens rotate, and the firmament rotates on an axis through the earth's poles, each firmamental particle (the ones comprising the ultradense lattice) also rotates with the same angular velocity. Ironically, this is precisely the reason the earth can't be moved. In MT&W's Gravitation, pg. 1119-1120, we are invited to ponder the following scenario: "Consider a rotating, solid sphere immersed in a viscous fluid. As it rotates, the sphere will drag the fluid along with it. At various points in the fluid, set down little rods, and watch how the fluid rotates as it flows past. Near the poles the fluid will clearly rotate the rods in the same direction as the sphere rotates. But near the equator, because the fluid is dragged more rapidly at small radii than at large, the end of a rod closest to the sphere is dragged by the fluid more rapidly than the far end of the rod. Consequently, the rod rotates in the direction opposite to the rotation of the sphere. This analogy can be made mathematically rigorous." Now reverse the situation. If we want to cause the sphere to rotate clockwise, we would need to turn the rods at the poles clockwise, and the ones at the equators counterclockwise. (Consider the equator as a big gear, and the firmamental particles as small gears that engage it. It is intuitively obvious that the small gears must always turn in contrary motion to the large one at the equator.) This picture is clear then: to turn the sphere, the rotation of the particles (MT&W's "rods" and this author's "gears") at the poles must be the opposite of that at the equator.
However, in the case of a rotating firmament, all the particles are rotating in the same direction, with the angular velocity common to the entire firmament. The equatorial inertial drag is in the opposite direction as that acting near the poles. Using calculus, one integrates the effect from the center of the Earth outward in infinitesimal shells, showing that the Earth is in fact locked in place, the resulting inertial shear being distributed throughout the Earth's internal volume. It could be demonstrated that were the Earth to be pushed out of its "station keeping" position, the uneven force distribution would return it to its equilibrium state. Intriguingly, the significance of these internal forces on seismic stress, plate tectonics, and the earth's magnetic field may prove central, if so be that these postulates survive the inevitable peer review to come.
(4) Consider again Grøn & Eriksen's position that a rotating cosmic mass imposes an upward force on a geostationary satellite. (They used the Earth as a synchronous satellite for the Moon in their article to illustrate the principle.) They posit that the centrifugal force on the satellite arises from a cosmic non-tidal gravitational field pulling up on the satellite. Consider, then, the behavior of light traveling to the Earth from distant celestial objects: would it not also be subject to the effects of this cosmic nontidal inertial pull? Logic would dictate that, yes, in accordance with the late Dr. Richard Feynman's Lectures in Physics, Vol. 2, pgs. 42-10 & 42-11, as well as the extended discussion in MT&W's Gravitation, pgs. 1055-1060, incoming light subject to the induced gravitational field will lose energy and thus decrease in frequency, according to the known relations that govern calculation of gravitational red shifts.
If true, then the rotation of the cosmic mass could be responsible for the red shift heretofore understood as a Doppler consequence of the Big Bang. This in turn would provide a new basis for measuring the distance of celestial objects, one wholly different than the system erected upon the Doppler view of the red shift, which could involve a significant remapping of the heavens.
But more intriguingly, this result, if confirmed, would be hostile to general relativity, because the theory would require the red shift to be observed whether it is the Earth or the heavens that are rotating, whereas on classical grounds it would only be expected if the heavens were rotating, and the result would be the same whether measured from the Earth, from a satellite, or from the space shuttle. At this point in time, the experimental evidence militates against relativity on this effect, so that relativity would either need to neutralize the red shift predicted under a rotating cosmos scenario, or abandon its core postulate.
It would then appear that geocentrists are more than willing to risk making scientific predictions to put their hypotheses to the test. Some have already passed muster, but others are too recent to have gone through the requisite shaking-out period. This is to be expected in the infancy of the development of a new dynamical theory that embraces every aspect of reality, from unthinkably massive and immense objects to the world of the ultramicroscopic reality underlying the atomic realm.
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