Solomon, in Ecclesiastes 10:10, writes: “If the iron be blunt, and he do not whet the edge, then must he put to more strength: but wisdom is profitable to direct”. This thought is introduced in verse 5 where Solomon states, “There is an evil which I have seen under the sun, as an error which proceedeth from the ruler.” I agree with Solomon, I prefer spiritual biblical wisdom over the philosophers, including William of Occam. Our rulers have set folly (vs. 6) by building all science upon the erroneous foundation of the Copernican revolution.

William of Occam (1280?-1349) was born at Occam England. He was a Franciscan and rigorously adhered to the simple life of the founder, Francis of Assisi (1181-1226). He strongly opposed the temporal and spiritual aggrandizements of the papacy, and was jailed for the same. He was a party to confraternities such as the Lollards (Wycliffe 14th century) and the Brethren of Common Life which influenced the Reformation through such as William Tyndal and Erasmus (ca. 1510) (See T.M. Lindsay, “Occam and His Connexion with The Reformation”, British Quarterly Review, July 1872). It seems that Occam is best known to us now by what has come to be known as Occam's Razor. Occam was a logician of great reputation and wrote extensively on this subject. Occam's Phrase in Latin was, “Essentia non stunt multiplicanda praeter necessitatem” which, in the original Oxford English Dictionary under ”Razor,” is given by: “that for purposes of explanation things not known to exist should not, unless it is absolutely necessary, be postulated as existing.” It would seem that Occam would have his razor cut away unneeded hypotheses. In the hands of present day relativistic atheistic evolutionary science this has become; that which is true has the simplest explanation; and we have the assured word of modern scientist on what is simplest. I have empathy for Occam but will have no truck with science's use of his razor. What scientist choose to call “simplest” is more often hopelessly complicated being fraught with paradoxes, contradictions and unexplainables, whereas they claim the opposite for those theories they hold out of favor. A prime example of this is the Ptolemiac geocentric explanation of planetary orbits versus celestial mechanical mathematical heliocentric explanation.

The latter is heralded as a paragon of simplicity and the former as being overwhelmingly complicated. Nothing could be further from fact, I could teach a 10 year old to appreciate and understand Ptolemy, but, in years of teaching mathematics and celestial mechanics in the University, rare was the student who truly comprehended the derivations of planetary orbits as found, for example, in Brouwer and Clemence's Celestial Mechanics (Academic Press, 1961). The historical development of planetary orbit theory is usually traced through the models of Ptolemy (Claudius Ptolemaeus, 85-165 A.D) Tycho Brahe (1546-1601), Johann Kepler (1571-1630) and Isaac Newton (1642-1727).

The Ptolemiac model is kinematic, i.e. the orbits are described without any regard to their cause. It utilizes the geometry of circles whereby a planet moves around a circle of a certain radius and that circle's center moves around another circle of a given radius, etc., so that given enough such circular motion superpositions the planetary orbit can be described to within the limit of observational accuracy. This method of epicycles has the modern algebraic-trigonometric representation known as Fourier analysis. This method uses actual past data to extrapolate into future predictions and can very accurately predict planetary orbits including small deviations (perturbations) that the mathematical celestial mechanics might miss. In fact, this is, in the final analysis, the method used to prepare the planetary Almanacs and Ephemerides used for navigation. Theory is no substitute for actual data. Fred Hoyle in his Astronomy (Doubleday, 1962) provides an appendix demonstrating the equivalence of Fourier analysis to planetary orbits for the elliptical orbit example. Copernicus (1473-1543) in his treatise, De Revolutionibus Orbium Coelestium on planetary orbits retained epicycles. Copernicus' heliocentric epicycles did not improve the accuracy beyond that of Ptolemiac geocentric epicycles (Owen Gingerich, “The Eye of Heaven, Ptolemy, Copernicus, Kepler”, Am. Inst. Physics, 1993, especially p 171).

The Tychonian model is likewise kinematical and preserves the method of epicycles, but has all the planets revolving about the sun and the sun revolving around the stationary earth. Tycho's model was more than a method of calculation, whereby Tycho proposed a model of reality as opposed to a model which might be real but was more important as a artifice of computation and prediction. Tycho sought, with his model, geocentric counter arguments against Copernicus' many speculations in his “Orbits” on behalf of heliocentricity.

The Keplerian model was a departure from those of Ptolemy, Copernicus and Tycho in that they were all kinematical and all used epicycles. Kepler, using Tycho's excellent data deduced algebraic expressions for planetary orbits. Kepler's three laws were 1) That all the planets traveled in ellipses about the sun with the sun at the focus of the ellipse. 2) that the square of the orbital period was proportional to the cube of the elliptical major (longer) axis, and 3) that if one draws a radius from the sun to the planet then this radius sweeps at equal areas in equal times. These three laws would be exact and sufficient to compute planetary orbits if, in fact, they were elliptical orbits. But they are not, although for sufficiently short periods of time they very nearly are. Therefore Kepler did not supplant geocentric epicycles. The algebraic manipulations needed to employ Kepler's laws for determining orbital positions would be enormous, I wonder if anybody attempted it before Newton's time. It was still simpler to use Ptolemiac epicycles even if Kepler' s laws had been exact.

Tycho believed the Bible including its cosmology, i.e. geocentricity, whereas his student and assistant Kepler succumbed to Copernicus' theories. However, Kepler was probably a Christian. I have read thousands of pages about and by Newton from which I conclude that he was a Christian, despite the many volumes alleging him to be otherwise! Newton held to a universal flood, a creation at about 4000 B.C., the Trinity, and, it would seem, did not contend against geocentricity. He used heliocentricity, just as I would, but I can not find where he championed Copernicanism. In his correspondences we find letters discussing geocentricity in an attentive manner, nor do I know of his opposing Giovanni (Jacques) Cassini over this matter although he contested Cassini's model for the Earth's shape (oblate vs. prolate spheroid).

Let us examine Newton's derivation of planetary orbits (i.e. Kepler's laws and additional results). 1) One needs the concepts of force and motion as embodied in Newton's Laws, of motion. This requires numerous esoteric assumptions regarding space, time, mater and interim, e.g. see Bishop Berkeley's opposition to Newton on the matter of absolute space. See how simple it is, and we are only on the first point. 2) Units and means of defining them must be established e.g. what is mass (Maxwell under “Matter” in the 9th ed. of the Encyclopedia Britanica gave up on trying to define it) and how do we measure it? The same applies to time, velocity, acceleration and force. Not one in 10,000 students upon studying classical physics has a clue what his textbook is saying about force, nor does the author. It's getting “simpler” isn't it? 3) Now that one has the tools of units, measurement and the ability to express dynamics, the particular force of gravity must be quantitatively determined. Newton did this with his famous inverse-square law, F=GmM/r² In this formula F is the force of gravity between two point masses of mass m and M and separated by distance r. We have more “simplicity” here in the mind boggling non-existent paradox producing notion of point masses, i.e. having no extension. Ptolemy is looking better and better, he used simple, and I mean simple, geometrical constructs, circles not metaphysical unrealizable such as point masses. Further, if r becomes very small, approaches zero, then the force F becomes infinite. I know of no physical infinite quantities, God spares us from experiencing such. Then we have the fudge factor G which science has not been able to measure with accuracy from Newton's time until this very time (e.g. see Science, vol. 208, p 640 May 1995). That's more simplicity.

Let's get more “simplicity.” 4) Having tacitly agreed upon points 1,2 and 3 one must mathematical embody them in some sort of equation i.e. something to solve whose solution is a planetary orbit. The thing that one solves is a differential equation. So now one must involve the differential and integral calculus, and in doing so all the assumptions that go along with it; using infinitessimals, the notion of functions, concept of continuity of a function, the limit of a function and other very difficult mathematical concepts. The fundamental concept here is continuity and this requires the invocation of the Axiom of Choice which leads to so many paradoxes (euphemisms for mistakes and wrong answers) that it renders mathematics the most experimental of experimental sciences (see M. Kline's Mathematics, The Loss of Certainty, Oxford U. Press, 1980). Liebnitz even accused Newton of conjuring “occult quantities” when in the exposition of his calculus (fluxions) Newton used infinitessimals. Newton, and Liebnitz, were not aware of 20th century paradoxes surrounding the use of infinitessimals, but nevertheless, Newton did not use them in Mathematical Principles of Natural Philosophy 1687, when he gave his solution for planetary orbits. Instead he used the Euclidean geometry known to Ptolemy thus avoiding some of the vagaries of the calculus and the quagmire of algebra when applied to geometry. I.E. he avoided analytic geometry, for good reasons (try proving Merely' s equi lateral triangle theorem algebraically).

As you can see “simplicity” abounds. 5) We next need the machinery to solve this differential equation which is written as d²r/dt2= -Gmr/(r•r)^3/2 where now r is vector radius from the sun of mass M to the earth (oh, by the way, you must also know vector analysis). Solving differential equations is a very difficult thing and solving this one takes great ingenuity, requiring enormous algebraic skill. Also note that the mass of the sun must be known, or at least the value of the product G times M. a number whose value is still in dispute. 6) The solution results in a sequence of algebraic-Trigonometric expressions (including Kepler's Laws) whose numerical evaluation is quite difficult. This evaluation requires a knowledge of numerical analysis. As a measure of the ”simplicity” of the Newtonian model for planetary orbits consider that the minimum number of prerequisite courses needed for a course in which the above equation is solved might include courses in physics, vector analysis, numerical analysis, differential equations and a 3 or 4 course sequence in calculus. 7) The above equation only yields the solution for the two-body problem, but in fact the situation is vastly complicated by the gravitational influences of the other planets as well as other perturbations. The mathematics and subsequent numerical evaluation now becomes a thousand-fold more complicated.

Let us recapitulate. In order to understand Ptolemy' s model one must be able to picture circles moving upon circles. This anybody can do. However in order to understand the Newtonian explanation one must understand the use of and assumptions embodied in:

1) Newton's Laws of motion
2) the quantities of mass, time and space and their units
3) the Law of gravity
4) the calculus
5) differential equation's
6) numerical analysis
7) the theory of perturbations