OCCAM'S RAZOR IN THE HANDS OF
COPERNICANS, A BLUNT INSTRUMENT
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 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 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
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 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 As you can see “simplicity” abounds. 5) We next need the machinery
to solve this differential equation which is written as d 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 motionI believe that Occam and Newton might agree that the Ptolemy model satisfies Occam's razor while the Celestial mechanical fails in the extreme. Science always invokes Occam's razor to prove such bizarre complicated patchwork humanistic theories such as evolution and relativity. |