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Mathematical probability is the fractional concentration of an element in a logical set. The word, probability, has the aura of the rationality of mathematics. Its synonym, chance, connotes a lack of rationale. The perfect deal is defined as four hands, each a flush of thirteen cards. Its probability is its fractional concentration and equals the probability of every other variant four-hand deal, namely one divided by the total number of variant four-hand deals. The probability is 4.474 x 10^(-28).

The following is an excerpt from the essay, “What is modern in the new atheism? – the inference of probability”, which was printed in the Delta Epsilon Sigma Journal, Volumes LVII Issue 2 (2012) and LVIII Issue 1 (2013). Links to the pdf files of the entire journal issues are:
http://deltaepsilonsigma.org/media/delta-epsilon-sigma/1DES_Journal_FALL12F.pdf
http://deltaepsilonsigma.org/media/delta-epsilon-sigma/Volume-LVIII-Spring2013-Number1.pdf

Imposing an arbitrary extra-mathematical numerical limit on probability

This brings us to the most common error shared not only by Dawkins and his critics, but by many others. It is a variant of the argument of ‘the perfect deal’, which, due to its low probability, cannot be explained by chance. The argument goes by many names. Dawkins calls it ‘the problem of improbability’, by which he claims that the improbability of evolution in a one-off event is ‘far beyond the reach of chance’. The argument is that of ‘irreducible complexity’. Most complexities are explained by mathematical probability, but not those of a probability close to zero. The argument is also called the anthropic argument. In this form the argument claims that the combined probability of the various factors necessary for life on earth is so close to zero that the combination of factors cannot be due to chance.

The argument is based on the distinction between the connotations of the synonyms, chance and probability. Its general form is: The probability of this outcome is so close to zero that this outcome cannot be due to chance. The argument implies that chance is some numerical limit imposed from outside the mathematics of probability.

The argument is a mathematical self-contradiction. It states that the fractional concentration of this element in this set is so close to zero that it cannot be the fractional concentration of this element in this set. The problem of improbability, under whatever name, is a fiction. Dawkins’ thesis in The God Delusion is that there is no solution to the fictitious problem of the improbability of God, whereas Darwin’s theory solves the fictitious problem of the improbability of evolution in a one-off event.

It is a fiction. There is no finite limit to the number of elements in a set. Consequently, there is neither a positive lower limit greater than zero for the fractional concentration of a specific element in a set nor an upper limit less than one for improbability. For a set of n unique elements, the probability, 1/n, cannot be too close to zero to be a valid probability, nor can the improbability, 1 – (1/n), be too close to one. All numerical values of probability are of equal validity, irrespective of how close they are to zero.

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The recognition that geocentrism is false is so nearly universal, that modern belief in it is viewed as iconic ignorance, if not stupidity. Witness the following recent, casual citations: (1) “Deep down in my heart of hearts, I might feel that the sun revolves around the earth…but before I start announcing this as a truth about the way the universe works, I should go ahead and examine the evidence to see if it is actually true. It is this kind of never-wavering requirement for proof that allows us to have a clear-eyed look at the universe.” (http://www.strangenotions.com/on-proving-god/) and (2) scoffing at “the (alleged) NASA plot to cover up geocentrism” (http://www.ncregister.com/blog/mark-shea/latest-real-jesus-shakes-christianity-to-its-very-foundations)

Geocentrism is not false because heliocentrism is true. Rather geocentrism is false because heliocentrism is false.

The Michelson-Morley experiment demonstrated that there is no absolute reference frame for motion. If the earth were moving with respect to an absolute reference frame, then the speed of light should depend upon direction. However, the experiment demonstrated that the speed of light is a constant, independent of direction. Notice that the correct inference is not that the earth is stationary with respect to an absolute reference frame, but that there is no absolute reference frame.

Consider the statement: The earth orbits the sun and not vice versa. That the earth orbits the sun is a statement affirming the heliocentric depiction of the relative motion of the earth and the sun. However, ‘and not vice versa’ is the affirmation of heliocentrism. In heliocentrism, the depiction is taken as absolute, excluding as false all other possible depictions. However, the relative motion of the sun and the planets can be accurately and interdependently depicted as heliocentric, geocentric as well as saturnocentric. Each depiction is compatible with and interdependent upon the others. The others must be valid for any one to be valid. To affirm any one of these depictions as absolute and thereby excluding the others as false is respectively, heliocentrism, geocentrism and saturnocentrism.

Any reference frame in analytical geometry is compatible with every other such reference frame. Reference frames in analytical geometry are linearly related to one another. Consequently, the choice of a reference frame does not affect the degree of any equation of physics. The following two illustrations should be intuitively convincing that reference frames are interchangeable.

Consider the perspective of an observer on the ground at an air show and the perspective of a pilot, who dives his craft toward the earth and pulls out of the dive. That depiction is in accord with the observer on the ground and in accord with the depiction of his motion in the pilot’s own mind. However, the motion observed by the pilot is the earth’s surface coming at him and then the earth’s surface receding. Both the land and the aircraft based motions are valid as observations and as depictions. They are compatible. The affirmation of one does not falsify the other. The affirmation of each depiction affirms the other.

Let a bicycle be ridden around the oval of a stadium. One recording camera is mounted on the bicycle frame facing the stands. Another is mounted on the rotating hub of the front wheel, facing the stands. A third camera is in the stands with a scope of the entire oval. Which record of the motion is actually true? Given the record of either the frame camera or the hub camera, one could figure out what a record of the motion would be like from the perspective of a camera in the stands. In other words, only if the stadium is moving about the bike, can it be true that the bike is moving around the oval of the stadium. In fact all three records of the motion must be true depictions of the motion for each and every one of them to be a true depiction of the motion.

The Michelson-Morley experiment demonstrated that there is no absolute reference frame for motion. Only if the sun moves around the rotating earth in a year can it be true that the rotating earth orbits the sun in a year.

The question of the earth orbiting the sun ‘or’ vice versa is not a question of what is really true, but a question of the utility of the depiction. If it were a question of what is really true, then the prevailing wisdom must label as false the listing of the times of daily sunrise and sunset. These times reference the location of the sun to the earth. In the prevailing wisdom the earth must be located with reference to the sun, not vice versa.

Galileo was not an advocate of the beauty, simplicity and utility of the Copernican heliocentric depiction of motion. Rather, he was an advocate of heliocentrism. The advocacy of heliocentrism is as ignorant and as stupid as the advocacy of geocentrism, although in Galileo’s time this may not have been so readily apparent. However, today we have no excuse for accepting heliocentrism as really true, but for the effectiveness of the propaganda falsely positing exclusivity.

The depiction of the relative motion of the sun and its planets as heliocentric and observed from a virtual observation point outside of the solar system is inferred from geocentric observation. The geocentric depiction as observed from a virtual observation point outside of the solar system would be fully compatible with the heliocentric depiction. Both are inferred from the same set of geocentric observations. It is exclusivity which renders heliocentrism vs. geocentrism nonsensical.