by Bruce Director

The foolishness of relying on pure mathematical models for the design and production of automobiles, nuclear weapons, or any other physical device, would be obvious to anyone with a minimal level of knowledge of the discoveries of Cusa, Kepler, Leibniz, Gauss, Riemann, et al. Unfortunately, such knowledge is virtually non-existent among the leaders of governments and businesses, today, as the frauds of the Mercedes A-class and the Cox report amply demonstrate. Fortunately, those who study the writings of Lyndon LaRouche need not suffer the afflictions of the aforementioned Lilliputians.

Take the case of Kepler's discovery of the physical characteristics of planetary motion enunciated in his New Astronomy. As we demonstrate below, through their own words, Kepler demolished, nearly 400 years ago, the mathematical modelers of his day.

In the introduction of that work Kepler states:

"The reader should be aware that there are two schools of thought among astronomers, one distinguished by its chief, Ptolemy and the assent of the large majority of the ancients, and the other attributed to more recent proponents, although it is the most ancient. The former treats the individual planets separately and assigns cause to the motions of each in its own orb, while the latter relates the planets to one another, and deduces from a single common cause those characteristics which are found to be common to their motions. The latter school is again subdivided. Copernicus, with Aristarchus or remotest antiquity, ascribes to the translational motion of our home, the earth, the cause of the planets appearing stationary and retrograde. Tycho Brahe, on the other hand, ascribes this cause to the sun, in whose vicinity he says the eccentric circles of all five planets are connected as if by a kind of knot (not physical, of course, but only quantitative). Further, he says that this knot, as it were, revolves about the motionless earth, along with the solar body.

For each of these three opinions concerning the world there are several other peculiarities which themselves also serve to distinguish these schools, but these peculiarities can each be easily altered and amended in such a way that, so far as astronomy, or the celestial appearances, are concerned, THE THREE OPINIONS ARE FOR PRACTICAL PURPOSES EQUIVALENT TO A HAIR'S BREADTH, AND PRODUCE THE SAME RESULT."

What Kepler is referring to is the fact that the observed motions of the stars, planets, sun, and moon, can be calculated equally by the three radically different mathematical models of Ptolemy, Copernicus, and Tycho Brahe.

The most elementary observations of the motions of heavenly bodies reveal two distinct motions. The so-called first motion, is the uniform daily movement across the sky of the sun, moon, stars, and planets from east to west. (Don't take my word for it though. Go out an look for yourself!) The so-called second motion, is movement from west to east of the planets, sun, and moon, with respect to the fixed stars, over longer periods of time. Upon careful observation, this second motion is seen to be non-uniform. The planets, moon, and sun move slower and faster at different stages in the second motion, and, the planets, at times appear to stop and move backward with respect to the stars, at different stages in the course of the second motion.

The observation of these two motions is not the stuff of casual sense experience, but a characteristic of human reason. In the first chapter of the New Astronomy, Kepler says:

"The testimony of the ages confirms that the motions of the planets are orbicular. It is an immediate presumption of reason, reflected in experience, that their gyrations are perfect circles. For among figures it is circles, and among bodies the heavens, that are considered the most perfect. However, when experience is seen to teach something different to those who pay careful attention, namely, that the planets deviate from a simple circular pattern, it gives rise to a powerful sense of wonder, which at length drives men to look into causes."

Neither Ptolemy, Copernicus, nor Tycho Brahe, however, ever laid claim to that "powerful sense of wonder," of which Kepler speaks.

In the opening of the Almagast, Ptolemy says, "Those who have been true philosophers, Syrus, seem to me to have very wisely separated the theoretical part of philosophy from the practical.... For indeed Aristotle quite properly divides also the theoretical into three immediate genera; the physical, the mathematical, and the theological."

Ptolemy goes on to say that man can know nothing certain of the theological nor physical:

"The theological because it is in no way phenomenal and attainable, but the physical because its matter is unstable and obscure, so that for this reason philosophers could never hope to agree on them; and meditating that only the mathematical, if approached enquiringly, would give its practitioners certain and trustworthy knowledge with demonstration both arithmetic and geometric resulting from indisputable procedures, we were led to cultivate most particularly as far as lay in our power this theoretical discipline."

Having dispensed with any pretense that his theory had any physical reality, Ptolemy developed his now infamous system of intricate earth-centered cycles, eccentrics, and epicylces to mathematically calculate the positions of the planets, stars, moon, and sun, over time. While Ptolemy's system can truthfully be called a fraud, the bigger frauds are those, who until this day, propounded this mathematical system, as physical hypothesis.

Copernicus replaced Ptolemy's complicated system, with the simpler and more beautiful sun-centered system, where the earth and the planets move in perfect circles about a stationary sun. Nevertheless, this was a purely mathematical model. In the Introduction to his "On the Revolutions of the Heavenly Spheres," Copernicus says:

"For it is the job of the astronomer to use painstaking and skilled observation in gathering together the history of the celestial movements, and then -- since he cannot by any line of reasoning reach the true causes of these movements -- to think up or construct whatever causes of hypotheses he pleases such that, by the assumption of these causes, those same movements can be calculated from the principles of geometry for the past and for the future. This artist is markedly outstanding in both of these respects; for it is not necessary that these hypotheses should be true, or even probable; but it is enough if they provide a calculus which fits the observations...."

As Kepler describes above, Tycho Brahe's mathematical model had all the planets revolving around the sun, and this knot moving around a stationary Earth. But as Kepler says, Brahe's system is not physical, but merely quantitative.

Since the systems of Ptolemy, Copernicus, and Brahe are all mathematically equivalent, and none lay claim to any physical reality, how can one distinguish which one is true? Only in the domain of physical measurement. This is precisely the revolutionary discovery that Kepler makes, following the path laid out by his mentor, Nicholas of Cusa.

Again, in the Introduction of the New Astronomy Kepler continues:

"My aim in the present work is chiefly to reform astronomical theory (especially of the motion of Mars) in all three forms of hypotheses, so that our computations from the tables correspond to the celestial phenomena. Hitherto, it has not been possible to do this with sufficient certainty. In fact, in August 1608, Mars was a little less than four degrees beyond the position given by calculation from the Prutenic tables. In August and September of 1593 this error was a little less than five degrees, while in my new calculation the error is entirely suppressed.

"... The eventual result of this consideration is the formulation of very clear arguments showing that only Copernicus's opinion concerning the world (with a few small changes) is true, that the other two accounts are false, and so on.

"Indeed, all things are so interconnected, involved, and intertwined with one another that after trying many different approaches to the reform of astronomical calculations, some well trodden by the ancients and others constructed in emulation of them and by their example, none other could succeed than the one founded upon motions' physical causes themselves, which I establish in this work."

Readers of previous pedagogical discussions, and the Fidelio article on Gauss' determination of the orbit of Ceres for will know something of Kepler's discoveries. Isn't it time we raised the level of thinking of the citizenry, so that they would demand such knowledge of their elected officials and designers of automobiles?

by Bruce Director

Several weeks ago we presented, in their own words, a demonstration that Kepler's determination of the principles of planetary motion, demolished the Aristotelian methods of "mathematical modeling," adhered to by Ptolemy, Brahe, and Copernicus. This week, we follow up with a further consequence of that demonstration: that all subsequent scientific inquiry that did not follow Kepler's method was not just wrong, but fraudulent.

As presented in the previous discussion, Kepler, in the "New Astronomy," set out to completely revolutionize astronomy (and all science) by putting it on a foundation of physical principles. As they testified themselves, Ptolemy, Copernicus, and Brahe were concerned only with developing formal descriptions of the observed motions of the planets. Truthfulness was limited to the logical-deductive consistency of those descriptions, and the consistency of those descriptions with observations. As Kepler stated, all three descriptions were equivalent "within a hair's breadth," but all three deviated from the observations by an amount greater than the margin of error associated with the capacity of the measuring instruments used for those observations.

The specific observed phenomena that concerned Kepler, Ptolemy, Brahe, and Copernicus, were the two unequal motions of the planets, observed by humankind since ancient times.

The first "inequality" was the observed non-uniform motion of the planets, in a cycle, from west to east, through the constellations of the zodiac. Each planet made this circuit in different lengths of time, and, as each travelled through its cycle, it appeared to move faster through certain constellations than others, that is, traversing a greater angular arc in the sky for a given time interval, depending on which constellation of the zodiac it was moving through.

The second "inequality" was the so-called "retrograde" motion, when the planet appeared to move from east to west through the zodiac. This was observed when the planet was rising in the east just as the sun set in the west. This configuration was known as "opposition."

Ptolemy, Copernicus, and Brahe all described these phenomena with radically different geometrical constructions, but all held firm to the belief that these apparent non-uniform motions, were just that; "apparent," not real. All three believed that the "true" motion of the planet had to be uniform circular motion. The two "inequalities" were simply optical illusions, owing to the complicated concoction of circles, that each had created.

Kepler took an entirely different approach:

"The testimony of the ages confirms that the motions of the planets are orbicular. It is an immediate presumption of reason, reflected in experience, that their gyrations are perfect circles. For among figures it is circles, and among bodies the heavens, that are considered the most perfect. However, when experience is seen to teach something different to those who pay careful attention, namely, that the planets deviate from simple circular path, it gives rise to a powerful sense of wonder, which at length drives men to look into causes."

Driven by this "powerful sense of wonder," Kepler looked into the causes. First he established the equality of the Ptolemaic, Brahean, and Copernican models. Then Kepler abandoned the false belief of embedded in all three models, that the "true" motion was uniform circular motion, and the non-uniform motion was simply apparent. Instead, Kepler took the apparent motion as the true. That is, that the planets actually did move non-uniformly. Once this conceptual bridge had been crossed, the geometrical construction of the planets moving on an orbit, about an eccentric and sweeping out equal areas in equal times, proceeded from the physical measurements themselves. The power that moved the planet, according to Kepler, had to be located at that eccentric.

Under this conception, the planet's distance from the eccentric about which it was moving, varied continuously. That is, as the planet moved about it's orbit, the distance from the planet to the eccentric was always getting longer or shorter, and consequently, the effect of the moving power was increasing as the distance decreased and diminishing as the distance increased. Then Kepler demonstrated that the moving power resided in the Sun, which was located at the eccentric point. When this conception was again tested against the physical measurements, Kepler refined his construction to an elliptical orbit with the Sun located at one of the foci. Later, Kepler demonstrated a third principle of planetary motion between the periodic times and the size of the orbit, mischaracterized today as his "Third Law." (The reader can consult chapter's 5-8 in the Summer 1998 Fidelio article on how Gauss Determined the Orbit of Ceres).

How absolutely banal, sterile, and fraudulent, is therefore, Newton's resort to action at a distance according to the inverse square law. This is ass backwards. For Newton, the planetary motion is reduced to a copulation along the straight line connecting the planet to the Sun. The physical space time curvature of Kepler is eliminated. Only straight-line copulation remains.

So fraudulent is Newton's view, that according to Riemann:

"Newton says: `That gravity should be innate, inherent, and essential to matter, so that one body can act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.' See the third letter to Bently."

Yet people continue to adhere to the false beliefs that underlie Ptolemy and Newton. With their asses facing the students, professors throughout the world present Newton's straight-line copulation as the basis for planetary motion, despite the final burial of Newton by Gauss with his discovery of the orbit of Ceres. In his {Theoria Motus} Gauss says:

"The laws above stated differ from those discovered by our own Kepler in no other respect than this, that they are given in a form applicable to all kinds of conic sections ... If we regard these laws as phenomena derived from innumerable and indubitable observations, geometry shows what action ought in consequence to be exerted upon bodies moving about the sun in order that these phenomena may be continually produced. In this way it is found that the action of the sun upon the bodies moving about it is exerted {as if} an attractive force, the intensity of which is reciprocally proportional to the square of the distance should urge the bodies towards the center of the sun. (emphasis supplied.)

Turn again to Kepler from the introduction of the {Mysterium Cosmographicum}:

"Though why is it necessary to reckon the value of divine things in cash like victuals? Or what use, I ask, is knowledge of the things of Nature to a hungry belly, what use is the whole of the rest of astronomy? Yet men of sense do not listen to the barbarism which clamors for these studies to be abandoned on that account. We accept painters, who delight our eyes, musicians, who delight our ears, though they bring no profit to our business. And the pleasure which is drawn from the work of each of these is considered not only civilized, but even honorable. Then how uncivilized, how foolish, to grudge the mind its own honorable pleasure, and not the eyes and ears. It is a denial of the nature of things to deny these recreations. For would that excellent Creator, who has introduced nothing into Nature without thoroughly foreseeing not only its necessity but its beauty and power to delight, have left only the mind of Man, the lord of all Nature made in his own image, without any delight? Rather, as we do not ask what hope of gain makes a little bird warble, since we know that it takes delight in singing because it is for that very singing that the bird was made, so there is no need to ask why the human mind undertakes such toil in seeking out these secrets of the heavens. For the reason why the mind was joined to the senses by our Maker is not only so that man should maintain himself, which many species of living things can do far more cleverly with the aid of even an irrational mind, but also so that from those things which we perceive with our eyes to exist we should strive towards the causes of their being and becoming, although we should get nothing else useful from them. And just as other animals, and the human body, are sustained by food and drink, so the very spirit of Man, which is something distinct from Man, is nourished, is increased, and in sa sense grows up on this diet for these things. Therefore as by the providence of nature nourishment is never lacking for living things, wo we can say with justice that the reason why there is such great variety in things and treasuries so well concealed in the fabric of the heavens, is so that fresh nourishment should never be lacking for the human mind and it should never disdain it as stale, nor be inactive, but should have in this universe an inexhaustible workshop in which to busy itself."

by Bruce Director

After reading the past two pedagogical discussions on this subject, there should be no doubt in your mind that Newton was a fraud. The question remains: why does Newton work? Not, why do Newton's theories work -- they don't -- but why does the fraud work?

The populist conspiracy theorist, or anyone else prone to superficial thinking might conclude that the fraud works through the suppression of Kepler. True, many of Kepler's writings have been obscured over the ages, not widely published or translated, nor taught as original sources in secondary schools or universities. Nevertheless, they are available for any thinking person to obtain and study. Furthermore, the physical anomalies, from which the principles on which Kepler's discoveries are based can be observed any night by anybody from any where on Earth.

No! it is not a lack of information, that keeps the fraud of Newton alive. Nor is the fraud perpetrated by controlling the purse strings of professors and scientists, or the raw political power of the British Royal Society, although that certainly is an element. None of that explains why generation after generation, Newton's fraud is accepted willingly, to the point where victims of this fraud will hysterically defend it when challenged.

There is something more sinister involved, a vulnerability inside the mind of these wretched creatures that leads them to prefer the straight-line copulative world of Newton; to desire a world uncomplicated by the primacy of curvilinear action; and to yearn for a universe free of disturbing discontinuities.

To find this flaw, start with the report published in the May 31, 1999 briefing, quoting St. Augustine's report from his Confessions of how his friend was drawn, against his better judgement, into lusting for the savagery of the Roman Circus. This begins to approximate the mindset that draws the unsuspecting dupe into Newton's world.

Or, turn to the insightful allegory "Mellonta Tauta" of Edgar Allen Poe, whose protagonist reports:

"Do you know that it is not more than a thousand years ago, since the metaphysicians consented to relieve the people of the singular fancy that there existed but {two possible roads for the attainment of Truth!} Believe it if you can! It appears that long, long ago, in the night of Time, there lived a Turkish philosopher (or Hindoo possibly) called Aries Tottle. This person introduced, or at all events propagated what was termed the deductive or {a priori} mode of investigation. He started with what he maintained to be axioms or `self-evident truths,' and thence proceeded `logically' to results. His greatest disciples were one Neuclid and one Cant. Well, Aries Tottle flourished supreme until the advent of one Hog, surnamed the `Ettrick Shepherd,' who preached an entirely different system, which he called the {a posteriori} or {inductive}. His plan referred altogether to Sensation. He proceeded by observing, analyzing and classifying facts -- {instantiae naturae}, as they were affectedly called -- into general laws. Aries Tottle's mode, in a word, was based on {noumena}; Hog's on {phenomena}. Well, so great was the admiration excited by this latter system that, at its first introduction, Aries Tottle fell into disrepute; but finally he recovered ground, and was permitted to divide the realm of Truth with his more modern rival. The savants now maintained that the Aristotelian and Baconian roads were the sole possible avenues to knowledge. `Baconian,' you must know, was an adjective invented as equivalent to Hog-ian and more euphonious and dignified.

"Now, my dear friend, I do assure you, most positively, that I represent this matter fairly, on the soundest authority; and you can easily understand how a notion so absurd on its very face must have operated to retard the progress of all true knowledge -- which makes its advances almost invariably by intuitive bounds. The ancient idea confined investigation to {crawling} and for hundreds of years so great was the infatuation about Hog especially, that a virtual end was put to all thinking properly so called. No man dared utter a truth for which he felt himself indebted to his Soul alone. It mattered not whether the truth was even {demonstrably} a truth, for the bullet-headed {savants} of the time regarded only {the road} by which he had attained it. They would not even look at the end. `Let us see the means,' they cried, `the means!' If, upon investigation of the means, it was found to come neither under the category Aries (that is to say Ram) or under the category Hog, why then the {savants} went no farther, but pronounced the `theorist' a fool, and would have nothing to do with him or his truth....

"Now I do not complain of these ancients so much because their logic is, by their own showing, utterly baseless, worthless and fantastic altogether, as because of their pompous and imbecile proscription of all {other} roads of Truth, of all {other} means for its attainment than the two preposterous paths -- the one of creeping and the one of crawling -- to {which} they have dared to confine the Soul that loves nothing so well as to {soar}.

"By the by, my dear friend, do you not think it would have puzzled these ancient dogmaticians to have determined by {which} of their two roads it was that the most important and most sublime of {all} their truths was, in effect, attained? I mean the truth of Gravitation. Newton owed it to Kepler. Kepler admitted that his three laws were {guessed at} -- these three laws of all laws which led the great Inglitch mathematician to his principle, the basis of all physical principle -- to go behind which we must enter the Kingdom of Metaphysics. Kepler guessed -- that is to say, {imagined}. He was essentially a `theorist' -- that word now of so much sanctity, formerly an epithet of contempt. Would it not have puzzled these old moles, too, to have explained by which of the two `roads' a cryptographist unriddles a cryptograph of more than usual secrecy, or by which of the two roads Champollion directed mankind to those enduring and almost innumerable truths which resulted from his deciphering the Hieroglyphics?"

For the moment, no more need be said.