In the midst of the present turmoil of global politics that we find
ourselves facing today, Lyndon LaRouche issued the challenge of
animating the discoveries of Johannes Kepler, in order that we may come
to understand the fundamentals of physical economics, an understanding
necessary to facing this crisis with the sense of optimism and
authority that the crisis requires. This particular site is
dedicated to fostering a comprehensive work-through of Kepler’s
Harmonices Mundi, published in 1619. However, to achieve the most
of such a work it is important to know the process that led to that
work. The discovery is not to be found on the pages of that, or
any book, but rather, takes a great deal of concentration and can only
be relived by retracing Kepler’s footsteps for yourself. For as
Kepler himself wrote, “indeed, the occasions by which people come to
understand celestial things seem to me not much less marvelous as the
celestial things itself.”
Our journey seems to begin on July 9/19 1595, when the 23 year old
Kepler, while teaching, made the first of a profound series of
discoveries. Kepler fully elaborates this discovery in his
Mysterium Cosmographicum, published less than a year later and
dedicated to the 18 year old Archduke Ferdinand. 25 years later,
in the footnotes to the 2nd publication, Kepler emphasizes the point
that all his later achievements were already scattered in seed form
among those pages.
But this work also is the product of an epistemological tradition
that Kepler inherited from, most notably, the Pythagoreans, Plato, and
Nicolas of Cusa. This tradition informed all of Kepler’s life’s
works. And he indeed had no misgivings about passing that
tradition on to the reader in that first work.
As you plunge into the pages of the Mysterium, one of the first
things you encounter is a greeting. But in this greeting, Kepler
tells you that God’s intention in creating the universe is revealed to
you by Pythagoras with the five regular solids. A bold
statement? The question that might arise in your mind: What
exactly does this bold statement imply?
To begin to unfold the answer, Kepler tells you the basis of his
method of investigation. The appearance of the universe is the effect
of universal principles. Meanwhile, the appearances are not the
principles themselves. How then does one contemplate the universe
in all its splendor? As Kepler suggests, referencing Paul, “like
the Sun in water or in a mirror.” This method is the same as
described by Plato in the Socratic dialogues and it is further
discussed by Cusa, in his De Docta Ignorantia.
The starting point for Kepler then, as for any scientist, is the
idea that the Universe is constructed from principles and that mankind,
made in the image of the Creator, could rediscover those principles and
put them to use in perfecting that Universe.
'For it neither is nor was right’ (as
Cicero in his book on the universe quotes from Plato’s Timaeus) ‘that
he who is the best should make anything except the most beautiful.’
Since, then, the Creator conceived the Idea of the Universe in his mind
(we speak in human fashion, so that being men we may understand), and
it is the Idea of that which is prior, indeed, as has just been said,
of that which is best, so that the Form of the future creation may
itself be the best: it is evident that by those laws which God himself
in his goodness prescribes for himself, the only thing of which he
could adopt the Idea for establishing the universe is his own essence…..
This pattern, this Idea, he wished to imprint on the universe, so that
it should become as good and as fine as possible; and so that it might
become capable of accepting this Idea, he created quantity; and the
wisest of all Creators devised quantity so that their whole essence, so
to speak, depended on these two characteristics, straightness and
curvedness, of which curvedness was to represent God….For it must not
be supposed that these characteristics which are so appropriate for the
portrayal of God came into existence randomly, or that God did not have
precisely that in mind but created quantity in matter for different
reasons and with different intention, and that the contrast between
straight and curved, and the resemblance to God, came into existence
subsequently of their own accord, as if by accident.
It is more probable that at the beginning of all things it was with a
definite intention that the straight and the curved were chosen by God
to delineate the divinity of the Creator in the universe; and that it
was in order that those should come into being that quantities existed,
and that it was in order that quantity should have its place that first
of all matter was created.
Kepler, Mysterium cosmographicum
Beginning with this conception of the "best of all possible worlds"
is essential to any rigorous scientific work. That idea is not
only epistemological but, it is the basis for any sound ontology.
For, if the universe were not created according to the greatest wisdom,
how could it have been created at all?
Plato’s Timaeus dialogue is one of the oldest, if not the oldest,
documents that presents a comprehensive image of a self-sufficient
Universe with a unique Creator. From that starting point, the
dialogue elaborates how the nature of the Universe is derived from this
source, detailing the cosmos, musical harmony, geometric figures, human
nature, and the elements. So, it should come as no surprise that
the discovery Kepler is sharing in the Mysterium is a re-affirmation of
the method of the ancients. Later in his life, writing in the
Harmonices Mundi, Kepler hypothesizes that his discovery, that the
distances between the planets were determined by the five Platonic
Solids, may have already been known to the Pythagoreans, although they
may have tried to obscure that fact.
As was just stated, on July 9/19 1595 Kepler realized that according
to the Copernican data, which had to be reworked, the distances that
determined the planetary circuits, were themselves determined by
something else, which could not be directly seen in the heavens but
could be known to the mind of man. These are the solids called
the cube, tetrahedron, dodecahedron, icosahedron, and octahedron.
All of this is unfolded to the reader of the Mysterium Cosmographicum,
if they take the time to work it through.
However, ambiguity still manages to creep in, that is ambiguities
other than the questionability of the Copernican data. The
distances of the planets from the sun are not uniform around the orbit,
nor are the distances between the planetary orbits. So, maybe
Kepler was able to grab a hold of one aspect of what was determining
these distances, but what about this eccentricity? Besides that
question there is another. An observer at any location (whether on the
earth or on the sun or on Mars) can only measure changes in movements
in terms of angles. But if these occur at different distances,
how can we know the true movements of the planets? What is the
relationship of the motions to the distances? And why are the
planets moving at all?
These are questions that Kepler begins to wrestle with in the
concluding chapters of the Mysterium Cosmographicum. On the
question of the motion of the planets he conclusively refutes
Aristotle, who thought that the orbital periods are in direct
proportion to the distances of the planets assuming the speed of each
planet to be the same. But, why should the speeds of the planets
be the same? What cause would produce that effect? Does the
planet even keep the same motion within its own orbit?
Finally, in the 22nd Chapter, at the end of the Mysterium, Kepler
takes up the question of the motions, raising the issue of the equant,
and of the physical causes for these motions being derived from the
sun. He refers back to this chapter in Book 3 of the New
Astronomy and, in fact, one could argue that all of Book 3 of that work
came out of this chapter.
The Next Revolution
Once the Mysterium was completed, Kepler, devoted to seeking out the
truth, attempted to contact Tycho Brahe, whose observations were
unparalleled. They communicated through a series of letters from
1597 to 1600, when they finally met in person. In October of that year
Kepler came to live with Brahe, whose observations were being put
together for the Rudolphine Tables, a task that Kepler took the next 20
years to complete, after Brahe’s death in 1601.
Kepler, seeing that Brahe had made use of the mean motion of the
sun, as opposed to the truer apparent motion, which would have been
more appropriate for Keplers investigations, asked to make use of the
observations. Brahe and his aide were busy then studying the
oppositions of Mars to the Sun, and Kepler eagerly joined them.
This, he describes, turned out to be a ‘divine arrangement’ because the
motions of Mars “provide the only possible access to the secrets of
astronomy, without which we would remain forever ignorant of those
The motions of Mars presented a paradox, which Kepler seized
upon. The results of these investigations led to the development
of a whole New Astronomy, which he expounds in a book with the same
name, taking up the particular case of the motions of Mars. These
motions produce an effect that cannot be explained by the long held
dogma that the planet is moving around an equant along a perfectly
circular path. There arises a slight deviation that Kepler knew cannot be simply ascribed to observational error.
In the spirit of Cusa, Kepler applies the method of Learned
Ignorance. He first attempts to find the eccentricity of the circle
which would give the correct longitudinal positions of the planet at
the corresponding times, as dictated by the equant. In fact, he is so
rigorous with this approach, that he is able to determine an orbit, for
this purpose, more precise than anyone to date. But, if he were to
leave it at that, he would be no true scientist. And so, in the persuit
of truth, he makes another attempt at the eccentricity. This time, he
turns to the story told by the latitudes, which takes into acount
another factor, untouched by the longitudes, distance. Here, the
hypothesis breaks down. The eccentricity arrived at in this manner
hints at a hidden secret. If one were to combine the results of these
experiments, they may see, as Kepler did, that the error increases from
2' of arc to 8', an error that Kepler says, led the way to a revolution.
Therefore, since his prevoius attempt failed, he knew that the truth
must lay elsewhere. Being a man of reason, Kepler seeks out the
physical causes that produce the orbit as an effect. In other words,
the reason why the planet acts as it does.
As he had already stated in the Mysterium Cosmographicum, the source
of the planets' motions, he believed, must be the sun. As it spins it
emits what he refers to as an immaterial species throughout the Solar
System. This immaterial species moves the planets, according to its
strength, around the sun as the sun rotates. Borrowing the image
of a lever, Kepler argues that the strength of the immaterial specie
weakens proportionally to its distance. This also supposes that
there is something substantial to the planets themselves. They
are not immaterial, as Aristotle had assumed. The planet’s power
and the strength of the sun’s motor virtue conspire to create the speed
of the planet. To get a sense of how this works, experiment. What
is the difference between moving a weight with a short sick rather than
a long one? Place a fulcrum at the center of a lever. In order to
keep the lever parallel with the floor or table, the weight at each end
of the lever has to be equal. If the weight on one side of the
lever is different than the other side, the lever rotates. This may
remind some of you of the experience at the playground when you were
younger. were you ever stuck up in the air on the see-saw?
Or, have you ever done that to someone else? Where would we have
to move the fulcrum to get it parallel once more? Similarly, in
the balance (if you don’t have one, see if you can come up with
something creative to test this) if the weight on either side is equal,
the balance will be even with the floor, but if not, it will
rotate. What principle governs this change? See what other
experiments you can come up with. If you apply this to the
planet, you can see how the planet sweeps the same area in equal times,
at any part of its orbit.
In this animation, we have the same body rotating
around the sun in perfect circles, but at different distances.
The speed is inversely proportional to these distances.
But, this still does not tell us what path is being traced out by
the planet’s orbit. Nor, does it tells us what impels the planet to
change its distance from the sun. Why not travel in a perfect
circle about the sun? Perhaps there is something else about the
sun-planet relationship that is determining this. This is a
question that had to be answered. Without a hypothesis of why the
planetary orbit takes the path that it does, there is no way of knowing
why the planet appears to be where it is at any given moment.
There would be no way solving the mystery of the 8' of arc that Kepler
keeps bumping into (For more on the mysterious 8' of arc, see the New Astronomy website and work through the book itself).
By determining a principle moving the planets, we find a new method
of measurement. The equant must yield this this principle if truth is
to prevail. Utilizing the principle that the speed of the planet is
inversely proportional to the distance, Kepler finds a new method for
determining the position of the planet at a particular time. From the
discrepancies that arise between the observations and the measurements
derived from each particular hypotheses, Kepler can move toward the
knowledge of what the true path must be. Using a circle to
calculate the position of a planet over a given period of time, yields
results that suffice for the motions at the extremes, but makes the
planet too slow in the middle longitudes. It must be too far away
by this model. On the other hand, the oval that he tried next had
the opposite effect. By this, the planet was too fast in the
middle longitudes. It must have been too close by this
hypothesis. The truth must lie somewhere in the middle, but the
only thing between a circle and an oval is another oval! So,
again he comes back to the physical causes. What causes the
planet to librate, or move away from the circle?
Kepler introduces the
principle of magnetism. The arrow in this animation is meant to depict
the magnetic threads of the planet. Here, the threads stay in the
same position as the planet moves around the sun. At different places
in the orbit, the threads are exposed to the sun in different ways.
Here Kepler makes use of the recent discovery of magnetism and
compares this to the planetary movements. Although he expresses
doubts about this, it seems reasonable given the proof by William
Gilbert that the Earth is a giant magnet.The sort of phenomenon
described by the speed/distance relationship is also exhibited by
magnets, i.e. they approach one another with increased speed as their
distance diminishes. Therefore, since the planet’s body is
magnetic, why not apply this to the relationship between the sun and
the planet? If the planet contains magnetic threads where one
side seeks the sun and the other side flees it, as Kepler hypothesizes,
the following effects coincide with observations. Another animation on the planet's magnetism is found here.
At aphelion and perihelion, both sides of the threads are equally
exposed to the suns rays, so, neither side wins over the other and the
planet is unaffected. But, as the solar species sweeps the planet
around the sun, the sun hits the magnetic threads at an oblique
angle. As it moves from aphelion to perihelion the friendly side
of the magnetic threads is facing the sun and so, the planet is pulled
toward it. Once the planet passes perihelion the side that flees
the sun causes the planet to be repulsed until it returns to its
aphelial position. Here Kepler, applies the principle found in
the balance to measure out the strength that this magnetic power has
over the planet as the planet revolves around the sun. He
measures this effect by taking the sine of the equated anomaly (angle
at the sun), which is equal to the sine of the complement of the angle
made by the threads and the suns rays.
But, astronomy tells us that the maximum deviation of the planet
from the circle occurs at quadrature, when the eccentric anomaly (angle
at the center) is 90 degrees. And, the greatest power of the sun on the
planet must occur when the threads are directly pointed at the
sun. But, according to our model, that occurs at 90 degrees of
equated anomaly, rather than eccentric. This signifies that
something else is occurring. Perhaps the magnetic threads are
themselves moving as they approach and recede from the sun.
Here the magnetic threads are being influenced by the sun in such a way
that the resulting libration of the planet can be measured by the
eccentric anomaly. At quadrature, where the greatest libration
occurs, the threads are directly facing the sun.
Kepler concludes that this can be corrected by taking the sine of
the eccentric anomaly instead. From this the actual magnitude of
the libration can be found, and therefore also the distance of the
planet produced thus. From these results, the planetary path, thus
traced out, is elliptical. And applying the distances of the ellipse to
determine the planet’s position at a given time causes the
discrepancies between the measurements and the calculations to vanish.
But, not by magic. Rather it is Kepler’s looking into physical
causes that does that.
But, upon making the revelation that the planetary orbits are
elliptical, an entire new array of questions is posed. Not all
ellipses are similar. In fact, the specific features of ellipses
can be very different based on their eccentricities. The combined
effect of the relatively large eccentricity of Mars and its proximity
to the Earth made the discovery of the elliptical orbit possible.
But, all the planetary paths are elliptical. Why are they not the
same ellipse? Why must they have different eccentricities? What
does this mean about the relationship of orbital periods to the
distances? How did they get there in the first place?
Why are not the librations of the
planets in the same ratio to their mean distance, that is, why is the
eccentricity of Mercury greatest, next, that of Mars, and then those of
Saturn, Jupiter, and the Earth, while that of Venus last?
The instrumental cause is the different strength of the threads,
whether that is produced by nature or by posture. But the final
cause is the same as the eccentricities themselves, namely, in order
that by reason of these eccentricities the movements of the planets
should become very fast and very slow in such measure as would suffice
for the harmonies to be exhibited through them. Book V of my
Harmonies has to do with this.