Kepler's Perpetual Check
by Alvaro Artagaveytia
A bit of information
To understand the title ʺKepler's Perpetual Checkʺ, it will be necessary to give some information to the reader who is not familiar with the game / sport / science of chess.
There are three possible outcomes. A game can be won, drawn or lost. The outcome is defined by two main scenarios*.
When one side (white or black) wins, it wins by what is called checkmate or by the abandonment of the losing side. This is then the case of a winner and a loser.
A draw is generally caused when the forces are balanced and such an outcome is agreed upon by common accord or by the triple repetition of a sequence of moves.
In the draw, there is also the particular case of perpetual or continuous check.
This is a series of repetitions in the siege of the opponent's king which the latter cannot avoid, but which in turn the side that does so cannot force by winning the endgame.
Finally, it is important to know that there are three distinct phases in a game:
The opening that deals with the arrangement of the pieces within the board trying to control in the best way the "battlefield" during the first moves.
The middlegame, which is when the real exchange of hostilities begins and leans (or remains balanced) towards one of the two sides that manages to take advantage.
And the endgame which is when the fight is precipitated a few moves before declaring a winner or eventually a "draw".
*There is also a time variable that determines that the players lose the game if they "drop the flag"; that is to say, if they fall outside the time allotted for a series of moves according to the previously agreed rhythm.
Nash's checkmate
In the novel written in 1998, Sylvia Nasar narrated the story of the American mathematician John Forbes Nash.
The reader will know this work best in the screenplay format that served the movie "A Beautiful Mind" starring Russell Crowe, who excellently plays a kind of chess game (in my imagination) between Nash and his schizophrenia.
When the disease is about to claim the psyche of the scientist, Nash realizes with an extraordinary resource that one of the characters that inhabit him, cannot be real; so that the actor exclaims:
She never gets old! Marcee can’t be real; she never gets old!
One of the demons cannot be real for the simple fact that she is a girl who, despite the passage of time, does not grow up. She is a kind of eternal child, unchanged. From this fact, the character renounces to continue dialoguing with his inner demons and wins the game.
Nash himself would write in 1994:
Gradually I began to intelligently reject some lines of thought that were deliriously influenced and had been characteristic of my orientation...so, presently, I have returned to thinking rationally, in the style that is characteristic of scientists...
The "rational way" is nothing other than the certainty of the advance -with variable speed- of science.
Thanks to the brilliant contribution of several historical characters, for example, Astronomy was able to free itself from the belief of the epicycles (the retrogradation of the stars in Astrology) to a certain model, but not before overcoming a few demons, as Nash did in his own way.
Incidentally, while Astronomy advances in its knowledge with the passing of time, Astrology without method looks more and more like a vestigial knowledge that, instead of growing, swells.
The imperial mathematician of Styria
Our main guest in this article built with his three laws the platform for others to build a firm bridge between Physics and Astronomy.
Of course, he lived troubled by his demons in the form of astrological belief until the end without being able to discard it completely, going through various periods between love and hate.
In order to get to know him better, we have to take a brief biographical detour through the man who took the discreet certainty of Nicolaus Copernicus about the falsity of geocentrism and with the opulent contribution of Tycho Brahe's celestial cartography:
...By the 1600s, Tycho needed the mathematical talents of the young Kepler for knowledge of his lifelong astronomical observations, while Kepler needed access to Tycho's astronomical data to verify his great mystery of the universe...
Jonathan Taborda in "The Restatement of Kepler's Laws in England."
would end up handing Isaac Newton a toolkit to assemble gravitational mechanics.
The Extermination of Geocentrism
In the town of Weil in southwestern Germany on December 27, 1571 at 14:30 our hero was born, who suffered all kinds of health problems throughout his life. Let's read some more about the character:
...Johannes was a sickly child, with thin limbs and a broad, doughy face, surrounded by dark kinky hair. He was born with a visual defect: myopia and, in addition, anocular polyopia (multiple vision). His stomach and gall bladder gave him constant discomfort. He had boils, rashes, and probably also hemorrhoids, for he himself tells us that he could not sit for long and had to walk back and forth.
Arthur Koestler in "The Sleepwalkers"
All these kinds of setbacks did not dent his character; instead of daunting him, they pushed him fiercely toward the limits of the intellectual capacity he possessed.
It seems appropriate to take into account that we are talking about the dawn of the seventeenth century; that is, in the midst of the rethinking of the static body of human knowledge in the West, which was carefully subjugated by the Church, although those sleepwalkers Koestler speaks of in his book already wanted to grope their way out of the mold of the beliefs of the time.
In order not to bore the reader and to be able to enter into the central theme of the article, we will repeat in a minimal form the three laws that Kepler formulated in his treatise "Astronomia Nova" and polished later in "Harmonices Mundi".
- The planets move elliptically around the Sun, which is located at one of the foci of the ellipse.
- The radius vector joining a planet to the Sun sweeps equal areas in equal times.
- The square of the orbital period of any planet is proportional to the cube of the radius of the orbit.
I will resist the temptation to comment on these wonders and the tortuous process by which he arrived at his postulation, because they escape in their volume the extension of this article, but I take the liberty of suggesting to the reader to investigate further into the first connection between Physics and Astronomy.
Also extremely interesting - and didactic - is the polemical exchange with Robert Fludd for all that this veritable earthquake meant for the astrological status quo.
But at the end of the day, we are here to witness the game between Kepler (with white) and Astrology (with black), since in our consideration Johannes Kepler with his mathematical model of relations between Astronomy and Physics lashed (perhaps unintentionally) on the astrological dogma, leaving it shaky from then on until our days, despite the more or less unsuccessful attempts of the practitioners of the black side to sustain their "science of the stars"; so let's go with it.
The opening
Astrology was championing as the refined knowledge of man's relationship with the universe at that time, and so, logically, our character could not have been oblivious to this from a very early age. We can already see it in the description he makes of his relatives and how he assigns virtues and defects everywhere to his relatives.
Regarding one of his aunts he writes:
Kunigund, born May 23, 1549. The moon could not have been worse placed. She died, mother of many children, apparently poisoned, on July 17, 1581.
We will pass quickly through the description - certainly rather stark - of his father:
Heinrich, my father, was born on January 19, 1547... He was a vicious man, inflexible, quarrelsome and doomed to end badly. Venus and Mars increased his wickedness. The fall of Jupiter impoverished him but gave him a rich wife. Saturn, in VII, made him study artillery. He had many enemies, and his was a marriage full of quarrels... He felt a vain love for honors, and encouraged vain hopes of attaining them; he was a vagabond... In 1577, he was in danger of being hanged. He sold his house and opened a tavern. In 1578, a violent burst of gunpowder burned and wounded my father's face... 1589: he treated my mother very badly. Finally, he went into exile and died.
The list of astrological use in Kepler's early life is practically endless and totally "natural" for the time, and it also appears in his ironic self-portrait around the age of 26:
In this man there are two opposite tendencies; on the one hand, he regrets wasting time; on the other, he is always deliberately wasting it. Indeed, Mercury makes one inclined to amusements, games and other light pleasures...
However, shortly before, that is to say in 1574 at the age of 23, the game begins to change from being at peace with Astrology with respect to its rival.
He is appointed mathematician of the province of Styria in the city of Graz, with the particularity that he is in charge of the chair of Astronomy and here appears the key that begins to change the wind of the contest since he is on the verge of refusing it:
...because of the unexpected and inferior nature of the position and because of my scanty knowledge in this branch of philosophy.
There awaits Astronomy (should I write it here with a lower case?).
It is a mere accessory discipline of Philosophy anchored in the Almagest and in Ptolemy's Tetrabiblos despite the Copernican rumors; so happy with his theory of epicycles that Nicolaus Copernicus himself had not been able to get rid of.
During his first year at the University, he writes profusely about the heavens, spirits and genii among other topics of astronomical philosophy; but something is beginning to change.
We know that Kepler's classes at the University were "...tiresome, perplexing and very unintelligible..." The genius of the imperial mathematician moved at breakneck speed in the association of ideas.
And the association of ideas is a dangerous business for the rhythm of dogmas.
During the four years he stayed at Graz, he had to carry out the task of the astronomical calendar (astrological in truth), which was one of the obligatory tasks although it was paid separately.
The astrological career of our white player began with these calendars and ended as court astrologer to the Duke of Waldstein.
For the time being, we observe that at the end of the opening phase, Black's side (Astrology), holds up relatively well against White, that is to say Kepler's intellect, although without gaining an advantage.
The middlegame
Over the next few years, and as his astronomical knowledge took hold, the game began to tilt dangerously in both directions, beginning with a rejection with overtones of disgust:
A spirit accustomed to mathematical deduction, when confronted with the fallacious foundations [of astrology] resists long, long, like a stubborn mule, to set foot in that filthy puddle, until he is forced to do so by blows and curses...
«Mysterium Cosmographicum» Preface to the Reader – Johannes Kepler
Astrology next regains some credit in our hero:
Let us at first look at the empirical side of the matter:
Belief in the effect of constellations proceeds, in the first place, from experience, which is so convincing that only people who have not examined it can deny it...
More fuel to the fire:
It is obvious that the sky exerts some influence on man; but what this thing is is something that remains intrinsically hidden.
We even have time to read some advanced hypothesis that gives the impression of the astrological set:
The natural soul of man is of no greater dimensions than those of a point; and in that point the form and aspect of the whole sky are potentially engraved, even if that sky be hundreds of times greater.
We could extend the notes again and again and the vacillation between the sides seems infinite. When he is convinced of a position that takes his mind off belief, Astrology rebels and escapes him once again, barely holding on while our professor is already a scholar in every sense and is at an enormous distance from the sages of his time (and ours, too).
The endgame
The denouement is close to the departure, when he has enunciated the third law that allows to establish the duration of the orbits of the stars around the Sun. There is still time to evaluate what will have happened with the asteroid belt, since it lacks a component to the system of cycles, but as I said before, these variants are so rich that they can be the subject of many specific articles.
Let us retrace our steps then to attend the end of the game which, as the reader presages, will end in a draw by perpetual check:
Truly, with all that I know of astrology, I do not know enough to dare to predict with certainty anything specific.
This sentence echoes over and over again in my head no longer only because of the perception of a brilliant mind, but because of the arrogance of practitioners -in which I include myself- of all times who, having -let's say- a paltry fraction of the encyclopedic knowledge of our hero, launch into prophesying left and right on any matter.
Let us briefly read once more Koestler trying to interpret Kepler's sentiment as the game culminates in a draw:
So that only the structure appears cosmically determined, and not the particular events. Within that structure, man is free. In Kepler's later years, this concept of the Gestalt of cosmic destiny becomes more abstract and appears more purified of dross...
Our imperial mathematician, like his colleague Nash with his schizophrenia, tried to exorcise the demons that consumed him in his astrological reverie.
The former won by checkmate to his pathology; our hero only managed a sad draw by repetition.
It is true that Kepler managed to place Astronomy on the pedestal of the sciences, displacing it from the philosophical stage and moving it to better neighborhoods far from the slums of knowledge.
That new Astronomy that was born thanks to the contribution of our character, -as well as Ulugh Beg, Tycho Brahe, Copernicus-,left Astrology -its twin sister- in the brothels out of all contact. From Descartes a few years later and onwards, they conveniently confronted them and compared their clothes, mirrors and lineages, so that there would be no reconciliation whatsoever and in passing they would forget the common maternal origin in the heavens.
The contrast was so successful that many happy practitioners of the current astrology (here unhappily with lower case), maintain the concept that "their science" has nothing to do with Astronomy.
However, the story will tell that in that city where belief, myth and science coexist at a prudential distance, a prostitute managed to tie her match with the father of modern astronomy.
About the author:
Alvaro Artagaveytia:
In active professional practice since 1984.
In 1988, he began to teach astrology, rescuing mainly the school of interpretation (predictive) called "Judiciaria".
In 2009, he started the teaching and research project through the Internet at https://astro.uy, currently condensed in the EVA (Virtual School of Astrology).
He is the author of five books, among which stands out the three-volume series "Fundamentos de Astrología Judiciaria".
He has also written "El Cordel de Urania" and "Lecciones de Astrodiagnosis".
Images:
Chess board: Image by Phil Shaw from Pixabay
Johannes Kepler: August Köhler, Public domain, via Wikimedia Commons
John Forbes Nash: Peter Badge / Typos1, CC BY-SA 3.0 , via Wikimedia Commons
Diagram: created by the author
House in Graz: Mrbeachguide, CC BY-SA 3.0 , via Wikimedia Commons
Chess board: Image by Steve Buissinne from Pixabay
© Alvaro Artagaveytia 2022
