History's greatest astronomer also cast horoscopes for money, and wrote about it.

Johannes Kepler is the figure who best shows how astronomy and astrology lived side by side. Imperial mathematician, discoverer of the laws of planetary motion, and practising astrologer: he made charts on commission, and part of his income came from it. The chart he made for General Wallenstein is one of the most studied astrological documents of the period.

What is interesting is what he thought about the subject. Kepler criticised sharply the astrology of his time, rules inherited without examination, the claim to predict concrete events, the table of meanings each author copied from the last. And at the same time he argued that there was a core there worthy of investigation, tied to the ANGLES between the planets.

In Tertius Interveniens he warns those who want to throw out astrology altogether not to throw out, along with it, what is real in it. It is an uncomfortable position, and it is the most honest of the three possible ones, harder to defend than "it's all true" and "it's all nonsense".

And he went further than criticism: he proposed new aspects, worked out from divisions of the circle that tradition did not use, such as the quintile, at 72 degrees. Whoever invents an aspect is saying that the inherited list can be revised, and few astrologers have dared that.

Before him, in the fifteenth century, Regiomontanus produced printed ephemerides and a house division system that bears his name and is still used by many people today. Germany was, for centuries, the place where the calculation tools the rest of Europe used were made, and printing, which was German, is what made these tables spread.

Germany gave astrology its most competent critic. Kepler is the best argument against using it without measurement, and against dismissing it without examination.

The printing press was born German, and one of the first things it printed in quantity was calendars with the positions of the stars. Regiomontanus set up in Nuremberg, in the 1470s, a printing workshop with a stated aim: to publish astronomical tables without the errors that copyists kept adding with every copy. It is a thoroughly modern idea, the machine serves to take the human hand out of transcribing numbers, and it was applied first to ephemerides.

The effect was enormous and little remembered. Before printing, a table of positions was an expensive manuscript, full of accumulated errors and restricted to those with access to libraries. After it, any practitioner with some money could buy the positions of the planets for the years ahead. Astrology spread through the same door as the Bible, and for the same reason.

Albrecht Dürer engraved in 1515 the first printed star maps of Europe, with both hemispheres and the constellation figures drawn by a first-rate artist over astronomers' data. And he left an engraving that is a document of practical astrology: the Melencolia I, from 1514, with a downcast figure surrounded by instruments and, in the corner, a four-by-four magic square. That square is Jupiter's, and melancholy is Saturn's illness.

The current reading, which comes from art historians and not astrologers, is that the engraving shows a astrological remedy: against Saturn's weight, Jupiter is called upon through the figure that corresponds to it. It is the procedure this series describes on the page about astrological magic, made by one of the greatest engravers in history, and dated within the square itself, which carries the year 1514 on its bottom row.

From Kepler's life, the episode that says the most about the time is not scientific. His mother, Katharina, was accused of witchcraft and spent more than a year imprisoned, under threat of torture. Kepler put down his work, went there and conducted the defence himself, answering each accusation point by point. She was acquitted and died a few months later. The imperial mathematician, who cast horoscopes for generals, had to prove in court that his own mother was not a witch, that was the line between respected knowledge and crime, and it ran straight through one family.

The aspects Kepler proposed came from a precise idea: if dividing the circle by two, three, four and six gives the inherited aspects, why stop there? He worked with regular polygons and arrived at new divisions, such as the quintile, at 72 degrees, the circle divided by five. His argument was not tradition, it was geometry, and it is a reminder that the list of aspects in any program is a choice, not a fact of nature.

In the 20th century, Germany produced two technical schools that are still in circulation: the Hamburg School, by Alfred Witte, which works with midpoints between planets instead of the classical aspects, and the cosmobiology of Reinhold Ebertin, who reduced the practice to a small set of combinations and published a reference book translated for half the world. The two share a distrust of excess symbol and a taste for short, checkable rule.

And the dark chapter: in 1941, after Hess's flight to Scotland, the Nazi regime banned astrology and arrested astrologers, seers and occultists in a coordinated action. At the same time, both sides of the war employed astrologers for propaganda, trying to guess what the other side would be reading in their own charts. It is the only period in which knowing astrology was, at the same time, a crime and a state job.

The Nuremberg ephemeris went further than its author. It was Regiomontanus's tables that Columbus took on board, alongside the almanac of the Portuguese Abraham Zacuto, and it was with them that he predicted the Jamaica eclipse told on the Spain page. A German calculated it, a Jew expelled from Castile checked it, a Genoese in the service of Spain used it, and that is how this story moves, respecting no border at all.

The chart Kepler made for Wallenstein has an ending worth telling. Handed over unsigned, it pleased him, and years later the general asked for a follow-up. Kepler pointed to serious difficulties around March 1634 and avoided saying what would happen. Wallenstein was assassinated in February of that year. It is the kind of hit that makes a career and that Kepler, on purpose, never used as propaganda: he wrote that an astrologer should not promise a dated event.

Kepler also cast and commented on his own chart, and those of the people in his household. In a text about himself, he crosses the position of the planets at birth with what he knew of his own temperament, the impatience, the difficulty with people, the stubbornness with numbers. He used astrology as a language of self-portrait, which is quite close to what this site calls a personality chart, and quite far from predicting next week.

The part of astrology that depends on PLACE, not just date, is the Ascendant: the degree of the zodiac rising on the horizon at the moment of birth. It changes every two hours and depends on the city's latitude.

And the twelve signs do not rise at the same speed. Some take over two hours to cross the horizon and others less than one, and that difference grows the further you are from the equator. I drew 200,000 instants between 1950 and 2010 and worked out the Ascendant for Berlin, at 53° north:

In Berlin, the most common Ascendant is Scorpio, at 12.1%, and the least common is Pisces, at 3.5%; one is 3.5 times more likely than the other, where a fair draw would give 8.3% to each sign.

Notice what this means: two people born at exactly the same time, one in Berlin and the other in a city at a different latitude, can have different Ascendants, and the frequency of each Ascendant changes with the place. The city of birth is not an administrative detail on a form: it enters into the count.

The pattern across this series is pure geometry, and it fits in one sentence: the further from the equator, the more uneven the draw. In Copenhagen, at 56 degrees north, the gap between the most common Ascendant and the least common one is 4.3 times; in São Paulo, at 23 degrees south, it drops to 1.5.

And the questions that come up most on this subject, with the short answer: