Dec 272020

Today is the birthday (1571) of Johannes Kepler, a German astronomer, mathematician, and astrologer (no doubt named after John the Apostle because this is his saint’s day ). Kepler is a key figure in the 17th-century scientific revolution, best known for his laws of planetary motion, and his books Astronomia nova, Harmonices Mundi, and Epitome Astronomiae Copernicanae. These works also provided one of the foundations for Newton’s theory of universal gravitation which augmented Kepler’s concepts of planetary motion.

Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He also taught mathematics in Linz, and was an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting (or Keplerian) telescope, and was mentioned in the telescopic discoveries of his contemporary Galileo Galilei. He was a corresponding member of the Accademia dei Lincei in Rome.

Kepler lived in an era when there was no clear distinction between astronomy and astrology, but there was a strong division between astronomy (a branch of mathematics within the liberal arts) and physics (a branch of natural philosophy). Kepler pulled together astronomical observations with mathematics and physics to build the foundations of astrophysics. He also incorporated religious arguments and reasoning into his work, motivated by the religious conviction and belief that God had created the world according to an intelligible plan that is accessible through reason. Kepler described his new astronomy as “celestial physics,” as “an excursion into Aristotle’s Metaphysics,” and as “a supplement to Aristotle’s On the Heavens,” transforming the ancient tradition of physical cosmology by treating astronomy as part of a universal mathematical physics. When Newton said that he saw so far because he stood on the shoulders of giants, Kepler was one of those giants.

Delving into all that Kepler accomplished is way too much for a short blog post, so let me focus on his perhaps most famous formulation, his laws of planetary motion.  The three laws state that:

  1. The orbit of a planet is an ellipse with the Sun at one of the two foci.
  2. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
  3. The square of a planet’s orbital period is proportional to the cube of the length of the semi-major axis of its orbit.

The elliptical orbits of planets were indicated by calculations of the orbit of Mars. From this, Kepler inferred that other bodies in the Solar System, including those farther away from the Sun, also have elliptical orbits. The second law helps to establish that when a planet is closer to the Sun, it travels faster. The third law expresses that the farther a planet is from the Sun, the slower its orbital speed, and vice versa. As such, Kepler refined the theories proposed by Copernicus.

If the eccentricities of the planetary orbits are taken as zero, then Kepler basically agreed with Copernicus:

1. The planetary orbit is a circle.
2. The Sun is at the center of the orbit.
3. The speed of the planet in the orbit is constant.

The eccentricities of the orbits of those planets, known to Copernicus and Kepler, are small, so the foregoing rules give fair approximations of planetary motion, but Kepler’s laws fit the observations better than does the model proposed by Copernicus. Kepler’s corrections are:

1. The planetary orbit is not a circle, but an ellipse.
2. The Sun is not at the center but at a focal point of the elliptical orbit.
3. Neither the linear speed nor the angular speed of the planet in the orbit is constant, but the area speed (closely linked historically with the concept of angular momentum) is constant.

If you are lost at this point – or don’t care about these points – I won’t beat you up, and I certainly won’t add any equations, or the like. It’s enough to be aware that the planetary orbits are elliptical rather than circular. Kepler shows us that physics is in a perpetual state of refinement (that never ceases). Newton added his bits and much later Einstein added his. Understanding is in a constant state of change, leading to a general acknowledgement that change is the only constant. Scientific theories never explain everything: there are always observations that cannot be accounted for by current theories. Hence the periodic revolutions in scientific thinking.

I will admit that my eyes have the habit of glazing over when I see something like r=p/1+ϵcosθ (or more complex) and it’s not because I do not understand the formula.  It’s because my interests do not lie in delving deeper into the implications.  There’s the nub of the matter. I accept the conclusions and move on. But . . . there are people like Kepler who are never satisfied. The work of Copernicus was fairly close to the truth, but the anomalies bothered Kepler and he worked tirelessly to get yet closer to the truth.  This is one of the reasons I get so aggravated with flat earthers and other science deniers.  They think that some vague intuitions based on limited sensory information can challenge the exhaustive work of dedicated professionals.  I despair – sometimes.

Kepler was born in Weil der Stadt, currently in the Stuttgart Region of the German state of Baden-Württemberg. Among other things, it is well-known for its Fasnetsküchle which will be available very soon (after Epiphany). Fasnetsküchle are similar to the so-called “Berliner,” or jelly doughnuts, or “Krapfen,” which are available year round. But the Swabian version is distinctly different: it must be flat and square or rectangular, never round nor as tall as a Berliner, and it’s not supposed to be filled with jam – it should be plain inside and out. True Swabians insist that Fasnetsküchle may not even be sprinkled with cinnamon or powdered sugar. But times change and you now find them with a dusting of sugar (and cinnamon).



2 cups whole milk, warmed to 110F/43C
4½ teaspoons active dry yeast (two packages)
¾ cup and 1 pinch granulated sugar, divided
5 to 6 cups all-purpose flour, divided
2 eggs
1 teaspoon vanilla extract
1¼ teaspoons salt
4 tablespoons unsalted butter, melted
oil for deep- frying (lard is traditional)


Pour the warm milk into bowl. Stir in the yeast and a pinch of granulated sugar. Let stand for 5 to 10 minutes, or until it has become bubbly. Add 2 cups of flour to the mixture and stir with a wooden spoon until a smooth batter forms. Cover with plastic wrap and set in a warm spot for 30 minutes. By now the mixture should have risen and become bubbly.

In a medium bowl, whisk the eggs until pale yellow and frothy (about three minutes). Add the sugar, vanilla extract and salt, and whisk until combined and smooth.

Add the egg mixture to the dough and hand-knead until mostly combined. Add the melted butter and mix. Gradually add three more cups of flour to the mixture and continue to knead until very soft dough comes together (it will be rather slack and a bit sticky.) If necessary, add up to another cup of flour, a spoonful at a time, until the dough firms. Transfer the dough to a lightly greased bowl, cover with plastic wrap, or a kitchen cloth, and let it set in a warm spot until dough has doubled in size (20 to 30 minutes).

Remove the dough from the bowl and turn out on to a floured work surface. With your fingers, or a rolling pin, push down the dough into an even layer. Sprinkle flour on the dough and roll it out to about ½-inch thickness. If the dough doesn’t hold its shape and springs back, cover with a damp towel and let it rest for a few more minutes and try again.

Cut out 3 x 3 inch squares or 3 x 4 rectangles of dough. Transfer the dough pieces to parchment-lined baking sheets. Gather scraps of dough and again roll out and cut until you have used up all of the dough. Cover the baking sheets loosely with a dish-towel, plastic wrap and place in a warm, draft-free spot until they are almost doubled in size, about 30 minutes.

Meanwhile, heat at least 1½ to 2 inches or more of deep frying shortening or oil in a heavy-bottomed pot or deep skillet over medium heat to 350F/176C. Carefully lower about three or four Küchle into the oil one at a time (be sure not to over-crowd the pan) and fry until the bottom is golden brown. Carefully turn them over and continue to fry until the other side is golden brown.

Remove with a slotted spoon, and drain on a wire rack. Repeat for the remaining Küchle. They are best eaten warm.

Aug 132018

Today is the birthday (1666) of William Wotton, an English theologian, classical scholar and linguist, who is largely forgotten nowadays, but in his day was known for his involvement in what became called the Quarrel of the Ancients and the Moderns. I’ll get to that in a minute. In Wales he is remembered as the collector and first translator of the ancient Welsh laws.

William Wotton was the second son of the Rev. Henry Wotton, rector of Wrentham, Suffolk. He was a child prodigy who could read verses from the Bible in English, Latin, Greek and Hebrew before he was 6 years old. In April 1676, when he was not yet 10 years old, he was sent to Catharine Hall, Cambridge, and sat for his B.A. in 1679 (13 years old). By this time Wotton had learned Arabic, Syriac, and Chaldee, as well as a knowledge of logic, philosophy, mathematics, geography, chronology, and history. His parents died whilst he was still at Cambridge, and as a teenager he was taken into the household of Gilbert Burnet, later bishop of Salisbury. He was awarded a fellowship at St John’s College, where he received his M.A. in 1683 and earned a B.D. in 1691. In 1686 he was appointed curate of Brimpton in Berkshire and the following year he was also elected a Fellow of the Royal Society. In January 1689 he was appointed vicar of Lacock in Wiltshire, which he held until his resignation in 1693. Soon after ordination he was also appointed chaplain to Daniel Finch, Earl of Nottingham, and tutor to his family. Finch presented him with the rectory of Milton Keynes in Buckinghamshire, in 1693.

Wotton began his scholarly career as the translator of Louis Dupin’s A new history of ecclesiastical writers, (13 vols. 1692–99). However, he is chiefly remembered for his share in the controversy about the respective merits of ancient and modern learning. In his Reflections upon Ancient and Modern Learning (1694, and again 1697) he took the part of the moderns, although in a fair and judicial spirit.  The “ancients versus moderns” debate began in France in the early 16th century with a number of “moderns” claiming that the renewed interest in Classical arts and philosophy during the Renaissance, should not be slavish imitation of the ancients, but should be tempered with an awareness of the accomplishments of modern times. The “ancients” championed ancient learning over the modern. The “quarrel” got erudite and pedantic, and I am not going to dissect it for you. Do your own research. Simplistically, it can be boiled down to the importance of “authority.” Should we admire ancient authors as sacred (i.e. authorities), or should we move on? Medieval scholasticism got mired in authority. To be a scholar you had to first read all the authorities on a subject, learn them inside-out, and then add your own bits of wisdom without contradicting any of the authorities. The orthodox rabbinical tradition works this way, and my education at Oxford in the 1970s was not so very different. Every week I was given an essay topic, for example, “Was the author of Mark’s gospel Paul’s traveling companion, John Mark?” or “When was John’s gospel written?” My job for the week was to distill out all the arguments from the authorities, divide them into camps, and conclude with my decision as to which of the camps (authorities) was correct. This was not quite Medieval scholasticism in that the authorities were allowed to disagree with one another, but I was not allowed to disagree with them. You can guess what I think of this as a method of education.

Swift attacked Wotton for pedantry in The Battle of the Books and A Tale of a Tub, but Wotton was far from being a pedant. He had a thorough command of the arguments, and was fair in his assessments. Wotton responded calling Swift’s Tale “one of the profanest banters upon the religion of Jesus Christ, as such, that ever yet appeared.”

Wotton wrote a History of Rome in 1701 at the request of Bishop Burnet, which was later used by the historian Edward Gibbon. In recognition, Burnet appointed him as a prebend of Salisbury from 1705. In 1707 Wotton was awarded a Lambeth degree of Doctor of Divinity by Archbishop Thomas Tenison in recognition of his writings in support of the established Church of England against the Deists. Around 1713 Wotton also developed ideas concerning the relationship between languages introducing the concept of an early proto-language by relating Icelandic, the Romance languages, and Greek. This pre-dated Sir William Jones’ famous lecture comparing Sanskrit with the Classical languages, by more than 70 years. These theories were later published after Wotton’s death, as A discourse concerning the confusion of languages at Babel (1730).

Throughout his adult life, Wotton was said to be “a most excellent preacher, but a drunken whoring soul”. He was also very extravagant, transforming his rectory into a 32-room mansion. He was, however, able to borrow money against future expectations of ecclesiastical preferment as a result of his close friendship with William Wake, then bishop of Lincoln. Between the summer of 1711 and the Spring of 1712, Wotton appears to have experienced a mid-life crisis, and he scandalized the neighborhood on many occasions by being found drunk in public, or else was known to have spent prolonged periods in local brothels. As a result, he was initially warned about his behavior by Wake, who later broke off their friendship and rescinded his promise of providing an additional living in Buckinghamshire. As soon as it became known that the rector’s expectations had been dashed, local businesses began to press for the payment of their debts. In May 1714, Wotton was forced to abandon his rectory at Milton Keynes to avoid his creditors, and for 7 years he lived in Carmarthen in south-west Wales under the assumed name of Dr. William Edwards.

Whilst in Carmarthen, Wotton turned his life around and returned to his studies. He was also able to re-establish his friendship with Wake, who had become Archbishop of Canterbury in December 1715. Wotton began to study Welsh, and produced an important bilingual parallel text edition of the Welsh and Latin texts of the medieval Welsh laws traditionally attributed to Hywel Dda. To do this he had first to identify and obtain transcripts of around 15 known manuscripts in either Latin or Medieval Welsh, and establish an authoritative text, and then begin the difficult task of translating the Mediaeval Welsh terminology which appeared in both the Latin and Welsh versions, but the meaning of which had been lost by the 18th century. From 1721 Wotton was assisted by the Welsh scholar Moses Williams. Wotton lived to complete the translation but was working on an accompanying glossary when he died. This was completed by Williams, and the whole work was published in 1730 by his son-in-law William Clarke in a large folio edition under the title Leges Wallicae.

Whilst in Carmarthen he also conducted surveys of the cathedrals of St David’s and Llandaff which were published by his friend Browne Willis in 1717 and 1718. He published Miscellaneous Discourses relating to the Traditions and Usages of the Scribes and Pharisees which included a translation of part of the Mishnah in 1718. Wotton had repaid his creditors and was able to return to Bath by October 1721 and London by June 1722 but was in very poor health. He was still working on his Leges Wallicae, when he died of dropsy in Buxted in Sussex, on 13th February 1727.

In the spirit of the quarrel of ancients and moderns we can put an ancient and modern recipe side by side. You would be forgiven for thinking that the modern recipe is superior. What you are not taking into account is that ALL recipes make assumptions about what the reader can be expected to know. If you read a modern recipe for a cake that begins “cream the butter and sugar” You probably know what “cream” means in this context, that is, if you have any baking experience. Someone reading the recipe 2,000 years from now might have no idea what it means, and think that 21st century recipes are incomplete. So, it’s not a question of saying that modern recipes are better than ancient ones, but, rather, that we know the implicit assumptions in modern recipes, but not in ancient ones.

Apicius gives this recipe for mussels in De re coquinaria (c. 1st century CE) and I have mentioned it before. Here’s the original Latin:

X. in metulis: liquamen porrum concisum cuminum passum satureiam, uinum; mixtum facies aquatius et ibi mitulos quoques.

Roughly translated:

10. For mussels: liquamen (fermented anchovy sauce), cut up leeks, cumin, passum (very sweet wine), savory, and wine. Mix these ingredients with water and add mussels.

On the surface this recipe does not seem much to go on, and a modern cook would normally want more detail, particularly as concerns quantities. The instructions are also pretty slim by modern standards. I could give a modern recipe thus:



2 lb fresh mussels
1 tbsp fish sauce
1 leek, chopped
1 tsp cumin
1 tbsp chopped fresh savory
½ cup sweet sherry
½ cup dry white wine


Make sure the mussels are thoroughly cleaned and beards removed. Discard any that are not tightly shut.

Place the ingredients, except the mussels, in a large saucepan. Add around 2 cups of cold water. Bring to a boil, add the mussels and cover. Cook for several minutes and check to see that all the mussels have opened.

Remove the mussels with a slotted spoon, and place them in a serving bowl. Carefully pour the cooking juices over the mussels, but make sure not to pour out the last part, because it may contain grit.

You might think that my recipe is better than the ancient one. Really there is not much difference between the two. Apicius does not say you have to boil the mussels, he assumes that you know this. He is making a number of assumptions. But my modern recipe makes many assumptions also. Apicius actually gives you a lot more freedom than I do. Sure, you can vary my quantities at will, but most cooks will try the quantities as given first, and then adjust them later. With Apicius, you have to make decisions about quantities from the start.  I’d be happy, for example, to use 3 or 4 leeks, and serve the mussels on a bed of them, with or without the sauce. This idea would not occur to you with the modern recipe because you are thinking of a watery sauce for the mussels.