Apr 292018

Today is the birthday (1854) of Jules Henri Poincaré, a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as “The Last Universalist,” since he excelled in all fields of the discipline as it existed during his lifetime. Outside of mathematics and science Poincaré is scarcely a household name, yet a reasonable argument can be made that both Einstein and Picasso were profoundly influenced by his work – yes, BOTH. I’ll try not to make your eyes glaze over with technicalities too much, and, instead, focus on generalities that just about anyone can grasp, including Poincaré’s ideas concerning original thinking, as well as his work habits.

As a mathematician and physicist, Poincaré, made a number of original and fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. He was responsible for formulating the Poincaré conjecture, which was one of the most famous unsolved problems in mathematics until it was solved in 2002–2003. In presenting the conjecture he helped found the field of topology. In his research on the three-body problem (calculating the motion of three interacting bodies – such as planets – using the laws of motion and gravity posited by Newton), Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. Poincaré was also one of the first to propose the existence of gravitational waves emanating from a body and propagating at the speed of light as a solution to problems in celestial mechanics. His proposal has proven correct experimentally.

Poincaré’s work itself was of great importance in numerous fields, but for the moment I would like to focus on that way in which he worked and how he construed the intellectual process. To begin, let me remind you that scientific discovery is almost never a step-by-step process. It requires imaginative leaps and “what-ifs” that are anything but logical. Poincaré tried to probe the mechanics of genius, and, though he explained his own process quite well superficially, he did not exactly provide much useful penetrating detail.

Poincaré’s work habits have been compared to a bee flying from flower to flower. One observer said:

Accustomed to neglecting details and to looking only at mountain tops, he went from one peak to another with surprising rapidity, and the facts he discovered, clustering around their center, were instantly and automatically pigeonholed in his memory.

The mathematician Darboux claimed he was un intuitif (intuitive), saying that this is demonstrated by the fact that he usually worked by visual representation. Poincaré himself wrote that he believed that logic was not a way to discover ideas, but a way to structure and manage ideas once imagination and intuition have uncovered them. Poincaré’s mental processes were not only interesting to Poincaré himself but also to Édouard Toulouse, a psychologist at the Psychology Laboratory of the School of Higher Studies in Paris. Toulouse wrote Henri Poincaré (published in 1910). In it, he discussed Poincaré’s personality and work habits:

He worked during the same hours each day for short periods of time. He did mathematical research for four hours a day, between 10 a.m. and noon then again from 5 p.m. to 7 p.m. He read articles in journals later in the evening.

His normal work habit was to solve a problem completely in his head, then commit the completed problem to paper.

His ability to visualize what he heard proved particularly useful when he attended lectures, since he was severely nearsighted and could not see what the lecturer wrote on the blackboard.

He was always in a rush and disliked going back for changes or corrections.

He never spent a long time on a problem since he believed that his unconscious would continue working on the problem while he consciously worked on another problem.

While most mathematicians worked from principles already established, Poincaré started from basic principles each time.

Not exactly helpful. What you get from this list is that Poincaré’s mind was a cauldron of stuff that he poked around in until he came up with something useful. I am, fortunately or unfortunately, familiar with the process, although my cauldron as not filled with as much technical stuff as his. Furthermore, filling your cauldron with stuff is not enough. You have to have ways of wading around in the stuff productively. Here Poincaré is not much help. He talks about intuition and imagination, but what are they and how do you get them? Poincaré studied his habits and gave a talk about his observations in 1908 at the Institute of General Psychology in Paris. He linked his way of thinking to how he made several discoveries. Some quotes are pertinent.

The chief aim of mathematics teaching is to develop certain faculties of the mind, and among these intuition is by no means the least valuable.

 It is by logic that we prove, but by intuition that we discover.

 Logic teaches us that on such and such a road we are sure of not meeting an obstacle; it does not tell us which is the road that leads to the desired end. For this, it is necessary to see the end from afar, and the faculty which teaches us to see is intuition. Without it, the geometrician would be like a writer well up in grammar but destitute of ideas.

All good up to a point. A good vocabulary and excellent command of grammar will not make you a poet; skilled brushwork and an array of paints will not make you an artist. No argument. What does make a Keats or a Picasso? Poincaré has no answer, and neither do I.

An array of pots and pans and a larder full of good ingredients will not make you a good cook either. Nor will training by the best chefs. I can give you recipes, however. They are the building blocks. Poincaré was born in Nancy, former capital of the duchy of Lorraine. Lorraine is, of course, the birthplace of quiche Lorraine, which you can find in qualities from wretched to divine the world over. It has become a rather mundane staple in many places. This recipe is serviceable, but you ought to go to Lorraine for a proper quiche. Even there you may be disappointed. You are best served by seeking the advice of a knowledgeable local. Eggs and cream in a pastry shell is not especially French, but the word “quiche” comes from Lorraine dialect (maybe from German, “kuchen”). The bacon was at one time lardons, and the cheese is a late addition also. Therefore, finding “authentic” quiche Lorraine is a lost cause.

Quiche Lorraine


For the crust

1 ¼ cups all-purpose flour
½ tsp salt
½ cup cold butter, cubed small
3 tbsp ice water

For the quiche

8 slices bacon
1½ cups shredded gruyere
1 shallot, minced
6 large eggs
1½ cups heavy cream
salt and black pepper


For the crust, sieve the flour and salt into a mixing bowl or food processor. Work the flour and butter together with your hands, or by pulsing in the food processor, until it resembles coarse sand.

Add the ice water one tablespoon at a time and work the mixture into a dough. Form into a disc, wrap in plastic wrap, and refrigerate until firm, (at least 30 minutes).

On a lightly floured surface, roll out crust until ¼” thick. Loosely drape it over a 9” pie plate (or quiche pan) and crimp the edges. Refrigerate until ready to use.

Preheat the oven to 350˚F/175˚C.

In a large, dry skillet over medium heat, cook the bacon until crispy. Drain and cool on wire racks and then break into bite-sized pieces.

Scatter the bacon pieces evenly on the pie crust and then spread over 1 cup of grated gruyere and the shallot.

In a large bowl, whisk together the eggs, cream, a pinch of cayenne and nutmeg, and season with salt and pepper to taste. Pour mixture over bacon and cheese. Sprinkle with the remaining cheese.

Bake for around 45 minutes until the crust is golden and the eggs are cooked through. Test by inserting a knife into the eggs near the center. It should come out clean when the eggs are cooked. Cool the quiche on a wire rack in the tin for 10 minutes before slicing into wedges and serving.

Dec 282017

Today is the birthday (1903) of John von Neumann (born, Neumann János Lajos) legendary mathematician who could well lay claim to being the greatest mathematician of all time, if I were given to superlatives. He made major contributions to a number of fields, including pure mathematics (foundations of mathematics, functional analysis, ergodic theory, representation theory, operator algebras, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and quantum statistical mechanics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics. Quite a mouthful. Next to von Neumann, the iconic genius, Einstein, who had an office down the hall from von Neumann at Princeton for many years, was second rate. Yet von Neumann tends to be forgotten in the popular mind these days, except perhaps indirectly when people refer to a “zero-sum game” which was a small part of the game theory he invented.

Writing something both interesting and useful – as well as being brief –  about von Neumann is a real challenge. I won’t say too much about his mathematical genius except to say that he was the rare person, indeed, who could see mathematical problems in their totality almost instantly, and could solve them almost as fast, because, unlike most other mathematical geniuses, he usually did not have to wade through calculations to find a solution, but could see the big picture with paths leading in and out intuitively. Such a mathematical mind does not come along very often.

Georg Pólya wrote that von Neumann was,

The only student of mine I was ever intimidated by. He was so quick. There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn’t say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.

I’m not sure whether I would include von Neumann on my list of people (alive or dead) I would like to have dinner with.  By all accounts he had a decent sense of humor, and was a good storyteller, but he could also be crudely insensitive, and tell off-color jokes without concern that he might offend.  His interest in women was strictly sexual, and the secretaries at Los Alamos had to put cardboard modesty screens on the front of their desks because he would quite blatantly ogle their legs when he was in the room even though he was a married man. I would go as far as to say that despite being an exceptionally intelligent man, he had little grasp of certain fundamental principles of living. In fact, he acknowledged as much on many occasions.  This famous quote may be the most telling:

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

An interesting quote to parse on many levels. There is no doubt that van Neumann found mathematics simple, even mathematical problems that stumped great minds. By comparison, he thought that life was much more complex, and, by implication, cannot be reduced to mathematical models. At one point he said:

There probably is a God. Many things are easier to explain if there is than if there isn’t.

Von Neumann took Pascal’s wager when he was near death and embraced Catholicism, while being overtly agnostic all his life (even though he was baptized in 1930 after his father’s death and before he married, for convenience only). Pascal argued that if death is the end, then you lose nothing by being a Christian. But if death leads to heaven or hell, it would be much better to die a Christian than not. Either way you win. The small trick here, which von Neumann apparently did not allow for, is that you have to be a believer, not just a Christian according to the letter of the law. Naturally he chose Catholicism for his church, presumably knowing that the Catholic church (overtly) places higher value on correct action over correct belief. This stance led to the Protestant Reformation, so, as an ordained Calvinist minister, you know what I think of von Neumann’s “conversion.” On the other hand, I don’t see it as a great sin.  If it brought him peace at the time of his death, it was worth it. As far as I am concerned, dogma, whether it be Catholic or Protestant, is worthless.

Von Neumann was born Neumann János Lajos to a wealthy, acculturated and non-observant Jewish family. His Hebrew name was Yonah. Von Neumann was born in Budapest, then in the kingdom of Hungary, part of the Austro-Hungarian Empire. His father, Neumann Miksa (English: Max Neumann) was a banker, who held a doctorate in law. He had moved to Budapest from Pécs at the end of the 1880s. In 1913, his father was elevated to the nobility for his service to the Austro-Hungarian Empire by Emperor Franz Joseph. The Neumann family thus acquired the hereditary appellation Margittai, meaning from Marghita (even though the family had no connection with the town). János became Margittai Neumann János (John Neumann of Marghita), which he later changed to the German Johann von Neumann.

Von Neumann was a child prodigy. As a 6 year old, he could divide two 8-digit numbers in his head, and, reputedly, could converse in ancient Greek. Formal schooling did not start in Hungary until the age of 10. Instead, governesses taught von Neumann, his brothers and his cousins. His father believed that knowledge of languages other than Hungarian was essential, so the children were tutored in English, French, German and Italian. By the age of 8, von Neumann was familiar with differential and integral calculus, but he was particularly interested in history, reading his way through Wilhelm Oncken’s 46-volume Allgemeine Geschichte in Einzeldarstellungen.

Von Neumann entered the Lutheran Fasori Evangelikus Gimnázium in 1911. This was one of the best schools in Budapest, part of a specialized education system designed for the elite. The school system produced a generation noted for intellectual achievement, that included Theodore von Kármán (b. 1881), George de Hevesy (b. 1885), Leó Szilárd (b. 1898), Dennis Gabor (b. 1900), Eugene Wigner (b. 1902), Edward Teller (b. 1908), and Paul Erdős (b. 1913). Collectively, they were sometimes known as Martians. Wigner was a year ahead of von Neumann at the Lutheran School. When asked why the Hungary of his generation had produced so many geniuses, Wigner, who won the Nobel Prize in Physics in 1963, replied that von Neumann was the only genius.

Although his father insisted von Neumann attend school at the grade level appropriate to his age, he agreed to hire private tutors to give him advanced instruction in those areas in which he had displayed an aptitude. At the age of 15, he began to study advanced calculus under the renowned analyst Gábor Szegő. On their first meeting, Szegő was so astounded with the boy’s mathematical talent that he was brought to tears. By the age of 19, von Neumann had published two major mathematical papers, the second of which gave the modern definition of ordinal numbers, which superseded Georg Cantor’s definition. Von Neumann entered Pázmány Péter University in Budapest, as a Ph.D. candidate in mathematics in 1923, even though his father tried to steer him towards chemical engineering as a more profitable career. For his doctoral thesis, he chose to produce an axiomatization of Cantor’s set theory. He passed his final examinations for his Ph.D. in 1926 and then went to the University of Göttingen on a grant from the Rockefeller Foundation to study mathematics under David Hilbert. He completed his habilitation on December 13, 1927, and he started his lectures as a privatdozent at the University of Berlin in 1928, being the youngest person (24 years old) ever elected privatdozent in its history in any subject. By the end of 1927, von Neumann had published 12 major papers in mathematics, and by the end of 1929, 32 papers, at a rate of nearly one major paper per month. In 1929, he briefly became a privatdozent at the University of Hamburg, where the prospects of becoming a tenured lecturer were better, but in October of that year a better offer presented itself when he was invited to Princeton University in Princeton, New Jersey. In 1933, he was offered a lifetime professorship on the faculty of the Institute for Advanced Study in Princeton, which is separate from the university, and had been founded 3 years earlier. He remained a mathematics professor there until his death.

Von Neumann’s personal values are pretty much an open book. He liked to eat and drink, and his second wife, Klara, said that “he could count everything except calories”. He enjoyed Yiddish and crude humor (especially limericks). He was a non-smoker. At Princeton he received complaints for regularly playing extremely loud German march music on his gramophone, which distracted those in neighboring offices, including Albert Einstein, from their work. Von Neumann did some of his best work in noisy, chaotic environments, and once admonished his wife for preparing a quiet study for him to work in. He never used it, preferring the couple’s living room with its television playing loudly. Despite being a notoriously bad driver, he nonetheless enjoyed driving—frequently while reading a book—occasioning numerous arrests, as well as accidents. When Cuthbert Hurd hired him as a consultant to IBM, Hurd often quietly paid the fines for his traffic tickets. Von Neumann once said,

I was proceeding down the road. The trees on the right were passing me in orderly fashion at 60 miles per hour. Suddenly one of them stepped in my path.

The paradox that intrigues me concerns his work on the Manhattan project. He was called in, for several weeks at a time, to help solve the problem of getting the fissionable material in a nuclear bomb to explode. Without von Neumann’s equations on implosion it is unlikely that the Manhattan project would have been successful, certainly not at the rate that it was. Without getting too technical the problem is fairly easy to state simplistically. To get fissionable material to set off an explosive chain reaction it has to be of a certain shape, mass, and density. Von Neumann worked on the concept of an explosive lens that, via conventional explosives, would cause the fissionable material to implode, forcing it into a compact spherical shape that would trigger a nuclear explosion.  As best as I can tell, von Neumann saw this as a technical problem, and was not particularly concerned about the lives that would be lost should the bomb be detonated. Indeed, he was present at several experimental explosions set off in the New Mexico desert, and it seems likely that his exposure to radioactive material is what caused the cancer that killed him.

After the war he became what many see as the prototype for Dr Strangelove in that he advocated stockpiling nuclear weapons in the arms race to create what he called Mutually Assured Destruction (MAD) between the Soviet Union and the United States. His reasoning was that MAD, through stockpiling weapons, would guarantee that they would not be used, rather than the opposite. No rational leader would initiate a first strike if the result would be not just the destruction of the other party, but one’s own destruction also. This reasoning is based, in part, on game theory (which he created), and assumes that the participants in the “game” are rational. That might have been true in von Neumann’s time, but I’m not sure about now. Not least, there are many more countries stockpiling nuclear weapons these days, so the “game” has become considerably more complex.

In 1955, von Neumann was diagnosed with what was either bone or pancreatic cancer. He was not able to accept the proximity of his own death very well, and he invited a Roman Catholic priest, Father Anselm Strittmatter, O.S.B., to visit him for consultation. Von Neumann reportedly said, “So long as there is the possibility of eternal damnation for nonbelievers it is more logical to be a believer at the end,” essentially saying that Pascal had a point. Father Strittmatter administered the last rites to him. On his deathbed, Von Neumann entertained his brother by reciting, by heart and word-for-word, the first few lines of each page of Goethe’s Faust. He died at age 53 on February 8, 1957, at the Walter Reed Army Medical Center in Washington, D.C., under military security lest he reveal military secrets while heavily medicated.

Von Neumann’s wife noted: “He likes sweets and rich dishes, preferably with a good nourishing sauce, based on cream.  He loves Mexican food.  When he was stationed at Los Alamos… he would drive 120 miles to dine at a favorite Mexican restaurant.” This gives you a lot of options to celebrate the man, but I’ll go with pollo a la crema, a classic Mexican dish. You’ll need crema Mexicana, but if you cannot find it, use a mix of half and half heavy cream and sour cream. Crema Mexicana is a cultured cream with a sour, tangy taste, used in sauces.

Pollo a la Crema


1 tbsp olive oil
2 boneless chicken breasts, cut into strips
1 onion, peeled and sliced
½ cup fresh mushrooms, sliced
½ cup green pepper, seeded and cut into strips
½ tbsp Spanish paprika
½ cup rich chicken stock
1 cup crema Mexicana


Heat the olive oil in large skillet over medium heat. Sauté the chicken strips, peppers and onion until the chicken is cooked on the outside and the onions and peppers are soft. Add the cream, mushrooms, paprika and chicken stock. Bring to a boil, uncovered, and simmer for about 5 minutes, or the chicken is tender. Do not overcook. The sauce may be a little thin, but it should be creamy.

Serve hot immediately with refried beans, rice, and flour tortillas.

Jan 272016

by Lewis Carroll (Charles Lutwidge Dodgson),photograph,2 June 1857

Today is the birthday (1832) of Charles Lutwidge Dodgson, better known by his pen name Lewis Carroll, an English writer, mathematician, logician, Anglican deacon, and photographer. His most famous works are Alice’s Adventures in Wonderland, and its sequel Through the Looking-Glass, but his work in mathematics and logic, though limited in scope and much less well known, is of enduring value.

I’ve had a hard time appreciating the Alice books all of my life. When I was 4 years old my father read me the first chapter of Wonderland as a bedtime story, and that night I had a nightmare that I still remember vividly—everything in the world swirling in a kaleidoscopic jumble. For decades thereafter I could not hear or read the tales, see the classic illustrations, or watch depictions in films without recoiling in horror. I’m a little better now. In fact I managed to control my infantile fears long enough to write a post on the Mad Hatter here 3 years ago: https://www.bookofdaystales.com/mad-hatter-day/ For the moment I’ll pass over these books and return a little later. Meanwhile, a little about his personal life, then his mathematics and photography, plus minor quirks.


During his early youth, Dodgson was educated at home in Croft-on-Tees in North Yorkshire. His reading lists preserved in the family archives testify to a precocious intellect: at the age of seven, he was reading books such as The Pilgrim’s Progress. He also suffered from a stammer – a condition shared by most of his siblings – that often influenced his social life throughout his years. At the age of twelve, he was sent to Richmond Grammar School (now part of Richmond School) in nearby Richmond.

In 1846, Dodgson entered Rugby School where he was evidently unhappy, as he wrote some years after leaving:

I cannot say … that any earthly considerations would induce me to go through my three years again … I can honestly say that if I could have been … secure from annoyance at night, the hardships of the daily life would have been comparative trifles to bear.

Scholastically, though, he excelled with apparent ease. “I have not had a more promising boy at his age since I came to Rugby”, observed mathematics master R. B. Mayor.

He left Rugby at the end of 1849 and entered Oxford University in May 1850 as a member of his father’s old college, Christ Church. He had been at Oxford only two days when he received a summons home. His mother had died of “inflammation of the brain” – perhaps meningitis or a stroke – at the age of 47. His early academic career wavered between high promise and irresistible distraction. He did not always work hard, but was exceptionally talented in mathematics and achievement came easily to him. In 1852, he was awarded first-class honours in Mathematics Moderations, and was shortly thereafter nominated to a Studentship by his father’s old friend Canon Edward Pusey. In 1854, he obtained first-class honours in the Final Honours School of Mathematics, placing first on the schools list. He remained at Christ Church studying and teaching, but the next year he failed an important scholarship through his self-confessed inability to apply himself to study. Even so, his talent as a mathematician won him the Christ Church Mathematical Lectureship in 1855, which he continued to hold for the next twenty-six years. Despite early unhappiness, Dodgson was to remain at Christ Church, in various capacities, until his death.


Traces of Dodgson (and Alice) can be found all around Christ Church to this day. For example, almost opposite opposite Christ Church is Alice’s Shop on St Aldate’s. It was formerly frequented in Victorian times by Alice Liddell, the inspiration for Alice’s Adventures in Wonderland and Through the Looking-Glass and What Alice Found There, who used to buy sweets there. She lived at Christ Church with her father Henry Liddell, who was Dean of the College and Cathedral.

The shop was featured as the Old Sheep Shop in Through the Looking-Glass. One of the original John Tenniel illustrations shows the inside of the shop. It was used as a setting in Chapter 5 of the book (Wool and Water) and is owned by a sheep in the story:

She looked at the Queen, who seemed to have suddenly wrapped herself up in wool. Alice rubbed her eyes, and looked again. She couldn’t make out what had happened at all. Was she in a shop? And was that really — was it really a sheep that was sitting on the other side of the counter? Rub as she could, she could make nothing more of it: she was in a little dark shop, leaning with her elbows on the counter, and opposite to her was an old Sheep, sitting in an arm-chair knitting, and every now and then leaving off to look at her through a great pair of spectacles.


The shop is characteristic of the dream-like qualities within the Looking-Glass world, in that every time Alice tries to focus on a specific object on its many shelves it changes shape and shifts to another shelf. At another point the shop itself vanishes and Alice finds herself outside with the sheep in a boat, having been given a pair of knitting needles which turn into oars in her hands. The sheep herself continues to make scornful, personal remarks and then finally, on appearing back in the shop, sells Alice an egg, which promptly turns into Humpty Dumpty.

The overwhelming commercial success of the first Alice book changed Dodgson’s life in many ways. The fame of his alter ego “Lewis Carroll” soon spread around the world. He was inundated with fan mail and with sometimes unwanted attention. According to one popular, but almost certainly apocryphal, story, Queen Victoria herself enjoyed Alice In Wonderland so much that she commanded that he dedicate his next book to her, and was accordingly presented with his next work, a scholarly mathematical volume entitled An Elementary Treatise on Determinants. Dodgson himself vehemently denied this story, commenting “… It is utterly false in every particular: nothing even resembling it has occurred”; and it is unlikely for other reasons. As T.B. Strong comments in a Times article, “It would have been clean contrary to all his practice to identify [the] author of Alice with the author of his mathematical works.” He also began earning quite substantial sums of money, but continued with his post at Christ Church even though he disliked teaching.


In 1856, Dodgson took up the new art form of photography under the influence first of his uncle Skeffington Lutwidge, and later of his Oxford friend Reginald Southey. He soon excelled at the art and became a well-known gentleman-photographer, and he seems even to have toyed with the idea of making a living out of it in his very early years.

A study by Roger Taylor and Edward Wakeling exhaustively lists every surviving print, and Taylor calculates that just over half of his surviving work depicts young girls, though about 60% of his original photographic portfolio is now missing. Dodgson also made many studies of men, women, boys, and landscapes; his subjects also include skeletons, dolls, dogs, statues, paintings, and trees. His pictures of children were taken with a parent in attendance and many of the pictures were taken in the Liddell garden because natural sunlight was required for good exposures.

lc13 lc11 lc5

He also found photography to be a useful entrée into higher social circles. During the most productive part of his career, he made portraits of notable sitters such as John Everett Millais, Ellen Terry, Dante Gabriel Rossetti, Julia Margaret Cameron, Michael Faraday, Lord Salisbury, and Alfred, Lord Tennyson.


By the time that Dodgson abruptly ceased photography (1880), he had established his own studio on the roof of Tom Quad at Christ Church, created around 3,000 images, and was a master of the medium, though fewer than 1,000 images have survived time and deliberate destruction. Dodgson reported that he stopped taking photographs because keeping his studio working was too time-consuming. He used the wet collodion process which required considerable skill and experience.


Controversy continues to surround Dodgson’s interest in Alice and other girls as photographic models. I honestly cannot make up my mind as to whether his interest was prurient, or simply part of a common Victorian aesthetic. For me, chronocentrism is as intriguing and troublesome as ethnocentrism. It’s impossible for me to put myself into the mind of a Victorian mathematician, or in the moral milieu of the time.

lc20 lc21

Dodgson invented a writing tablet called the nyctograph that allowed note-taking in the dark, thus eliminating the need to get out of bed and strike a light when one woke with an idea. I find this so incredibly personal; I have never had the urge to wake in the middle of the night and write my ideas down. The device consisted of a gridded card with sixteen squares and system of symbols representing an alphabet of Dodgson’s design, using letter shapes similar to the Graffiti writing system on a Palm device.

He also devised a number of games, including an early version of what today is known as Scrabble. He appears to have invented — or at least certainly popularized — the “doublet” (word ladder), a form of brain-teaser that is still popular today, changing one word into another by altering one letter at a time, each successive change always resulting in a genuine word. For instance, CAT is transformed into DOG by the following steps: CAT, COT, DOT, DOG.

Within the academic discipline of mathematics, Dodgson worked primarily in the fields of geometry, linear and matrix algebra, mathematical logic, and recreational mathematics, producing nearly a dozen books under his real name. Dodgson also developed new ideas in linear algebra (e.g., the first printed proof of the Kronecker-Capelli theorem), probability, and the study of elections (e.g., Dodgson’s method) and committees; some of this work was not published until well after his death.


His mathematical work attracted renewed interest in the late 20th century. Martin Gardner’s book on logic machines and diagrams, and William Warren Bartley’s posthumous publication of the second part of Carroll’s symbolic logic book have sparked a reevaluation of Carroll’s contributions to symbolic logic. Robbins’ and Rumsey’s investigation of Dodgson condensation, a method of evaluating determinants, led them to the Alternating Sign Matrix conjecture, now a theorem. The discovery in the 1990s of additional ciphers that Carroll had constructed, in addition to his “Memoria Technica”, showed that he had employed sophisticated mathematical ideas in their creation.

Dodgson’s life remained little changed over the last twenty years of his life, throughout his growing wealth and fame. He continued to teach at Christ Church until 1881, and remained in residence there until his death. He died of pneumonia following influenza on 14 January 1898 at his sisters’ home, “The Chestnuts” in Guildford. He was two weeks away from turning 66 years old. He is buried in Guildford at the Mount Cemetery.


Here’s a few favorite quotations:

It’s no use going back to yesterday, because I was a different person then.

She generally gave herself very good advice, (though she very seldom followed it).

“But I don’t want to go among mad people,” Alice remarked.
“Oh, you can’t help that,” said the Cat: “we’re all mad here. I’m mad. You’re mad.”
“How do you know I’m mad?” said Alice.
“You must be,” said the Cat, “or you wouldn’t have come here.”

“Begin at the beginning,” the King said, very gravely, “and go on till you come to the end: then stop.”

“Would you tell me, please, which way I ought to go from here?”
“That depends a good deal on where you want to get to.”
“I don’t much care where –”
“Then it doesn’t matter which way you go.”

“I wonder if the snow loves the trees and fields, that it kisses them so gently? And then it covers them up snug, you know, with a white quilt; and perhaps it says “Go to sleep, darlings, till the summer comes again.”

One of the deep secrets of life is that all that is really worth the doing is what we do for others.

If everybody minded their own business, the world would go around a great deal faster than it does.

“Alice laughed. ‘There’s no use trying,’ she said. ‘One can’t believe impossible things.’
I daresay you haven’t had much practice,’ said the Queen. ‘When I was your age, I always did it for half-an-hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast.

I’m not strange, weird, off, nor crazy, my reality is just different from yours.

If you drink much from a bottle marked ‘poison’ it is certain to disagree with you sooner or later.

English mathematician, writer and photographer Charles Lutwidge Dodgson, better known as Lewis Carroll (1832 - 1898) with Mrs George Macdonald and four children relaxing in a garden. (Photo by Lewis Carroll/Getty Images)

In Hints for Etiquette: Or, Dining Out Made Easy, Dodgson mocks dining habits of his era:

As caterers for the public taste, we can conscientiously recommend this book to all diners-out who are perfectly unacquainted with the usages of society. However we may regret that our author has confined himself to warning rather than advice, we are bound in justice to say that nothing here stated will be found to contradict the habits of the best circles. The following examples exhibit a depth of penetration and a fullness of experience rarely met with:


In proceeding to the dining-room, the gentleman gives one arm to the lady he escorts– it is unusual to offer both.


The practice of taking soup with the next gentleman but one is now wisely discontinued; but the custom of asking your host his opinion of the weather immediately on the removal of the first course still prevails.


To use a fork with your soup, intimating at the same time to your hostess that you are reserving the spoon for beefsteaks, is a practice wholly exploded.


On meat being placed before you, there is no possible objection to your eating it, if so disposed; still in all such delicate cases, be guided entirely by the conduct of those around you.


It is always allowable to ask for artichoke jelly with your boiled venison; however there are houses where this is not supplied.


The method of helping roast turkey with two carving-forks is praticable, but deficient in grace.

I am so thoroughly reminded of Mrs Beeton’s rules and admonitions by this parody. Here she is on oysters – tribute to the Walrus and the Carpenter:



  1. INGREDIENTS.—3 dozen oysters, 2 oz. butter, 1 tablespoonful of ketchup, a little chopped lemon-peel, 1/2 teaspoonful of chopped parsley.

 Mode.—Boil the oysters for 1 minute in their own liquor, and drain them; fry them with the butter, ketchup, lemon-peel, and parsley; lay them on a dish, and garnish with fried potatoes, toasted sippets, and parsley. This is a delicious delicacy, and is a favourite Italian dish.

 Time.—5 minutes. Average cost for this quantity, 1s. 9d.

 Seasonable from September to April.

 Sufficient for 4 persons.


THE EDIBLE OYSTER:—This shell-fish is almost universally distributed near the shores of seas in all latitudes, and they especially abound on the coasts of France and Britain. The coasts most celebrated, in England, for them, are those of Essex and Suffolk. Here they are dredged up by means of a net with an iron scraper at the mouth, that is dragged by a rope from a boat over the beds. As soon as taken from their native beds, they are stored in pits, formed for the purpose, furnished with sluices, through which, at the spring tides, the water is suffered to flow. This water, being stagnant, soon becomes green in warm weather; and, in a few days afterwards, the oysters acquire the same tinge, which increases their value in the market. They do not, however, attain their perfection and become fit for sale till the end of six or eight weeks. Oysters are not considered proper for the table till they are about a year and a half old; so that the brood of one spring are not to be taken for sale, till, at least, the September twelvemonth afterwards.



INGREDIENTS.—Oysters, say 1 pint, 1 oz. butter, flour, 2 tablespoonfuls of white stock, 2 tablespoonfuls of cream; pepper and salt to taste; bread crumbs, oiled butter.

Mode.—Scald the oysters in their own liquor, take them out, beard them, and strain the liquor free from grit. Put 1 oz. of batter into a stewpan; when melted, dredge in sufficient flour to dry it up; add the stock, cream, and strained liquor, and give one boil. Put in the oysters and seasoning; let them gradually heat through, but not boil. Have ready the scallop-shells buttered; lay in the oysters, and as much of the liquid as they will hold; cover them over with bread crumbs, over which drop a little oiled butter. Brown them in the oven, or before the fire, and serve quickly, and very hot.

Time.—Altogether, 1/4 hour.

Average cost for this quantity, 3s. 6d.

Sufficient for 5 or 6 persons.


Prepare the oysters as in the preceding recipe, and put them in a scallop-shell or saucer, and between each layer sprinkle over a few bread crumbs, pepper, salt, and grated nutmeg; place small pieces of butter over, and bake before the fire in a Dutch oven. Put sufficient bread crumbs on the top to make a smooth surface, as the oysters should not be seen.

Time.—About 1/4 hour.

Average cost, 3s. 2d.

Seasonable from September to April.


  1. INGREDIENTS.—1 pint of oysters, 1 oz. of butter, flour, 1/3 pint of cream; cayenne and salt to taste; 1 blade of pounded mace.

 Mode.—Scald the oysters in their own liquor, take them out, beard them, and strain the liquor; put the butter into a stewpan, dredge in sufficient flour to dry it up, add the oyster-liquor and mace, and stir it over a sharp fire with a wooden spoon; when it comes to a boil, add the cream, oysters, and seasoning. Let all simmer for 1 or 2 minutes, but not longer, or the oysters would harden. Serve on a hot dish, and garnish with croutons, or toasted sippets of bread. A small piece of lemon-peel boiled with the oyster-liquor, and taken out before the cream is added, will be found an improvement.

 Time.—Altogether 15 minutes.

 Average cost for this quantity, 3s. 6d.

 Seasonable from September to April.

 Sufficient for 6 persons.

 THE OYSTER AND THE SCALLOP.—The oyster is described as a bivalve shell-fish, having the valves generally unequal. The hinge is without teeth, but furnished with a somewhat oval cavity, and mostly with lateral transverse grooves. From a similarity in the structure of the hinge, oysters and scallops have been classified as one tribe; but they differ very essentially both in their external appearance and their habits. Oysters adhere to rocks, or, as in two or three species, to roots of trees on the shore; while the scallops are always detached, and usually lurk in the sand.

 OYSTER PATTIES (an Entree).

289. INGREDIENTS.—2 dozen oysters, 2 oz. butter, 3 tablespoonfuls of cream, a little lemon-juice, 1 blade of pounded mace; cayenne to taste.

Mode.—Scald the oysters in their own liquor, beard them, and cut each one into 3 pieces. Put the butter into a stewpan, dredge in sufficient flour to dry it up; add the strained oyster-liquor with the other ingredients; put in the oysters, and let them heat gradually, but not boil fast. Make the patty-cases as directed for lobster patties, No. 277: fill with the oyster mixture, and replace the covers.

Time.—2 minutes for the oysters to simmer in the mixture.

Average cost, exclusive of the patty-cases, 1s. 1d.

Seasonable from September to April.

THE OYSTER FISHERY.—The oyster fishery in Britain is esteemed of so much importance, that it is regulated by a Court of Admiralty. In the month of May, the fishermen are allowed to take the oysters, in order to separate the spawn from the cultch, the latter of which is thrown in again, to preserve the bed for the future. After this month, it is felony to carry away the cultch, and otherwise punishable to take any oyster, between the shells of which, when closed, a shilling will rattle.


  1. Put them in a tub, and cover them with salt and water. Let them remain for 12 hours, when they are to be taken out, and allowed to stand for another 12 hours without water. If left without water every alternate 12 hours, they will be much better than if constantly kept in it. Never put the same water twice to them.


 INGREDIENTS.—1/2 pint of oysters, 2 eggs, 1/2 pint of milk, sufficient flour to make the batter; pepper and salt to taste; when liked, a little nutmeg; hot lard.

 Mode.—Scald the oysters in their own liquor, beard them, and lay them on a cloth, to drain thoroughly. Break the eggs into a basin, mix the flour with them, add the milk gradually, with nutmeg and seasoning, and put the oysters in the batter. Make some lard hot in a deep frying-pan, put in the oysters, one at a time; when done, take them up with a sharp-pointed skewer, and dish them on a napkin. Fried oysters are frequently used for garnishing boiled fish, and then a few bread crumbs should be added to the flour.

Time.—5 or 6 minutes.

Average cost for this quantity, 1s. 10d.

Seasonable from September to April.

Sufficient for 3 persons.

EXCELLENCE OF THE ENGLISH OYSTER.—The French assert that the English oysters, which are esteemed the best in Europe, were originally procured from Cancalle Bay, near St. Malo; but they assign no proof for this. It is a fact, however, that the oysters eaten in ancient Rome were nourished in the channel which then parted the Isle of Thanet from England, and which has since been filled up, and converted into meadows.


“O Oysters,” said the Carpenter,
“You’ve had a pleasant run!
Shall we be trotting home again?’
But answer came there none–
And this was scarcely odd, because
They’d eaten every one.


May 182015


Today is the birthday (1048) of Omar Khayyám; born Ghiyāth ad-Dīn Abu’l-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām Nīshāpūrī (Persian: ‏غیاثالدینابوالفتحعمرابراهیمخیامنیشابورﻯ‎, ), Persian mathematician, astronomer, philosopher, and poet. He also wrote treatises on mechanics, geography, mineralogy, music, and Islamic theology. He was born in Nishapur, in northeastern Iran also known as Persia, and at a young age he moved to Samarkand and obtained his education there. Afterwards he moved to Bukhara and became established as one of the major mathematicians and astronomers of the medieval period. He is the author of one of the most important treatises on algebra written before modern times, the Treatise on Demonstration of Problems of Algebra, which includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle. He also made major contributions to calendar reform which were more accurate than the Gregorian reform made centuries later. His significance as a philosopher and teacher, and his few extant philosophical works, have not received the same attention as his scientific and poetic writings. Al-Zamakhshari referred to him as “the philosopher of the world”. He taught the philosophy of Avicenna for decades in Nishapur.

Outside Iran and Persian-speaking countries, Khayyám has had an impact on literature and societies through the translation of his works and popularization by other scholars. The greatest such impact was in English-speaking countries; the English scholar Thomas Hyde (1636–1703) was the first non-Persian to study him. The most influential of all was Edward FitzGerald (1809–83),[6] who made Khayyám the most famous poet of the East in the West through his celebrated translation and adaptations of Khayyám’s rather small number of quatrains (Persian: رباعیات‎ rubāʿiyāt) in the Rubaiyat of Omar Khayyam.

He spent part of his childhood in the town of Balkh (in present-day northern Afghanistan), studying under the well-known scholar Sheikh Muhammad Mansuri. He later studied under Imam Mowaffaq Nishapuri, who was considered one of the greatest teachers of the Khorasan region. Throughout his life, Omar Khayyám was tireless in his efforts; by day he would teach algebra and geometry, in the evening he would attend the Seljuq court as an adviser of Malik-Shah I, and at night he would study astronomy and complete important aspects of the Jalali calendar.

Omar Khayyám’s years in Isfahan were very productive ones, but after the death of the Seljuq Sultan Malik-Shah I (presumably by the Assassins sect), the Sultan’s widow turned against him as an adviser, and as a result, he soon set out on his Hajj or pilgrimage to Mecca and Medina. He was then allowed to work as a court astrologer, and was permitted to return to Nishapur, where he was renowned for his works, and continued to teach mathematics, astronomy and even medicine.


I’ll spare you a long rambling discourse on the importance of his mathematical work and simply say that he was centuries ahead of the West which owed him a great debt when his works were finally discovered and translated. I get a little tired of reminding Westerners what a great debt in general the West owes the Medieval Islamic world, not just in preserving the great works of the classical Greek world (including Euclid, Pythagoras, Plato and Aristotle – which Westerners undervalued and generally lost), but in moving their ideas forward. From idiotic Western history textbooks you might, if you are lucky, get a nod to the great Islamic writers of the age, but otherwise you get the impression that the West moved forward all on its own. Particularly in the modern political climate people like Khayyám deserve a great deal more respect. I take it as a personal mission here to right this wrong. See, for example:




Let me simply say that it took the West 600 years to catch up with Khayyám in the fields of geometry and algebra, and even then many of their “advances” were eventually proven wrong !!


The Jalali calendar was introduced by Omar Khayyám alongside other mathematicians and astronomers in Nishapur. Today it is one of the oldest calendars in the world as well as the most accurate solar calendar still in use. Since the calendar uses astronomical calculation for determining the vernal equinox, it has no intrinsic error, but this makes it an observation based calendar.

The Jalali calendar remained in use across Greater Iran from the 11th to the 20th centuries. It is the basis of the Iranian calendar, which is followed today in Iran and Afghanistan. While the Jalali calendar is more accurate than the Gregorian, it is based on actual solar transit, similar to Hindu calendars, and requires an ephemeris (table) for calculating dates. The lengths of the months can vary between 29 and 31 days depending on the moment when the sun crosses into a new zodiacal area (an attribute common to most Hindu calendars). This means that seasonal errors are lower than in the Gregorian calendar.

Omar Khayyám was a notable poet during the reign of the Seljuk ruler Malik-Shah I. Scholars believe he wrote about a thousand four-line verses (quatrains) or rubaiyat, many now lost. He was introduced to the English-speaking world through the Rubáiyát of Omar Khayyám, which are poetic, rather than literal, translations by Edward FitzGerald (1809–1883). Other English translations of parts of the rubáiyát  exist, but FitzGerald’s are the most well known. Ironically, FitzGerald’s translations reintroduced Khayyám to Iranians who had long ignored.


Here’s a small sample – well known in English:

The Moving Finger writes; and, having writ,

 Moves on: nor all thy Piety nor Wit,

Shall lure it back to cancel half a Line,

 Nor all thy Tears wash out a Word of it.


A Book of Verses underneath the Bough,

 A Jug of Wine, a Loaf of Bread—and Thou,

Beside me singing in the Wilderness,

 And oh, Wilderness is Paradise enow.


And that inverted Bowl we call The Sky,

 Whereunder crawling coop’t we live and die,

Lift not thy hands to It for help—for It

 Rolls impotently on as Thou or I.


I sent my Soul through the Invisible,

 Some letter of that After-life to spell:

And by and by my Soul return’d to me,

 And answer’d “I Myself am Heav’n and Hell:”

Modern scholars are generally dissatisfied with Fitzgerald’s translation, believing it to be more Western than Eastern, not truly reflecting Khayyám’s philosophy. But if it gets you started, I’m happy. However, it’s a good plan to seek out more literal translations with commentary.

Anything approximating a usable recipe from Khayyám’s era does not exist. Even recipes from as late as the 16th century need heavy interpretation. So instead here is a recipe for Ash Reshteh a modern bean and noodle soup that has its roots in medieval Persia – and, yes, Persia had noodles centuries before Marco Polo supposedly brought them back from China. I’m using a video because, as ever, I am pressed for time.



Oct 202014


Today is the birthday (1632) of Sir Christopher Michael Wren PRS, one of the most highly acclaimed English architects in history. He was accorded responsibility for rebuilding 52 churches in the City of London after the Great Fire in 1666, including his masterpiece, St. Paul’s Cathedral, on Ludgate Hill in London, completed in 1710 (see https://www.bookofdaystales.com/great-fire-of-london/ ). What many people do not realize is that Wren was a notable anatomist, astronomer, geometer, and mathematician-physicist, as well as an architect, and was instrumental in founding the Royal Society, the prime scientific society in Britain to this day. His scientific work was highly regarded by Isaac Newton and Blaise Pascal.

Here’s a small gallery of Wren’s major architectural works just so that I do not ignore that aspect of his life completely.

wren8 wren7 wren6 wren5 wren3 wren2

Now, however, I would like to outline his accomplishments outside of architecture. On 25 June 1650, Wren entered Wadham College, Oxford, where he studied Latin and the works of Aristotle. There was no formal scientific education at Oxford at that time, but there was a circle of scientists who worked together outside their formal studies. Wren became closely associated with John Wilkins, the Warden of Wadham. The Wilkins circle was a group whose activities led to the formation of the Royal Society, consisting of a number of distinguished mathematicians, and experimental natural philosophers (physicists, biologists and chemists), including Robert Boyle and Robert Hooke (see https://www.bookofdaystales.com/robert-hooke/ ). He graduated with a B.A. in 1651, and two years later received his M.A. At Oxford then, as now, the M.A. is awarded after 2 years without further study. The degree system is based on the old trade guilds where apprentices become bachelors of the guild, and having pursued their craft for 2 years become masters by producing a “masterpiece.”

Portrait of Sir Christopher Wren

Having received his M.A. in 1653, Wren was elected a fellow of All Souls College in the same year and began an active period of research and experiment in Oxford. His days as a fellow of All Souls ended when he was appointed Professor of Astronomy at Gresham College in London in 1657. He was provided with a set of rooms and a stipend and was required to give weekly lectures in both Latin and English to all who wished to attend; admission was free. Wren took up this new work with enthusiasm. He continued to meet the men with whom he had frequent discussions in Oxford. They attended his London lectures and in 1660, initiated formal weekly meetings. It was from these meetings that the Royal Society, England’s premier scientific body, was to develop. He undoubtedly played a major role in these meetings; his great breadth of expertise in so many different subjects helping in the exchange of ideas between the various scientists.

In 1662, they proposed a society “for the promotion of Physico-Mathematicall Experimental Learning.” This body received its Royal Charter from Charles II and “The Royal Society of London for Improving Natural Knowledge” was formed. In addition to being a founder member of the Society, Wren was president of the Royal Society from 1680 to 1682.

In 1661, Wren was elected Savilian Professor of Astronomy at Oxford, and in 1669 he was appointed Surveyor of Works to Charles II. From 1661 until 1668 Wren’s life was based in Oxford, although his attendance at meetings of the Royal Society meant that he had to make occasional trips to London.

The main sources for Wren’s scientific achievements are the records of the Royal Society. His scientific works ranged from astronomy, optics, the problem of finding longitude at sea, cosmology, mechanics, microscopy, surveying, medicine and meteorology. He observed, measured, dissected, built models, and employed, invented and improved a variety of instruments. It was also around these times that his attention turned to architecture. One of Wren’s friends, another great scientist and architect and a fellow Westminster Schoolboy, Robert Hooke said of him “Since the time of Archimedes there scarce ever met in one man in so great perfection such a mechanical hand and so philosophical mind.”


When a fellow of All Souls, Wren constructed a transparent beehive for scientific observation; he began observing the moon, which was to lead to the invention of micrometers for the telescope. He experimented on terrestrial magnetism and had taken part in medical experiments while at Wadham College, performing the first successful injection of a substance into the bloodstream (of a dog).


In Gresham College, he did experiments involving determining longitude through magnetic variation and through lunar observation to help with navigation, and helped construct a 35-foot (11 m) telescope with Sir Paul Neile. Wren also studied and improved the microscope and telescope at this time. He had been making observations of the planet Saturn from around 1652 with the aim of explaining its appearance. His hypothesis was written up in De corpore saturni but before the work was published, Huygens presented his theory of the rings of Saturn. Immediately Wren recognized this as a better hypothesis than his own and De corpore saturni was never published. In addition, he constructed an exquisitely detailed lunar model and presented it to the king. Also his contribution to mathematics should be noted; in 1658, he found the length of an arc of the cycloid using an exhaustion proof based on dissections to reduce the problem to summing segments of chords of a circle which are in geometric progression.


A year into Wren’s appointment as a Savilian Professor in Oxford, the Royal Society was created and Wren became an active member. As Savilian Professor, Wren studied mechanics thoroughly, especially elastic collisions and pendulum motions. He also directed his far-ranging intelligence to the study of meteorology: in 1662 he invented the tipping bucket rain gauge and, in 1663, designed a “weather-clock” that would record temperature, humidity, rainfall and barometric pressure. A working weather clock based on Wren’s design was completed by Robert Hooke in 1679.


In addition, Wren experimented on muscle functionality, hypothesizing that the swelling and shrinking of muscles might proceed from a fermentative motion arising from the mixture of two heterogeneous fluids. Although this is incorrect, it was at least founded upon observation and may mark a new outlook on medicine: specialization.

Wren contributed to optics. He published a description of an engine to create perspective drawings and he discussed the grinding of conical lenses and mirrors. Out of this work came another of Wren’s important mathematical results, namely that the hyperboloid of revolution is a ruled surface. These results were published in 1669. In subsequent years, Wren continued with his work with the Royal Society, although after the 1680s his scientific interests seem to have waned: no doubt his architectural and official duties absorbed more time.

It was a problem posed by Wren that serves as an ultimate source to the conception of Newton’s Principia Mathematica Philosophiae Naturalis. Robert Hooke had theorized that planets, moving in a vacuum, describe orbits around the Sun because of a rectilinear inertial motion outward from the Sun and an accelerated motion towards the Sun. Wren’s challenge to Halley and Hooke, for the reward of a book worth thirty shillings, was to provide, within the context of Hooke’s hypothesis, a mathematical theory linking the Kepler’s laws with a specific force law. Halley took the problem to Newton for advice, prompting the latter to write a nine-page answer, De motu corporum in gyrum, which was later to be expanded into the Principia.


Wren also studied other areas, ranging from agriculture, ballistics, water and freezing, light and refraction, to name only a few. Thomas Birch’s History of the Royal Society is one of the most important sources of our knowledge not only of the origins of the Society, but also the day to day running of the Society. It is in these records that most of Wren’s known scientific works are recorded.

It was probably around this time that Wren was drawn into redesigning a battered St Paul’s Cathedral. Making a trip to Paris in 1665, Wren studied the architecture, which had reached a climax of creativity, and perused the drawings of Bernini, the great Italian sculptor and architect, who himself was visiting Paris at the time. Returning from Paris, he made his first design for St Paul’s. A week later, however, the Great Fire destroyed two-thirds of the city.

Additionally, he was sufficiently active in public affairs to be returned as Member of Parliament for Old Windsor in 1680, 1689 and 1690, but did not take his seat.

By 1669 Wren’s career was well established and it may have been his appointment as Surveyor of the King’s Works in early 1669 that persuaded him that he could finally afford to take a wife. In 1669 the 37-year-old Wren married his childhood neighbour, the 33-year-old Faith Coghill, daughter of Sir John Coghill of Bletchingdon. Little is known of Faith’s life or demeanor, but a love letter from Wren survives, which reads, in part:

I have sent your Watch at last & envy the felicity of it, that it should be soe near your side & soe often enjoy your Eye. … .but have a care for it, for I have put such a spell into it; that every Beating of the Balance will tell you ’tis the Pulse of my Heart, which labors as much to serve you and more trewly than the Watch; for the Watch I beleeve will sometimes lie, and sometimes be idle & unwilling … but as for me you may be confident I shall never …

This brief marriage produced two children: Gilbert, born October 1672, who suffered from convulsions and died at about 18 months old, and Christopher, born February 1675. The younger Christopher was trained by his father to be an architect. It was this Christopher that supervised the topping out ceremony of St Paul’s in 1710 and wrote the famous Parentalia, or, Memoirs of the family of the Wrens. Faith Wren died of smallpox on 3 September 1675. She was buried in the chancel of St Martin-in-the-Fields beside the infant Gilbert. A few days later Wren’s mother-in-law, Lady Coghill, arrived to take the infant Christopher back with her to Oxfordshire to raise.

In 1677, 17 months after the death of his first wife, Wren married once again. He married Jane Fitzwilliam, daughter of William FitzWilliam, 2nd baron FitzWilliam and his wife Jane Perry, the daughter of a prosperous London merchant.

She was a mystery to Wren’s friends and companions. Robert Hooke, who often saw Wren two or three times every week, had, as he recorded in his diary, never even heard of her, and was not to meet her till six weeks after the marriage. As with the first marriage, this too produced two children: a daughter Jane (1677–1702); and a son William, “Poor Billy” born June 1679, who was developmentally delayed.

Like the first, this second marriage was also brief. Jane Wren died of tuberculosis in September 1680. She was buried alongside Faith and Gilbert in the chancel of St Martin-in-the-Fields. Wren was never to marry again; he lived to be over 90 years old and of those years was married only nine.

The Wren family estate was at The Old Court House in the area of Hampton Court. He had been given a lease on the property by Queen Anne in lieu of salary arrears for building St Paul’s.[8] For convenience Wren also leased a house on St James’s Street in London. According to a 19th-century legend, he would often go to London to pay unofficial visits to St Paul’s, to check on the progress of “my greatest work”. On one of these trips to London, at the age of ninety, he caught a chill which worsened over the next few days. On 25 February 1723 a servant who tried to awaken Wren from his nap found that he had died.

Wren was laid to rest on 5 March 1723. His remains were placed in the south-east corner of the crypt of St Paul’s beside those of his daughter Jane, his sister Susan Holder, and her husband William. The plain stone plaque was written by Wren’s eldest son and heir, Christopher Wren, Jr. The inscription, which is also inscribed in a circle of black marble on the main floor beneath the centre of the dome, reads:



Here in its foundations lies the architect of this church and city, Christopher Wren, who lived beyond ninety years, not for his own profit but for the public good. Reader, if you seek his monument – look around you. Died 25 Feb. 1723, age 91.

It turns out that Wren had some interest in cookery as evidenced by a recipe for gooseberry wine recorded by the diarist John Evelyn. Among his manuscripts, now in the British Library, is a volume of “receipts” (recipes): for the stillroom, the sickroom and the kitchen. Those of cookery are now printed in this book:


The recipes range wide over the repertoire of the seventeenth-century household; from liver puddings to excellent syllabubs. They include items picked up on his travels in Europe, as well as favorites given him by friends, including that for gooseberry wine contributed by Sir Christopher Wren.


Living in southern China does not make it exactly easy for me to get hold of this book, so I have had to compromise. Go here and you will find an excellent recipe .http://www.theguardian.com/lifeandstyle/allotment/2011/jun/09/allotments-gardens It is more complex than Wren’s, I have no doubt, but fruit wines are all made in basically the same way: mash up the fruit, boil it, when cooled add yeast and sugar, let ferment, strain and bottle. Worth a shot.

Jun 192013



Today is the birthday (1623) of Blaise Pascal who gives the lie to the old phrase, “jack of all trades, master of none.” He was brilliant in so many spheres including mathematics, physics, philosophy, theology, and literature, as well as an ingenious inventor, using his abstract theories for concrete applications.  His work still resonates throughout our lives, whether you are jacking up a car with a hydraulic jack, internally basting a turkey with a syringe, stepping on the brakes, or simply eating olive oil made in a hydraulic press.  He was a thinking person’s thinker, and greatly to be admired.  Even if you have never heard of him before, he has touched your life in many ways.

Pascal was born in Clermont-Ferrand which sits on the plain of Limagne in the Massif Central, in central France.  It is the prefecture of the Puy-de-Dôme department within the province of Auvergne.  Pascal’s mother died when he was 3 years old, and his father, Étienne Pascal, who had an interest in science and mathematics decided to teach Blaise at home because he showed extraordinary intellectual ability at a very early age. By the age of 16 Pascal had produced his “Essai pour les coniques” (“Essay on Conics”) which includes his proof for what is now called Pascal’s theorem (if you are not happy with mathematics you don’t need to know).  This work was so precocious that when it was shown to René Descartes he scoffed and would not believe it had been written by a teenager.

After an unfortunate tussle with Cardinal Richlieu had been resolved, the cardinal appointed Pascal’s father as king’s commissioner of taxes in Rouen in 1639. Because of numerous uprisings in the city the tax records were a complete disaster. In 1642, in an effort to ease his father’s endless, exhausting calculations, and recalculations, of taxes owed and paid, Pascal, 18 years old, constructed a mechanical calculator capable of addition and subtraction, called Pascal’s calculator or the Pascaline —  first step on the road to more advanced calculating machines, and ultimately the computer.

Pascal’s contributions to mathematics over the course of his life are staggering.  There’s his many uses of the so-called Pascal’s Triangle (see illustration), which you may have encountered in high school math.  There’s his foundational work in probability theory, that he partnered on with Pierre de Fermat, and which produced key concepts (such as the “weighted average”) that are fundamental to the computational aspects of modern economics and social science.  And, dear to my heart, he showed that no matter how rigorous a proof is in mathematics it ultimately rests on propositions that cannot be proven and must be accepted on faith alone because they are “self evident.” Mathematics, the deity of all science, is grounded in faith !!!!

Besides work in mathematics, Pascal made major contributions to physical science.  He finally overturned the assertion by Aristotle that vacuums cannot exist, building on the work of Galileo and Torricelli, and proposed methods for creating vacuum pumps.  He established a fundamental principle of the transmission of pressure in fluids now known as Pascal’s Law, which led him to develop hydraulic systems such as the hydraulic lift and the syringe.

As if all of this were not enough, Pascal in later life made significant inroads into theology, philosophy, and French literature due to a radical personal change in his life.  On 23 November 1654, between 10:30 and 12:30 at night, Pascal had an intense religious vision and immediately recorded the experience in a brief note to himself which began: “Fire. God of Abraham, God of Isaac, God of Jacob, not of the philosophers and the scholars…” and concluded by quoting Psalm 119:16: “I will not forget thy word. Amen.” He sewed this document into his coat and always transferred it when he changed clothes. A servant discovered it only by chance after his death. Subsequent to his vision he abandoned mathematics and science, and devoted himself to philosophical writings, culminating in Pensées which is widely considered to be a masterpiece of reasoning as well as a landmark in French prose. In Pensées, Pascal surveys several philosophical paradoxes: infinity and nothing, faith and reason, soul and matter, death and life, meaning and vanity — culminating in Pascal’s Wager (the idea that it is better to believe in God than not because the rewards are so great if God exists, and you lose nothing if he does not).

Pascal’s last major achievement, returning to his mechanical genius, was inaugurating what was perhaps the first bus line, moving passengers within Paris in a carriage with many seats. He died in 1662 at the age of 39 in intense pain caused by a malignant tumor that spread to his brain.  Such immense accomplishments in such a short span.

I had to think long and hard about a recipe suitable for the memory of Pascal.  After all, the syringe can be used for many things including cake decorating, squirting brandy into baked mince pies, internally basting turkey meat before roasting, and, with the aid of tubing and gelling agents, making all manner of wild and whacky vegetable forms of “spaghetti.” Home hydraulic presses are now used to make fruit and vegetable juices of very high quality.  Vacuum cooking in the modern era has produced sous-vide ( French for “under vacuum”), a method of cooking food sealed in airtight bags, with the air pumped out, in a water bath for longer than normal cooking times—72 hours in some cases—at an accurately regulated temperature much lower than normally used for cooking, typically around 55 °C (131 °F) to 60 °C (140 °F). This method produces incredibly tender and juicy meats.  All these culinary endeavors rely on Pascal’s work.  But most of them are not really for the average home cook, although some kits are available on the market (look up “molecular gastronomy”).  Instead I have chosen simplicity.

Pascal’s home town of Clermont-Ferrand is famous for its cheeses and its potatoes.  So here is a traditional potato gratinée from Clermont excerpted from Joël Robuchon’s Le Meilleur et le plus simple de la pomme de terre (The Best and Easiest Potatoes). The recipe and notes are verbatim (in translation).  You can substitute any good melting cheese for the Cantal.


Pommes de terre gratinées clermontoises

This recipe from the city of Clermont-Ferrand is made using the wonderful cheese that is called Cantal. The Auvergne, like Normandy, has three excellent cheeses. And in my opinion, along with those Norman cheeses, the Cantal, Fourme d’Ambert, and Saint-Nectaire cheeses of the Auvergne region are among the world’s finest.

Makes 4 or 5 servings.

2 to 2½ lbs. boiling potatoes (1 kg)
4 Tbsp. butter (50 g)
1¼ cups heavy cream (300 ml)
5 oz. Cantal cheese (150 g)
salt and pepper

Select potatoes that are all about the same size. Peel them and cook them whole in boiling, salted water
for 30 minutes.

Turn on the oven to 180°C (350°F). As soon as the potatoes are cooked, drain them and then dry them out slightly in the oven as it heats up.

Lay the potatoes out on a clean dish towel and, using the back of a big fork, flatten them slightly so that they resemble little cakes of soap.

Butter a baking dish and arrange the potatoes in it. Season them with salt, freshly ground pepper, and grated nutmeg.

Grate or crumble the cheese. Meanwhile, heat the cream to the simmering point and pour it over the potatoes. Sprinkle the cheese over all.

Set the pan in the hot oven and let it cook and brown, for 5 minutes or longer.

Serve the potatoes hot out of the oven as a side dish with roasted meat.

Jun 142013

Nilakantha Somayaji   Nilak Tantrasamgraha
Today is the birthday of Kellular Nilakantha Somayaji brilliant mathematician and astronomer from South Malabar in India – one of a growing number of non-Western scholars who are being “discovered” by modern academicians and accorded their due as forerunners of the so-called Enlightenment in the West (see my post on Ibn Khaldoun: May 27).  I am reminded of a much loved blogger, Pip Wilson, whose Book of Days provided me much information on anniversaries before it went belly up.  Instead of the Euro-centric expression “when Captain Cook discovered the SE coast of Australia,” he would write “when aborigines discovered Captain Cook.”

We know quite a few details about Nilakantha’s life because he was, unlike his contemporaries, careful to document many autobiographical details.  So, for example, he notes in Siddhanta-darpana that he was born on Kali-day 1,660,181 which works out to 14th June 1444. His date of death is not known, but one commentator says he was at least 100 years old when he died.  Nilakantha was born into a Namputiri Brahmin family which came from South Malabar in Kerala, in the south of India. The family followed the Ashvalayana sutra which was a manual of sacrificial ceremonies in the Rigveda, a collection of Vedic hymns. He worshipped the personified deity Soma who was the “master of plants” and the healer of disease. This explains the name Somayaji which means he was from a family qualified to conduct the Soma sacrificial rituals, and probably at some time in his life went through a series of these rituals to earn the title.

In Nilakantha’s time the study of astronomy was one of the six orthodox Hindu sacred teachings, and so lay somewhere between what we would call astronomy and astrology today.  Studying the motions of the planets was not simply a scientific investigation, but a means of predicting and setting the times and dates for significant rituals and life events.  He became a member of the now famous Kerala School of Astronomy and Mathematics which flourished between the 14th and 16th centuries, and which produced a number of significant mathematical findings well before they were discovered in the West.  These findings never found their way outside of Kerala at the time, however, although there are occasional far-fetched speculations that they reached the West via traders.

In all, Nilakantha wrote 10 treatises on astronomy and mathematical computation, a few of which have survived. The most extensive is the Tantrasamgraha, completed in 1501, which consists of 432 verses in Sanskrit divided into eight chapters, and which spawned a number of commentaries, also extant.  The work, plus commentaries, shows the depths of the mathematical accomplishments of the Kerala School, including Nilakantha’s model for the motions of the planets Mercury and Venus. His equations remained the most accurate until the time of Johannes Kepler in the 17th century. He was very close to describing a heliocentric view of the solar system.  His model has Mercury, Venus, Mars, Jupiter, and Saturn orbiting the sun, but has the sun orbiting the earth.  The work also includes a wealth of information on topics ranging from the prediction of lunar and solar eclipses, to accurate calculations of the solar calendar, along with descriptions of the mathematics needed to arrive at their conclusions.  Among these latter are algebraic and geometric theorems that form the basis for differential and integral calculus, although the Kerala School never got that far. Much of the mathematics in the treatise predates Western discoveries in these fields by 200 years.

Several other of Nilakantha’s works survive although they are much shorter.  Among them is the Aryabhatiyabhasya which is a commentary on the astronomical calculations of Aryabhata. In this work Nilakantha refers to two eclipses which he observed, the first on 6 March 1467 and the second on 28 July 1501 at Anantaksetra. Nilakantha also refers in the Aryabhatiyabhasya to other works which he wrote such as the Grahanirnaya on eclipses which have not survived.  The Western world of mathematics and science is finally giving credit to pioneers in their fields in the non-Western world. It is well overdue for the general public also to accept the fact that the Western world has made many significant discoveries in these fields but was by no means the first for many of them.  Nilakantha Samayaji should be as well known a name as Copernicus, Galileo, and Newton.

Kerala was the center of the spice trade for millennia and, as such, has a rich and diverse cuisine to this day, including both vegetarian and non-vegetarian dishes.  Here is a simple vegetarian curry with spices and coconut milk. It would normally be served with anywhere up to 10 or more dishes with rice as part of a large family dinner.

Kerala Vegetable Curry


1lb (½ k) potatoes peeled and diced
½ cup (75 g) peas
½ cup (75 g)  carrot peeled and diced
1 large onion thinly sliced
5 green chiles cut into thin slivers
¼ tsp (1 g) powdered cloves
1 tsp (5 g) powdered cinnamon
1 tbsp (15 g) grated fresh ginger
2 tbsp coconut oil
1 cup (2.4 dl) coconut milk
ground black pepper and salt to taste


Put all the ingredients except the coconut milk and coconut oil into a heavy cooking pot.

Add 3/4 cup water. Bring to a boil.

Cover the pot and simmer on medium heat for 5 to 10 minutes.  The potatoes should be cooked but still firm.

Remove the lid and continue cooking until there is barely any liquid left.

Add the coconut milk and simmer over a low flame for 2 minutes.

Add the coconut oil, stir to mix and serve.

Serves 4 to 6 (as part of a larger set of dishes)

May 182013


Today is the birthday of Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (1872). He was was a British philosopher, logician, mathematician, historian, pacifist, and social critic. He was born in Monmouthshire, into one of the most prominent aristocratic families in Britain. He was awarded the 1950 Nobel Prize in literature “in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought”.

He is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege and his protégé, and my hero, Ludwig Wittgenstein. He is widely held to be one of the 20th century’s premier logicians, mathematicians, and philosophers. His work has had a considerable influence on logic, mathematics, set theory, linguistics, computer science, and philosophy, especially philosophy of language, epistemology, and metaphysics.

bertr russ

Russell was a prominent anti-war activist; he championed anti-imperialism, and went to prison for his pacifism during World War I. Later, he campaigned against Adolf Hitler, then criticized Stalinist totalitarianism, attacked the United States of America’s involvement in the Vietnam War, and was an outspoken proponent of nuclear disarmament. He was briefly jailed again in 1961, following his conviction on public order charges brought after a large central London peace demonstration in commemoration of Hiroshima Day. The cartoon above appeared in the Evening Standard at the time.

Russell was a humanist who wrote extensively on the human condition.  The following quotations are representative:

“War does not determine who is right – only who is left.”

“I believe in using words, not fists. I believe in my outrage knowing people are living in boxes on the street. I believe in honesty. I believe in a good time. I believe in good food. I believe in sex.”

“Three passions, simple but overwhelmingly strong, have governed my life: the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind.”

The following tale is based on what is sometimes called “Russell’s chicken” – an evaluation of the limits of inductive reasoning:

On a farm, there was a flock of chickens. One chicken started talking with another, remarking: “How good our farmer has been to us. I think he is an awfully nice man, because he comes every morning to feed us.” The other chicken nodded in agreement, adding “and he has been feeding each and everyone of us here every day like clockwork, every day without fail since we were all just little baby chicks.” Indeed, when queried, most of the other chickens clucked in agreement about how benevolent their farmer was.

But there was one chicken, intelligent but eccentric, who countered saying “How do you know he is all that good? I remember, not too long ago, that there were some older chickens who were taken away, and I haven’t seen them since. Whatever happened to them?”

Some of the chickens may have slept a little uneasily that night, but in the morning the farmer came as usual, this time scattering even more corn around. The chickens ate this with gusto, and this dispelled any remaining doubts about the benevolence of the farmer. “You see, there is nothing to worry about. Our farmer had a little extra food, so he gave it to us because he likes us! He is a good man,” remarked one chicken to the others, and they all nodded in agreement, all of them, that is, except one. The intelligent but eccentric chicken became even more agitated. “He is just fattening us up! We are going to be slaughtered in a week’s time!” he squawked in alarm. But nobody listened. All the other chickens just thought he was a troublemaker.

A week later, all the chickens were placed into cages, loaded on to a truck, and driven to the slaughterhouse.

Moral of the story: You cannot always induce the truth from past experience!

In honor of Russell’s chicken I give you a recipe for coq au vin, one of the first dishes I learned to cook when I was a student at Oxford (Russell went to Cambridge). There are hundreds of recipes for classic coq au vin but they are all variations on a theme: chicken simmered in wine with onions, bacon, mushrooms, and vegetables. My cooking mentor, Robert Carrier, in his recipe insists that when you cook with wine you should not use some cheap plonk, but a wine you would be willing to serve at table. Cheap ingredients produce cheap results. Like all fine soups and stews, coq au vin is best if made the day before it is needed, and refrigerated overnight to marry and mature all the flavors.  Therefore, you should allow three days to make the finished dish. Be warned: when preparing this dish you need a lot of bowls and plates to reserve cooked ingredients before they are all combined.

Coq au Vin


For marinating the chicken

1 bottle French Burgundy or California Pinot Noir
1 large onion, sliced
2 celery stalks, sliced
1 large carrot, peeled, sliced
1 large garlic clove, peeled, flattened
1 teaspoon whole black peppercorns
2 tablespoons olive oil
1 6-pound roasting chicken, backbone removed, cut into 8 pieces (2 drumsticks, 2 thighs, 2 wings with top quarter of adjoining breast, 2 breasts)

For cooking the chicken

1 tablespoon extra virgin olive oil
6 ounces thick-cut bacon slices, cut crosswise into small pieces
3 tablespoons all purpose flour
2 large shallots, chopped
2 large garlic cloves, chopped
4 large fresh thyme sprigs
4 large fresh parsley sprigs
2 bay leaves
2 cups low-salt chicken broth
4 tablespoons (1/2 stick) butter
1 pound assorted mushrooms (dark mushrooms such as crimini or stemmed shiitake are best but any mushrooms will do)
20 pearl onions
Chopped fresh parsley for garnish
½ lb of baby potatoes, or large potatoes peeled and chopped into bite sized chunks.


First Day: Marinating the chicken

Combine the wine, onion, celery, carrot, garlic, and peppercorns in large pot. Bring to a boil over high heat. Reduce the heat to medium and simmer for 5 minutes. Cool completely then mix in the oil. Place the chicken pieces in a large glass bowl. Pour the wine mixture over the chicken; stir to coat. Cover and refrigerate at least 1 day and up to 2 days, turning the chicken occasionally. Alternatively you can use two large ziplock bags that between them can accommodate the chicken and marinade.  Divide the chicken evenly between the two bags and place half in each.  Divide the marinade evenly between the two bags.  Close the bags almost completely leaving small opening. Squeeze as much air as possible out of the bags. Close the hole and lay the bags flat on the counter.  Shift the chicken around so that there is one layer. And place flat in the refrigerator for 1 to 2 days  I prefer this method because the marinade evenly coats the chicken and does not need to be turned, although once in a while, if you like, you can flip the bags over.

Second day: cooking the chicken:

Using tongs, transfer the chicken pieces from the marinade to paper towels to drain; pat dry. Strain the marinade reserving the vegetables and liquid separately.

Bring a pot of water to a rapid boil and put in the pearl onions. After 30 seconds drain the onions and plunge them into a boil of iced water. When they are cool they can be peeled easily by simply squeezing the skin.  The onions will pop out. Reserve in a small bowl.

Heat the oil in a heavy large pot (wide enough to hold chicken in single layer) over medium-high heat. Add the bacon and sauté until crisp and brown. Using a slotted spoon, transfer the bacon to a small bowl. Add the chicken, skin side down, to the drippings in the pot. Sauté until brown, about 8 minutes per side. Transfer the chicken to large bowl. Add the vegetables reserved from marinade to the pot. Sauté until brown, about 10 minutes. Mix in the flour; stir 2 minutes. Gradually whisk in the reserved marinade liquid and bring to a boil, whisking constantly. Cook until the sauce thickens, whisking occasionally, about 2 minutes. Mix in the shallots, garlic, herb sprigs, and bay leaves, and then the broth. Return the chicken to the pot, arranging the chicken skin side up in single layer. Bring to a gentle simmer. Cover the pot and simmer the chicken for 30 minutes. Using tongs, turn the chicken over. Cover and simmer until tender, about 15 minutes longer.

Meanwhile, melt 3 tablespoons of butter in a heavy large skillet over medium heat. Add the mushrooms and sauté until tender, about 8 minutes. Transfer the mushrooms to a plate. Melt the remaining 1 tablespoon of butter in the same skillet. Add the onions and sauté until beginning to brown, about 8 minutes. Transfer onions to a plate. Reserve the skillet.

Boil the potatoes until just tender and keep warm.

Using tongs, transfer the chicken to a plate. Strain the sauce from the pot into the reserved skillet, pressing on the solids in the strainer to extract all the sauce and discard the solids. Bring the sauce to a simmer, scraping up browned bits. Return the sauce to the pot. Add the onions to the pot and bring to a simmer over medium heat. Cover and cook until the onions are almost tender, about 8 minutes. Add the mushrooms and bacon. Simmer uncovered until the onions are very tender and the sauce is slightly reduced, about 12 minutes. Tilt the pot and spoon off any excess fat from top of sauce. Season the sauce with salt and pepper. Return the chicken to the sauce. (This can be made 1 day ahead. Cool slightly. Chill uncovered until cold, then cover and keep chilled. Warm over low heat when ready to serve.)

Arrange the chicken on a large rimmed platter. Spoon the sauce and the vegetables and bacon over the chicken. Sprinkle with parsley. Serve with boiled potatoes.

Get someone else to do the washing up.

Serves 4