Apr 142019
 

Today is the birthday (1629) of Christiaan Huygens FRS, a Dutch physicist, mathematician, astronomer and inventor, who is widely regarded as one of the greatest scientists of all time and a major figure in the scientific revolution, even though his name is not a household word these days. In physics, Huygens made groundbreaking contributions in optics and mechanics, while as an astronomer he is chiefly known for his studies of the rings of Saturn and the discovery of its moon Titan. As an inventor, he improved the design of the telescope with the invention of the Huygenian eyepiece. His most famous invention, however, was the pendulum clock in 1656, which was a breakthrough in timekeeping and became the most accurate timekeeper for almost 300 years. Because he was the first to use mathematical formulae to describe the laws of physics, Huygens has been called the first theoretical physicist and the founder of mathematical physics. Huygens is one of the giants whose shoulders Newton stood on to be able to see so far.

In 1659, Huygens was the first to derive the now standard formula for the centripetal force in his work De vi centrifuga. The formula played a central role in classical mechanics and became known as the second of Newton’s laws of motion. Huygens was also the first to formulate the correct laws of elastic collision in his work De motu corporum ex percussione, but his findings were not published until 1703, after his death. In the field of optics, he is best known for his wave theory of light, which he proposed in 1678 and described in 1690 in his Treatise on Light, which is regarded as the first mathematical theory of light. His theory was initially rejected in favor of Isaac Newton’s corpuscular theory of light, until Augustin-Jean Fresnel adopted Huygens’ principle in 1818 and showed that it could explain the rectilinear propagation and diffraction effects of light. Today this principle is known as the Huygens–Fresnel principle.

Huygens invented the pendulum clock in 1656, which he patented the following year. In addition to this invention, his research in horology resulted in an extensive analysis of the pendulum in his 1673 book Horologium Oscillatorium, which is regarded as one of the most important 17th-century works in mechanics. While the first part of the book contains descriptions of clock designs, most of the book is an analysis of pendulum motion and a theory of curves.

In 1655, Huygens began grinding lenses with his brother Constantijn in order to build telescopes to conduct astronomical research. He designed a 50-power refracting telescope with which he discovered that the ring of Saturn was “a thin, flat ring, nowhere touching, and inclined to the ecliptic.” It was with this telescope that he also discovered the first of Saturn’s moons, Titan. He eventually developed in 1662 what is now called the Huygenian eyepiece, a telescope with two lenses, which diminished the amount of light dispersion.

As a mathematician, Huygens was a pioneer on probability and wrote his first treatise on probability theory in 1657 with the work Van Rekeningh in Spelen van Gluck. Frans van Schooten, who was the private tutor of Huygens, translated the work as De ratiociniis in ludo aleae (“On Reasoning in Games of Chance”). The work is a systematic treatise on probability and deals with games of chance and in particular the problem of points (the division of stakes when there is no clear winner). The modern concept of probability grew out of the use of expectation values by Huygens and Blaise Pascal (who encouraged him to write the work).

The last years of Huygens, who never married, were characterized by loneliness and depression. As a rationalist, he refused to believe in an immanent supreme being, and could not accept the Christian faith of his upbringing. Although Huygens did not believe in a supernatural being, he did hypothesize on the possibility of extraterrestrial life in his Cosmotheoros, which was published shortly before his death in 1695. He speculated that extraterrestrial life was possible on planets similar to Earth and wrote that the availability of water in liquid form was a necessity for life.

This recipe for a pie filled with brie, pears, and eggs is a little before Huygens’ time, but it is an interesting challenge and can yield excellent results. Fruit and cheese can make superb combinations. It comes from Eenen nyeuwen coock boeck (A new cookbook), written by Gheeraert Vorselman and published in Antwerp in 1560.  The recipe is more than a little vague, but can be made serviceable.

Een keesgheback
Legget in coppen kese van Brij ende harde eyeren tsamen gestooten met peren ende hier toe neemt men suker ende heel doyeren van eyeren.

A Cheese Pie
Put some Brie cheese and hardboiled eggs, mashed together, with pears in a pie. Add sugar and whole egg yolks.

Not much to go on, I admit. It looks like a version of quiche. That is, take a pie shell and fill it with a mix of sliced pears and hardboiled eggs and Brie mixed together. Beat egg yolks (and sugar), and pour over the pie filling. Bake until the crust is golden and the eggs are set.

Aug 042016
 

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Today is the birthday (1834) of John Venn, English mathematician and logician, primarily remembered for his use of diagrams, which we now call Venn diagrams, to help explain concepts in set theory. Venn was not exactly a giant in his field, but I’d settle for having something reasonably commonplace named after me. Venn diagrams have served me very well in my own work.

Venn was born in Hull, and educated at private schools in London before studying mathematics at Cambridge University, at Gonville and Caius College where he subsequently became a fellow and then head of the college.

Venn’s father was an Anglican clergyman and Venn followed suit in the late 1850s, as was normal for fellows at Cambridge at the time. In fact, after receiving his degree in 1857 he did parish work for a few years before devoting himself full time to mathematics. Even after he left the clergy in the 1880s he continued being involved in the church, although he found strict Anglicanism incompatible with logic and mathematics.

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Venn’s first major publication was The Logic of Chance (1866), a significant accounting of the laws of probability. He then turned to George Boole’s work in logic and produced Symbolic Logic in 1881. It was in this work that he introduced Venn diagrams which he had been using as a teaching device for several years:

I began at once somewhat more steady work on the subjects and books which I should have to lecture on. I now first hit upon the diagrammatical device of representing propositions by inclusive and exclusive circles. Of course the device was not new then, but it was so obviously representative of the way in which any one, who approached the subject from the mathematical side, would attempt to visualise propositions, that it was forced upon me almost at once.

As Venn notes, other mathematicians, notably Gottfried Leibniz and Leonhard Euler, had used similar diagrams earlier, but Venn popularized them as well as extending their application to a wide variety of fields outside of mathematics and logic, and making their application more rigorous than previous attempts.

Venn diagrams don’t actually serve a technical function in mathematics or logic, but they do make certain concepts easier to grasp by displaying them visually. Here’s a simple example showing the Greek, Russian, and Roman alphabets each contained within circles which are drawn to overlap. Symbols in common between two of the alphabets are shown at the intersections of their circles, and symbols common to all three are shown in the central intersection.

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Venn diagrams also have the possibility of excluding items from any of the circles, such as in the example below of a diagram concerning “people I know” and the use of social media. Harry uses neither Facebook nor Twitter so fits inside the rectangle representing people I know but outside the circles representing social media.

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Venn was elected to the Royal Society in 1883 and continued to publish other works, including The Principles of Empirical or Inductive Logic (1889) and volumes on the history of Cambridge and a list of its alumni, compiled with the aid of his son, John Archibald Venn.

Venn died on April 4, 1923, in Cambridge at the age of 88. He is memorialized by a stained glass window at his old college.

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When dealing with mathematical subjects before I’ve focused on mathematical objects. The Venn diagram is not a mathematical object per se, but it does lend itself to cooking ideas. This site gives an idea for a Venn diagram pie. http://www.quirkbooks.com/post/happy-pi-day-make-venn-pie-agram  It was created for Pi Day (3/14 in countries that use month/day format), so it is more about being a pie than being an accurate Venn diagram. But you can take the original and modify it.

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The site shows you how to cut two disposable pie pans to make the Venn diagram shape, and the crust conforms to the general idea of sets – no crust and full crust intersect to make a lattice crust. The recipe fails with the fillings. It just suggests using three different ones. It shouldn’t be too difficult to come up with categories such as fruit and dairy, so that one side is fruit, no dairy, the other is dairy, no fruit, and the middle is fruit and dairy. I’ll leave it to you.