Thursday, April 21, 2011

Mathematicians in Paris - V

David Eugene Smith (from
 David Eugene Smith, whose  Historical-Mathematical Paris (1923) I was my guide in some of walks in Paris, started his notes with  the epicenter of Paris Île de la Cité. So far in my story I have wondered from there to the intellectual Left Bank. Now it is time to remember that on the Île de la Cité near the North Tower of Notre Dame until 1748 was the small church of Saint-Jean-le-Rond on the steps of which Jean le Rond d'Alambert was found.

Jean le Rond d'Alambert (from Wikipedia)
I first learned about d'Alambert as a freshman in university when we studied limits and used d'Alambert's ratio test. A little snapshot about him prompted me to find more and I looked for his biography (no Internet those days! :-) ). I became fascinated by his many talents and interests (not so much with his personality). Geometry stayed d'Alambert's favorite subject as he wrote in 1777 letter to Lagrange:
What annoys me the most is the fact that geometry, which is the only occupation that truly interests me, is the one thing that I cannot do. All that I do in literature, although very well received in our public sessions of the French Academy, is for me only a way to fill the time for lack of anything better to do. 
While connected with French Academy of Sciences on the Left Bank, d'Alambert was a frequent guest at M-me Geoffrin's salon at No.374 Rue Saint Honore. Later he moved in the house of another well known hostess of her own salon Julie de Lespinasse. I will return to places on Rue Saint Honore later.

(from Wikipedia)
 Monk and medieval philosopher Abailard had his cell on Ile de Cite - he studied Euclid in connection with his own lectures in logic. It is hard to tell how much geometry studies occupied his time or whether he used them to keep his thoughts away from his beloved Héloïse, who was first his brilliant student and later became known for her own exceptional scholarship. Perhaps their love letters is the origin of romantic love, they are revealing us one of the most celebrated love story. Six hundreds years later Josephine Bonaparte was so moved by this order that she arranged for the remains of both lovers to be together at their final resting place in Pere Lachese cemetery.
Mausoleum to Monge in Pere Lachese cemetery
 (Mathematicians buried in Pere Lachaise cemetery are:  Arago, Poinsot, Delambre, Monge (interred to Pantheon but his mausoleum still there), Hachette, Fourier, Chasles and founder of positivism and sociology Comte.)

Some places of historical-mathematical interest on the Right Bank:
 On Rue de Rivoli  you cannot miss 52 m tall tower - Tour Saint Jacques , all that remains there from former 16th century church.  Blaise Pascal replicated Torichelli's experiment with barometer there - carried it up to the top of the tower and checked that mercury level has dropped. Pascal's statue now is at the base of the tower.

In 1979 I saw Pascal's calculator in Zwinger Museum in Dresden, this time I missed the opportunity to see the other copy signed by Pascal in Musee des Arts et Metiers. This museum is on my list to visit next time I am in Paris.

The Palais du Louvre is known first and foremost as a museum which houses one of the most stunning collections of artworks in the world. Yet for almost seven hundred years the buildings constituted one of the principal residences of the kings and emperors of France. It became museum in 1793 and at that time the art collection was not large enough to fill all complex, so part of it was used for government offices and even residencies. For example, mathematician Legendre was asking for quarters for himself in the older part of the Louvre.

On  a rainy day it was great to visit Louvre and to walk through it not rushing. We could look at the details and notice mathematical constructions in architecture or in famous artworks.
This time though we did not try to check all the possible uses of golden ratio in Venus de Milo or Mona Lisa like we tried in Milan couple years ago when finally got a chance to see The Last Supper and then alerted security guards performing suspicious activities by their standards. I was trying to follow straight lines with my fingers in front of my eyes to check whether they really intersect in a point just above the head of Jesus, David used his notebook to locate the vanishing point more precisely. Security guards surrounded us and demanded to inspect our hands. After they found nothing, they stared at us very puzzled. Then I politely said that we are mathematicians, which they took as some particular medical diagnosis.
I wish I would've come to Paris with my children when they were very young to show how much math is there around. This thought came in mind again today when I read David Bornstein's A Better Way to teach Math - "...very early in school many kids get the idea that they’re not in the smart group, especially in math. We kind of force a choice on them: to decide that either they’re dumb or math is dumb." Imagine walking in Paris with a little curious mind and big eyes next to you. In front of Louvre there will be a question - what is this big glass thing? Imagine all the different stories you can tell about pyramids - mathematical or not.

How about asking question whether these are also pyramids on the wall of this new building? Or - what is a diagonal? That answer I would know how to answer but I would not be able to answer next logical question - why the supermarket is called Diagonal? In middle school geometry class students have hard time learning all those various geometric terms. Don't you think it would be great idea to call various offices in school in those names? It always helps to remember when you have associations connected to the term.

I can imagine some more questions -why this is Point Zero? What is zero? What it means omega? What is the symbol next to that word?

Indeed, I am getting carried away from what I started to write about.  To speed thin gs up in my description I will just now quote David Eugene Smith about places connected with Voltaire and marquise du Châtelet
In the frontispiece to their translation of Newton, du Châtelet is depicted as the muse of Voltaire, reflecting Newton's heavenly insights down to Voltaire.
 - translator of Isaac Newton's Principia Mathematica in French. Returning back to my earlier thoughts of early childhood education and  underestimating children abilities to learn - Emilie du Chatelet was fluent in Latin, Greek, Italian, and German by the age of 12.

From David Eugene Smith's Historical-mathematical Paris:

If we rank Voltaire in our guild because of his work on the philosophy of Newton, we shall naturally find many spots in Paris connected with his name, and portraits and statues in great number and often of much excellence. The present Rue Moliere, running from the Avenue de l'Opera to the Rue Richelieu, for example, was once the Rue Traversiere, and at the old number 25 was a house which was rented to the Marquise du Chatelet,4 and there Voltaire lived for some time, setting up a little theatre for his plays. Around the corner, at No. 8 of the Rue de Richelieu, the street on which the Bibliotheque Nationale fronts, was the cafe of Charlotte Bourette, who was known as the Muse Limonadiere, and whom Voltaire esteemed for her wit.

Farther up the Rue de Richelieu, at No. 102, stood a house which Voltaire owned and in which his niece, Mme. Denis, lived after the death of the Marquise du Chatelet. Next door, at No. 100, stood the house of Voltaire's friend, Mme. de St. Julien, whom he often visited.
Rue Richelieu No.102

 Voltaire also lived (1732 and 1733) at what is now,No. 20, Rue de Valois, in the same vicinity, east' of the Palais Royal. Not far from here, at No. 161, Rue Saint-Honore, is the Cafe de la Regence, which I well recall as still prominent in the artistic life of Paris when I was a boy. (note: DS wrote this in 1923!)
no cafe there anymore

 Its predecessor stood a little to the east, at the Place du Palais Royal, and was frequented by Voltaire as well as by Benjamin Franklin, Diderot, Napoleon, and other makers of history. Over on the Ile Saint-Louis, at No. 2, on the Rue Saint-Louis-en-l'Ile, is the hotel (man- sion) of Nicolas Lambert de Thorigny, sometime president of the Cour des Comptes, built in 1680. The Marquise du Chatelet lived there for a time, and Voltaire was, as usual, a guest of the house. His sister, Mme. Mignot, mother of Mme. Denis (to whom Voltaire was greatly attached), lived at No. 133, Rue Saint-Antoine, a continuation of the Rue de Rivoli and leading into the Place de la Bastille.
Hotel de Sully on Rue Saint-Antoine
The Place de la Bastille

 Although the Bastille has long since ceased to exist, when the wanderer stands upon its ancient site he may reflect that Voltaire was twice imprisoned there, for his rash utterances on the rights of man. Voltaire was baptized (1694) in the church of Saint-Andre-des-Arcs, which was built in 1210. 2 and her family, Tonnelier de Breteuil, there are various interesting spots connected with each. The family owned a hotel at No. 14, Rue Portefoin, a little to the southeast of the Conservatoire des Arts et Metiers. They also owned (1760) a place at No. 56, Rue des Francs-Bourgeois, near the Palais des Archives Nationales, and somewhat earlier (1728) one at No. 4, Place des Vosges, on the same street. In 1752 the marquise was living at No. 18 of the same Place.

Place de Vosges

It stood on the present Place Saint-Andre-des-Arts,1 near the Point Saint- Michel, and was demolished about 1800. In 1793 it became the Temple de la Revolution. Voltaire once worked as a clerk in the office of Maitre Alain, No. 1, Rue des Grands-Degres, so called from the steps leading down to the quai, and he became a mason in the lodge of the Ne uf Soeurs which stood at No. 80 of the Rue Bonaparte; but the atmosphere of the Quartier Latin was perhaps not so well suited to his maturer years, although he lived for a time in Rue Mazarine and in 1743 was living at No. 23, Rue Fontaine Moliere. He died in the house of the Marquise de Villette, at No. 27, Quai Voltaire, as an inscription states. The present name of the quai, formerly the Quai des Theatins, was given in memory of this event, as was that of the Rue Voltaire which branches off at No. 211. His final resting-place is appropriately in the Pantheon, the Valhalla of France. As to busts, bas-reliefs, and statues of Voltaire, Paris has been over-generous. Houdon's bust in the Comedie Franqaise is the best known, but the statue by Caille (1885) on the Quai Malaquais is also familiar to every visitor to the book- stalls on the Rive Gauche. "

the Comédie-Française

Place Franz Liszt in Paris(from wikipedia)

 David Smith mentioned that near Gare Saint Lazare Franz Liszt lived at No. 63 Rue de Provence. The great composer and pianist was supporting the young arithmetic prodigy Henri Mondeux. On April 30, 1841 Liszt gave au benefice de jeune Patre Mathematicien. May be this fact should be more popularized in order to encourage present day music stars to give benefit concerts to support mathematicians, particularly when government is cutting NSF funds.

Maupertuis is buried in Eglise Saint Roch on rue Saint Honore and Lagrange lived at No. 124 rue Saint Honore. I went to explore Rue Saint Honore but nowadays it has become fanciest shopping address in the world may be, so from mathematical world I felt thrown in another type of the world but about it - next time.

Sunday, April 10, 2011

New York Hall of Science

On April 5th I visited New York Hall of Sciences - I was kindly invited to give a talk for the Staff Professional development seminar. I was caught in traffic while driving there from Brooklyn - 11 miles took more than an hour. Because of that I arrived just before my talk and did not have time to look around beforehand. But I did later and saw interesting things.
It is still possible (until April 24) to see a wonderful travelling exhibit 1001 Inventions which previously was shown in Istanbul and London.
So called "dark ages" in Europe was the Golden Age in Muslim civilization. Innovations from that period are still in use today. I liked very much how visitors are invited to push buttons at particular exhibits by mischievous story tellers who wave at you.

One of the stories I listened was about Islamic architecture and developing the infrastructure in cities. It also mentioned amazing geometric constructions which later were copied by Western architects.

The story about the astrolabe is told by woman and this was not the only one about creative and smart women. More can be found on 1001 Inventions website. But this movie will give a better visual idea about this fascinating exhibit:

Director of NY Hall of Science Eric Siegel proudly showed me and David a permanent exhibit Mathematica. It was designed in 1961 for IBM and is the first interactive exhibition devoted to math.

The long wall of math history starts from approximately 12th century.
The first model we both noticed in the exhibit of course is the pseudosphere -surface with constant negative curvature I was just mentioning in my talk.
Sometimes when I talk about hyperbolic plane my audience is asking me where are hyperbolas on it, and I have to disappoint them telling that there are none.
This surface is hyperboloid which also has negative curvature on its surface but the curvature is not constant. It is an interesting surface that can be built with straight steel beams. It allows minimisation of wind cross-section while retaining structural integrity with minimal material. Cooling towers is one of the application examples in architecture.

This is a nice demonstration of stereographic projection.

My favorite depiction of stereographic projection is by Peter Paul Rubens:

When applied in photography, stereographic projection produces fun images.

Pseudosphere can be seen in another demonstration - about planetary motion. It visually shows black hole idea.

Yet another surface with negative curvature (but not constant!) is helicoid as the demonstration of DNA structure shows. (In Crocheting Adventures with the Hyperbolic Planes I wrote about the connections between helicoid and catenoid and have pictures of crocheted models that show this connection.)

The next surface has both - positive and negative curvature (can you see where?).
If this already reminded you about the mathematical models I wrote in my previous post, then the next picture is even closer to art:

I really liked this delicate string model of helicoid tucked in between braid and sphere packing demonstration. I wish it could have its own case to be fully appreciated.

Also Reye Configuration could use more space (some more pictures of Reye configuration). But of course I understand space issues in exhibits...

I was happy to see the visual depiction of one of my favorite geometry theorems - Pascal theorem (sometimes called Hexagrammum Mysticum Theorem). It is a generalization of ancient Pappus theorem, and Pascal found this generalization when he was only 16!
At the time when Pascal was playing with geometry, he had no idea that this theorem will be later mentioned in projective geometry. There is a nice demonstration of projective geometry in Mathematica. This is a configuration how you see it from the side:
And this is what you see when looking to the same configuration through the hole.

Do not see anything? Good reason to go and visit NY Hall of Science yourself! Much more to see than I can show here, for example, some math magic too:

When we arrived at NY Hall of Science there were many school buses and the hallway was full with happy primary school kids. B y the time we were leaving exhibit halls were mostly empty since school day was over. While I am totally agreeing that we should talk to children about science in early age, I was still thinking about the tendency of turning science museums into children playgrounds. What happens to children curiosity later? Is it consumed by computers and video games and we do not see anymore teenagers in science museums? I remembered my first ever visit to science museum. It was in 1994 in Finland - this year Heureka is celebrating 20 years. It is not as old as Exploratorium or Ontario Science Center, which are twice as old, but still Heureka was one of the first. I have not had a chance to visit it again, so I cannot tell whether I would have the same impression now. But in 1994 we all adults had great fun to look at the exhibits and I do remember many teenagers and adults there and exhibits were engaging us. In US I have met with many people working in science centers and they all confirm the same thing I have notices - science centers are places where parents take their children like they take them to the playground, and children behave there as in playground - they play. It is good first to play but there is no follow up. Except for some volunteers I have not seen any teenager coming to science center - who is going to return to the playground? As a result exhibits are being tailored to the kinder garden level. What happens? Like in NY Hall of Science little kids will pass this very nice Mathematica exhibit - it is above kinder garden or primary school level, it will stay in their memory as something impossible to understand and that's it. I wish I am too pessimistic in these thoughts and wrong...
On my way back to Ithaca I was driving across Tapan Zee bridge
According to 2009 AAA report this bridge is "worst of the worst in New York", some say even in the whole country by now. Still in use.
Attitude to safety like this?
If something endangers them these geese will simply fly away. Bridges, education... Well, may be not my business, may be I am thinking about restricted areas like this park - on my way out I noticed the sign that it is "only for the use to Westchester County residents". So much for "free country"...

Fortunately, these ones did not object us walking there.

Friday, April 1, 2011

Mathematicians in Paris - IV (mathematical models)

When in 1977 I started to teach geometry in the University of Latvia, there was a small collection of old mathematical models with their titles in German on little uniform signs attached to their sides or bottoms - some plaster models and some were string models. All we knew that they were from early 20th century. I remembered those models used in geometry classes when we studied quadratic surfaces. With computers more and more becoming a part of teacher education, the use of the models became old fashioned and they were neglected. Nobody objected when I collected what was left of them and displayed on a shelf next to my desk in an office I shared with three other people. (oh, that office was a big improvement - for my first 5 years as a faculty I shared a desk with two other people...). By then the string models were damaged and the plaster models looked quite sad also, but I still enjoyed to look at them as to little sculptures. I even tricked one of my students to repair one of the string models by promising to count it as a final exam for the class. He happily agreed thinking that he got a good deal. When he arrived in my office 5 minutes before the final exam - as was the deadline for turning in his work - he said: "You knew it! It was easy to take it apart but in order to put it back together correctly, I had to study everything about those surfaces! Well, now I really know them."
 When I last visited my former office in Riga couple years ago, models were gone and nobody knew where.
I remembered those models in Latvia  when I saw some mathematical models on a shelf in Cornell Mathematics Library. When in 2002 I joined a team in Cornell to develop kinematic model digital library, I discovered that some of the models in the kinematic model collection were purely mathematical and I became interested in the history of models, even wrote couple papers, (the latest).
Universities late 19th century and early 20th century used to have these model collections displayed as in an art museum - you can see it in the picture of Cornell Kinematic model collection at its beginnings as published in Scientific American in 1885. Some places still have these nice model collections and have displayed them, I wish one day to go and see mathematical models in West Point ( Prof Fred Rickey has researched the history of Olivier models) recently I saw nice models in Vassar College. Some of the model collections are digitized, like The Altgeld Mathematical models collection in Illinois.
[It can be tricky to search for mathematical models on the Internet because nowadays mathematical model does not mean only the tactile model you can physically hold in your hands. Google search may return results like "mathematical model of compile time garbage collection". ]
Angela Vierling-Claassen has gathered a list of Collections of mathematical models and also has some notes on Influence of mathematical models on art.

When in Paris, we never made to Conservatoire des Arts et Métiers (on a list for next time!) but we did visited  mathematical models collection in the Institut Henri Poincare. Our guides there were Brigitte Yvon-Deyme and Dominique Dartron - thank you both so much for your kindness and your time! (photos of models in this posting are used by permission of Bibliotheque IHP).
In my introduction to Crocheting Adventures with the Hyperbolic Planes I mentioned the International Congress of Mathematicians in 1954. I was trying to find some picture from this Congress but did not have any success before a book was sent to a print. Now I have a picture I would've loved to have in the book - it was the very first thing David spotted on a wall in IHP.
During the library hours anybody can visit the library to see several cases of the models on a permanent display. 
With a little wink in her eyes M-me Yvon-Deyme pointed out that most of the visitors come to see models not out of mathematical curiousity but they are  people interested in art, particularly the ones who wish to see models photographed by Man Ray.  In the 1930s, the surrealists were interested in various geometries. According to Neil Baldwin, Max Ernst "had taken Man Ray to see the objects on display at the Poincare institute in Paris and had photographed them in a deliberately impressionistic style". These are some of Man Ray's pictures.

The last photo is an interesting mathematical object - can somebody come up with the equation describing it?

Man Ray's photographs were published in Cahiers d'Art (May 1936, No. 1-2, p. 21-26.) and the series was first shown at the New Burlington Gallery (June 11- July 4, 1936).
Man Ray very much agreed with Henri Vuibert who wrote in 1912:
To help students see in space, we materialized the major figures of geometry and descriptive geometry. The use of figures in relief would provide valuable aid to education, especially if one was building these figures by the students." (Anaglyphs The geometric . Paris: Librairie Vuibert, 1912, p. 8).
Man Ray returned to these mathematical models about a decade later when he created series of paintings Shakespearean Equations.

Man Ray Shakespearean Equations: Twelfth Night, 1948 :Hirshhorn Museum

Man Ray Shakespearean Equations: King Lear, 1948: Hirshhorn Museum
In this excerpt (part 5) from Jean-Paul Fargier documentary about Man Ray notice how photos of mathematical models are transforming into paintings. Some more mathematical models appear in part 7.

Surrealists interest sparked public interest about IHP mathematical models and since then the models of the IHP have participated in many exhibitions starting with the one at the Palais de la Découverte, built for the Exposition Internationale des Arts in 1937.

On a personal note here I should add that my interest about 1937 exhibition was because of mathematical models and surprised I discovered that famous sculpture Worker and Kolkhoz Woman by Vera Mukhina (born in Riga!) was the centerpiece of Soviet Pavillion in this exhibition. For me that sculpture always associated with the VDNH (Exhibition of Achievements of the People's Economy) in Moscow and also with the opening of Mosfilm movies.

Here are some of my photos of mathematical models in IHP in Paris.

These constant width solids caught my interest because they are generalization of the curves with constant width
Among all of the IHP mathematical models there will now also be a place for crocheted hyperbolic plane :-)

PS. Geometry continues to be the inspiration for artists - as one can see it in current exhibit Geometric Days.