Showing posts with label Paris. Show all posts
Showing posts with label Paris. Show all posts

Thursday, May 5, 2016

Blaise Pascal


Most of us know him because of the triangle that was named for him, but Blaise Pascal (1623-1662) did many other things, including creating an early calculating device, which was later named the Pascaline in his honor.  The Pascalines pictured above are all from the 17th and 18th centuries - one is signed by Pascal!  They reside in the Musee des arts et metiers (CNAM) in Paris.  

Pascal invented this calculating machine when he was only 19 years old in order to assist his father, a tax collector, in his exhausting, tedious work of calculating and recalculating what was paid and what was owed.  It was able to carry out addition and subtraction - and also multiplication (as repeated addition) and division (as repeated subtraction).  This may not sound like much to us, with our fancy graphing calculators and our scientific calculators on our smart phones, but it was Pascal and others like him who paved the way for the technology that we enjoy today!

When Pascal was a child his father, who was an avid amateur mathematician himself, came to the strange conclusion that his son should not study mathematics before the age of fifteen.  He therefore removed all mathematics texts from the house.  This ban only raised young Pascal's curiosity about the subject, and he started working on geometry in secret.  When his father saw the results Pascal was achieving he removed the ban and allowed his son to access mathematical texts.
 Above - the man himself.  Below - the triangle named for him.  As so often happens with things, though this object bears his name, he did not invent it.  It was known in China at least as early as the the year 1300, and it was also known to mathematician Omar Khayyam who lived almost 600 years before Pascal, from 1048 to 1131.  But Pascal did do a tremendous amount of study of this triangle.  Among the other patterns you can find inside it (and they are countless - see if you can find some!) are what are known as the "binomial coefficients," and it was Pascal's work on this that paved the way for Sir Isaac Newton to develop the general theorem of binomial coefficients that includes fractional and negative powers.
Because I am a mathematician I often think of Pascal as a mathematician, but he actually focused far more on theology than he did on mathematics. His book Pensees, a collection of fragments on theology and philosophy, is probably his best-known work, and it includes such quotes as:

"Men never do evil so completely and cheerfully as when they do it from religious conviction."

"All of humanity's problems stem from man's inability to sit quietly in a room alone."

"When I consider the brief span of my life absorbed in to the eternity which precedes and will succeed it  .  .  .  .  the small space I occupy and which I seem swallowed up in the infinite immensity of spaces of which I know nothing and which know nothing of me, I take fright and am amazed to see myself here rather than there:  there is no reason for me to be here rather than there, now rather than then.  How put me here?  By whose command and act were this place and time allotted to me?"

It also includes the basis for another item that bears his name: "Pascal's Wager," which begins with the assumption that in deciding whether or not to believe in God all humans are betting their lives and are compelled to do so.  He concludes that a rational person should live as though God exists.  If God does not exist, then this person loses only a finite amount (some pleasures in this brief life).  However, if God does exist then a person who believes in Him receives infinite reward (Heaven) and avoids infinite losses (Hell).

Pascal, along with Pierre de Fermat, laid the foundation for probability theory.  This was prompted when a gambling question was brought up by Antoine Gombaud, Gevalier de Mere.  The question had to do with how to split the pot of money if gamblers had to end a certain game early.  This question had come up before and was treated by earlier mathematicians, but they leaned toward splitting the pot based on the proportion of rounds already won or lost.  Whereas Pascal and Fermat looked at what would happen if the game had continued.  This was a major shift in thinking, as prior to this things that "would happen" were considered to be in God's hands alone and could not be quantified.

Though he loved mathematics and was a brilliant mathematician, he often took long breaks from mathematics.  This was particularly the case when his father became seriously injured and was cared for by brothers of the Jansenist theological movement.  Pascal was greatly influenced by them and came to feel that mathematics was a distraction from concerns about his mortal soul and should thus be avoided.

Eventually he became so overwhelmed by his thoughts of eternal destruction that it was making him ill, and his doctor recommended going back to the activities of a young man, so he took up mathematics again.  He set it aside more than once, and one story of him picking it back up again is that he had a terrible, unbearable toothache - so bad that it was keeping him awake, so he began to do mathematics in order to distract himself and take his mind off the pain.  It worked.
 Pascal lived much of his life in Paris and is buried there.  He had become ill while in his twenties and never fully regained his health.  He lived most of his adult life in great pain and died having only reached the age of 39.  Despite this he continued to engage in life - particularly the life of the mind and soul.  He explored mathematics, philosophy and theology and produced much.  I'm betting he has won his wager!



Tuesday, May 3, 2016

Au Revior Paris

Love Locks
I've seen quite a few "love locks" in various places in Europe, especially Paris, but nowhere near as many as on this bridge, the Passerelle de SolfĂ©rino, which I was crossing in order to get to Musee de l'Orangerie, a museum of impressionist and post-impressionist art.  The Orangerie is most famous for it's collection of eight Water Lilies murals by Claude Monet, for which a space was created and for which the murals were then created.  They occupy two oval-shaped rooms.


Yes, in fact, I did have to wait forever for people to be out of the way in order to get those pictures!
After 5 weeks still not rocking the selfies - two weeks to go to try to nail this.
Monet seemed to be the big draw here, but there was much else as well - including the likes of Picasso, Cezanne, Renoir, Matisse, Rousseau, etc.
Cezanne
Picasso, of course - 
Surprisingly not Picasso!
This one's for you, Barb ;-)
Even the cafeteria was artsy!

After this was my time in Jardin des Tuileries, which I've already posted about here - then La Place de la Concorde where the guillotine was set up during the French Revolution and then on to Champs Elysees and the Arc de Triomphe.  (There were mathematical travels in the midst of that as well, but I'm trying not to do double-duty with the pictures - though I should add the Place de la Concorde images to Sophie Germain's post, as she grew up during the Revolution.) OK - on with the pictures.
Place de la Concorde
Place de la Concorde
Place de la Concorde
Looking from Place de la Concorde down Champs Elysees to Arc de Triomph - it's all right there together.
Champs Elysees
Some shops along Champs Elysess:





Don't worry, hubby; I didn't do any shopping! :-)
Arc de Triomphe


Dinner on Champs Elysees!

 I was all excited to find a place with the option of a "mini" margharita (aka CHEESE!) pizza, but I'm so focused on speaking as much French as I can that I think I forgot to say "mini."  Alas  .  .  .

Saturday was mostly math stuff.  The Pantheon counts as math stuff AND tourism, so a few pictures of that - then went on to Garnier's Opera House (famous for Phantom) but have already posted on that.

This is where Foucault's Pendulum originally hung
The crypt of the Pantheon:





Mathematician Joseph-Louis Lagrange is on the top left near the window.  He's why I went to the Pantheon, but I couldn't get near his "sepulture."
 On Sunday I took time to walk along the Seine from the Eiffel Tower to Notre Dame as a "good-bye" to Paris.  It was not only a Sunday, but it was May Day, which is a huge holiday in Paris; many museums that only close a couple of days a year close on Christmas Day and May Day.  So many people were out - many just sitting by the river reading and sun-bathing on what was a rare sunny day this week.  After packing I went out at night to see if the Eiffel Tower was lit up - was it ever!!



My pretty coconut and strawberry ice-cream by the octagonal basin in Jardin des Tuileries.

Looking toward Ile de la Cite



She sure found a great spot for reading!









Happy May Day!!!




Au Revior Paris!


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It goes without saying, but I'm up and running again!  Yea!!  Thanks for support via prayer and via advice.  AVG.com and malwarebytes.org (special thanks to Joan!) worked wonders!  I'm cautiously optimistic.  Prior to having such computer issues I had posted a "teaser" that I didn't get a chance to complete.  I finally finished that post.  The initial image was of the chandelier from the Garnier Opera house - in other words, the chandelier from Phantom of the Opera.  This opera house was one of the most stunning things I saw in Paris, and that's saying something!  If you want to see the post you can scroll down a few or click here.