Wednesday, February 18, 2009

Wednesday Math, Vol. 61: The one where French people are rude to each other

One of the difficulties of teaching history to young people is the tendency for people of all ages to think that everything that happened before they were born kinda sorta all happened at the same time and in about the same place. So kids get confused and think George Washington and Jesus Christ hung out together and the wood for the cross was made from the cherry tree Washington cut down. While that sentence is completely false, of course, sometimes famous people in the past did live at the same time and in the same locale, and so it is with two great French mathematicians and philosophers, Blaise Pascal and René Descartes, both of whom were in Paris in the first half of the 1600's, part of the generation of great French mathematicians who laid some of the important ground work for Newton, whose best work is done in the second half of the 1600's.

So Pascal has bought this cool new invention from Italy called a barometer, and for a while he goes nuts taking barometric readings. As we know, barometric readings in the exact same place change over time, but one consistent difference intrigued Pascal, which is that barometric readings would get lower at higher altitudes. For example, there was a consistent difference for the air pressure at the entrance to Notre Dame cathedral and the air pressure on the roof, which was always a little bit lower measured only minutes apart. Pascal didn't have a balloon to ride in and didn't take a trip to the Alps, but from these readings, he speculated that air pressure kept going down as you went up in altitude, and there must be a point at some distance above the earth where air pressure is so low, it is effectively a vacuum, that thing which nature allegedly abhors.

He told Descartes this speculation, and René started thinking, which he was pretty good at, and he goes all hypothetical question asker on Pascal's derriere.

Where does this vacuum start? Pascal couldn't be precise, but by his calculations air pressure was probably around zero somewhere between five and ten miles about the earth's surface.

Does the vacuum end? Pascal couldn't see how.

How far away is the sun? Top scientists like Pascal and Descartes in the 1600's may not have had measurements as precise as we have today, but they would have known the sun was tens of millions of miles away.

Isn't a flame extinguished in a vacuum? Why doesn't the sun flicker out if there is no air for it to burn in Pascal's alleged universal vacuum? Pascal didn't know.

Of course, the answers to these questions deal both with gravity, which no one understood very well until Newton comes along later in the century, and the idea of nuclear reaction, which causes the sun to keep burning for a very, very long time, which isn't even a scientific concept until hundreds of years after Pascal and Descartes are dead.

While both of them have come to valid conclusions, because Descartes got Pascal to say he didn't know something, obviously Descartes won the argument. This put something of a damper on their relationship. In a letter to a friend, Descartes wrote the wonderful put down, "Monsieur Pascal has too much vacuum in his head."

So if you feel a French person has been rude to you, don't take it personally. That's how they roll, and some of them are pretty good at it.


Lisa said...

I'd love a friend with a vacuum. Especially if he/she knew how to use it and would come to my house once a week to show me.

Speaking French would be optional.

Mathman6293 said...

Your post proves that my spouse will comment on a math blog as long as you are talking about some French guys. Bon.

Now, I can't even remember what I was going to say. Must have been something about how futile I now feel about teaching the M.A.D. knowing that it is relatively unimportant and the kids won't remember it anyway. But I also taught a little of Pascal's triangle this week, too.

Mathman6293 said...

And thanks for the interesting History lesson.

Lisa said...

MathMan - if you were here right now, I would be like Gomez Addams to your French-speaking Morticia.

You spoke French!

Wait - this post was about math?