Free Pascal's Wager by James A. Connor Page A

comfortable, acceptable, with hints of great expectation sprinkled through. Inwardly, they were hyperintelligent, given to emotional extremes, and not a little eccentric. Though Blaise had shown the first signs of great promise, it was Jacqueline who kept winning prizes for her poetry, and it was this rather than romance that consumed her life. Blaise had yearned for celebrity since childhood, and Jacqueline’s early success must have galled him in his private room, though he would have smiled and applauded her in public. Moreover, while Blaise was utterly under his father’s thumb, following out his father’s program, Jacqueline showed an alarming independence, something that was simply not done among their kind.
    While in Rouen, the family had met Pierre Corneille, the Norman tragedian, who quickly befriended them and encouraged Jacqueline to pursue the life of a poet and playwright. It seemed at first that she was on the verge of doing so. Meanwhile, Blaise received a copy of Desargues’ book on conic sections and, egged on by his father and by Mersenne, set out to make his own contributions. Living in Rouen at the time, he was off in the provinces, like Fermat in Toulouse, and had to rely on letters and gossip for news of the intellectual tides of Mersenne’s academy. But the monk, the great communicator, kept everyone apprised of the latest, and made sure that the right books ended up in the right hands.
    While Blaise scribbled his notes on conic sections, crowds gathered in the street below and shouted angry insults at the government employees in the neighborhood. Richelieu’s gluttonous taxes, the very thing that the Pascal family had come to Rouen to administer, had crushed the common people into rebellion. Brush fires of plague had also erupted in parts of the city and throughout Normandy. In the summer of 1639, just as thePascal family had taken up residence, the city exploded with riots. Gangs of looters roamed the streets, singing bawdy songs and throwing curses. For the first year of the Pascal family’s stay in Rouen, they must have felt as if the people’s vengeance would swallow them whole.
    Finally, Blaise sent his first work of serious mathematics off to Père Mersenne. It was a short piece, a pamphlet entitled Essai pour les co-niques , or Essay on Conics . In it, Blaise outlined his proof for what has been called the Mystic Hexagram. Here is a short description of the concept:
1. Take a cone:

2. Take a simple plane, and slice the cone in two.

3. If the plane is straight across, the section cut out will be a circle. This is the specialized case:

4. If the plane is at an angle, the section cut out will be an ellipse. This is the more general case, because ellipses can be squat or long, thin or nearly round:
Because Pascal wanted to prove a general theorem, he took the case of an ellipse:

5. Draw a hexagram, a six-sided figure, inside the ellipse. The hexagramdoes not have to be regular.

6. Now, take a pencil and make big dots on the vertices of the hexagram, and draw lines between the vertices. Then, extend the lines out to where they cross.

7. The three points of intersection where the lines cross will always form a straight line, for any conic section and any hexagram.
    Mersenne was deeply impressed when he received a copy of Blaise’s pamphlet. Everyday geniuses like Descartes are one thing, but a child prodigy is another. There is something divine about a child, even a teenager, who shows promise beyond his years. Blaise was thirteen years old when he first began attending Mersenne’s seminar, and everyone thought that he showed great promise. But unfulfilled promise is only air until the prodigy actually does something, and Blaise’s pamphlet was not only the first sign of that fulfillment but also the vindication that Mersenne had been waiting for. He had been telling everyone about the bright young son of Étienne Pascal for years, and if that boy had done nothing with his talent, it