Showing posts with label Math history.. Show all posts
Showing posts with label Math history.. Show all posts
Monday, August 24, 2015
Friday, June 12, 2015
Tuesday, July 3, 2012
Saturday, June 16, 2012
Wednesday, July 6, 2011
Links to the stories about the computer scientists.
Stories about John Von Neumann, Alan Turing, Grace Hopper and Donald Knuth. There is also a section about Edsger Dijkstra, but there won't be any questions about his life story.
Monday, June 20, 2011
Wednesday, April 27, 2011
Descartes and Pascal.
There were many people who came before Newton that helped pave the way for the invention of calculus, the mathematical tool that make modern physics possible.

Blaise Pascal was a French philosopher and mathematician. A very devout man, he put forward the idea that everyone should have faith in Jesus as the Lord and savior for mathematical reasons. The payoff for believing was life eternal and the payoff for not believing was hell, so the better situation was infinitely better than the worse. Even if there was only a small but finite chance it was true, the infinite payoff made it worth taking the chance.

The most famous mathematical object that bears his name is Pascal's Triangle. Pascal did not invent it and he called it the arithmetical triangle. (It's bad form to name stuff after yourself in math). While he didn't invent it, his treatise on its properties cataloged almost everything that was known about the array of numbers at the time, so other people studying it took to calling it Pascal's Triangle after he was dead.
René Descartes was also a French mathematician and philosopher. His most famous philosophical statement is "I think, therefore I am." (In Latin, Cogito Ergo Sum.) His point was that he must exist because he is both the originator and only witness to his own thoughts, which are the start of anything he can bring into existence. (Movies like The Matrix and Inception actually explore this philosophical idea a little deeper.)

Cartesian coordinates are named for Descartes, and this simple idea was able to link the fields of algebra and geometry in new and important ways. Cartesian coordinates can be extended into three dimensions (x, y, z) rather easily, and the math is not that hard to extend his ideas into four dimensions and beyond.

Pascal and Descartes had a major falling out over, of all things, a barometer, which was a new invention at the time, developed by the Italian Torricelli in 1643. Pascal bought one and had it shipped from Italy. He began measuring air pressure everywhere he could take his cool new toy. He noticed the air pressure on the roof of the cathedral of Notre Dame was always lower than it was on the ground floor, so he postulated (correctly) that as you go up in altitude, the air pressure goes down. He took this small amount of data to the correct conclusion that if you get high enough above sea level, eventually the air pressure must shrink to effectively zero, and the space around the earth was a vacuum.
Descartes heard his argument and was not convinced. His counter-argument was that the Sun was a fire and fires cannot burn in vacuums. Pascal did not have an answer for this, so Descartes considered that he won the argument. (In fact, both of them are right. the Sun is a nuclear furnace, so it does not need the oxygen of an atmosphere to burn. The ideas of nuclear physics were still centuries away, so neither of them could have known how it worked.)
Descartes wrote a letter to a friend that had this insulting sentence: "Monsieur Pascal has too much vacuum in his brain."
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Blaise Pascal was a French philosopher and mathematician. A very devout man, he put forward the idea that everyone should have faith in Jesus as the Lord and savior for mathematical reasons. The payoff for believing was life eternal and the payoff for not believing was hell, so the better situation was infinitely better than the worse. Even if there was only a small but finite chance it was true, the infinite payoff made it worth taking the chance.

The most famous mathematical object that bears his name is Pascal's Triangle. Pascal did not invent it and he called it the arithmetical triangle. (It's bad form to name stuff after yourself in math). While he didn't invent it, his treatise on its properties cataloged almost everything that was known about the array of numbers at the time, so other people studying it took to calling it Pascal's Triangle after he was dead.
René Descartes was also a French mathematician and philosopher. His most famous philosophical statement is "I think, therefore I am." (In Latin, Cogito Ergo Sum.) His point was that he must exist because he is both the originator and only witness to his own thoughts, which are the start of anything he can bring into existence. (Movies like The Matrix and Inception actually explore this philosophical idea a little deeper.)
Cartesian coordinates are named for Descartes, and this simple idea was able to link the fields of algebra and geometry in new and important ways. Cartesian coordinates can be extended into three dimensions (x, y, z) rather easily, and the math is not that hard to extend his ideas into four dimensions and beyond.

Pascal and Descartes had a major falling out over, of all things, a barometer, which was a new invention at the time, developed by the Italian Torricelli in 1643. Pascal bought one and had it shipped from Italy. He began measuring air pressure everywhere he could take his cool new toy. He noticed the air pressure on the roof of the cathedral of Notre Dame was always lower than it was on the ground floor, so he postulated (correctly) that as you go up in altitude, the air pressure goes down. He took this small amount of data to the correct conclusion that if you get high enough above sea level, eventually the air pressure must shrink to effectively zero, and the space around the earth was a vacuum.
Descartes heard his argument and was not convinced. His counter-argument was that the Sun was a fire and fires cannot burn in vacuums. Pascal did not have an answer for this, so Descartes considered that he won the argument. (In fact, both of them are right. the Sun is a nuclear furnace, so it does not need the oxygen of an atmosphere to burn. The ideas of nuclear physics were still centuries away, so neither of them could have known how it worked.)
Descartes wrote a letter to a friend that had this insulting sentence: "Monsieur Pascal has too much vacuum in his brain."
<br>
Tuesday, March 8, 2011
Five eccentric 19th British mathematicians who started mathematical logic.
Mathematical logic got its first great boost forward in the 19th Century, though at the time there was little practical use to it.

George Boole is considered the originator of modern mathematical logic, so much so that the field is called Boolean Algebra. He wrote his important treatise The Laws of Thought in the 1850s.

Augustus de Morgan is another important pioneer. The ways to distribute a not sign ~ through parentheses are called de Morgan's laws.
~(p v q) = ~p ^ ~q
~(p ^ q) = ~p v ~q
He was one of the first professors at University College London, the first major school in Great Britain that accepted students who were not Church of England, which meant that Catholics, Jews, protestants of denominations other that Church of England and those who professed no faith whatsoever could get a first class education in Great Britain.
~(p v q) = ~p ^ ~q
~(p ^ q) = ~p v ~q
He was one of the first professors at University College London, the first major school in Great Britain that accepted students who were not Church of England, which meant that Catholics, Jews, protestants of denominations other that Church of England and those who professed no faith whatsoever could get a first class education in Great Britain.

Charles Babbage was another British logician, and he wanted to take mathematical logic to the next step. He designed the world's first mechanical computers, the Difference Engine and the Analytical Engine, both of which were designed to run on steam. Problems arose when trying to build the machines and neither was ever completed.

This did not stop Countess Ada Lovelace, the only legitimate daughter of the famed British poet Lord Byron, from designing programs for Babbage's machines. The Countess Lovelace was educated by de Morgan and is given credit as the first computer programmer. the language Ada is named after her.

The best known of the British eccentrics fascinated with logic in the 19th Century was Charles Dodgson a.k.a. Lewis Carroll. While still famous for Alice in Wonderland, he was also a mathematician, clergyman and photographer, and enjoyed putting together logic puzzles based on the ideas of syllogism using silly but logical statements. For example:
(a) No ducks waltz.
(b) No officers ever decline to waltz.
(c) All my poultry are ducks.
Therefore (d) None of my poultry are officers.
(a) No ducks waltz.
(b) No officers ever decline to waltz.
(c) All my poultry are ducks.
Therefore (d) None of my poultry are officers.
Here is also a link to the biographies of five 20th Century mathematicians who made great contributions to the field of computer science when it was much more practical.
Tuesday, January 25, 2011
Wednesday, June 30, 2010
Monday, June 21, 2010
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