A Nightmare

After a long pause, a comic. Friday this time.

Math Wizard in Action!

Standing astride the World of Math, Quadratic Formula staff in hand and readying the Theta Bomb, he prepares to deliver a beatdown to a smack-talking triangle.

This is exactly what it feels like to solve difficult problems.

My current favorite math history book is Robert Kaplan's The Nothing That Is, which discusses the history of the development of the number and the philosophical issues surrounding it as well as the very concepts of nothing, nonexistence, and absence.

Towards the end he examines how these ideas can make what seem like sensible questions into utter hash. Treating "nothing" as any other object (though linguistically a noun) leads to questions like "Why is there something rather than nothing?" Speaking as though "nonexistence" is just an alternative activity, people are said to experience their own absence in proclamations regarding who would have been better off if they had never lived. The final chapter is called "The Unthinkable" for good reason.

The title comes from a Wallace Stevens poem.

The Yanghui Triangle

What is that? Well, it's used to find the coefficients of a binomial expansion. Just like Pascal's triangle. Actually, it is the same thing. Yanghui was a Chinese mathematician from the thirteenth century who did work with binomial expansions and created a triangular array to contain them. One interesting thing about the document we have of the ancient Chinese version of the triangle is that it appears to contain an error. Here is a high resolution image where you can try to find it:


An ancient scribe must have been having an off day. Notice also that for some reason, the symbol for "ten" looks a lot like the Arabic numerals version, just turned on its side. There is more history of the triangle, and the answer to where the mistake is, here.

Mathematical Personalities: Gerolamo Cardano

Sorry about the lack of updates, but the life has been busy.

Down to business.

The Italian Renaissance was one of those interesting times in world history in which the great increase in knowledge and trade led to an explosion of wealth, which led to more knowledge and trade, and so on...but we have to remember that these are not modern people. This was a time that was altogether more violent and chaotic than anything we see today (in the Western world, anyway) because for some reason the people of that time and place really knew how to work the chaos into something rather creative. I mentioned Cardano before, but in the context of the solution to the cubic equation, which is a great story. Now I want to mention some other things about the man. The events of his life illustrate the differences between that era and this.

Remember that the modern world comes largely from the Enlightenment with heavy doses of Modernism and Postmodernism thrown into the mix. This all happened after the Renaissance, and the 16th century was more like the medieval world than like ours. His mother fled the plague. He had trouble starting a career in medicine because his parents were not married. He was a gambler and wrote a book on the subject that was the first to make probability into a science. While he contributed to the sciences and mathematics, he was an astrologer as well and was arrested for heresy after casting the horoscope of Jesus.

People who are brilliant enough to make lasting contributions to mathematics have a tendency to be eccentric. Add to this the fact that many discoveries were made before what we would call the modern era, and we find that the people of the history of mathematics are incredible to study.

mathematics, astronomy, religion

I found something on the Library of Congress website: a collection of images from the Vatican Library of mathematical manuscripts from between the ninth and fifteenth centuries.

Saturday Comic:


The background is an ultra deep field photo taken by the Hubble Space Telescope and credit is due to ESA and NASA.

Pascal's quote is from the Pensées, numbers 205-206.

Reputation

Rooster image from here.
All kinds of quotations about mathematics and by mathematicians can be found here.


According to St. Augustine:

The good Christian should beware of mathematicians, and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.

This makes much more sense when you realize that in this context, a "mathematician" is what we would call an "astrologer".

An interesting essay and a comic.

I found something interesting on Reddit today, which is somewhat connected to the content of yesterday's posting. Here is an essay by a teacher and mathematician arguing that math education is too focused on notation and formulas instead of teaching kids about the art of discovering elegant numerical patterns and relationships. He suggests that mathematics should be art and play.

Also, here is the math subreddit.