Archive for November, 2009

What do René Descartes and Friday the 13th have to do with each other?

A few years ago, I read the book The Mystery of the Aleph by Amir Aczel and enjoyed it immensely.  In this book, he tells the story of Georg Cantor and his efforts to comprehend and mathematize infinity.

I recently picked up a copy of another one of his books,  Descartes’ Secret Notebook.

I always mention to my beginning algebra classes that Descartes’ accomplishment of combining algebra and geometry into the one discipline of analytic geometry was a masterful stroke of genius.  Even though my students often don’t appreciate the import of this accomplishment, I always make a point to mention it because I am continually amazed at this conceptual achievement.

As I read through Descartes’ Secret Notebook, what struck me the most was Descartes’ involvement in the heliocentric controversy that roiled European science and mathematics throughout the 16th and 17th centuries.  This is a well-known controversy, but I think the vehemence of opposition to the scientists and mathematicians of that era who espoused the heliocentric theory is sometimes not appreciated.

At least for me, reading the story of Descartes’ life drives home the intellectual difficulties that were created by the Catholic church’s opposition to heliocentric theory.

This is what ties Rene Descartes to Friday the 13th (at least in my mind).

I recently corresponded with Carl Bialik, who writes the Numbers Guy column at the Wall Street Journal.  His column on numerology several weeks ago considered people’s attachment of mystical properties (both good and bad) to different numbers.

In response to his question about what creates a superstition around a particular number (or type of number), my opinion was that it was due to a difference between appearance and reality.

I think that when mathematics or science arrives at a conclusion that contradicts our common sense, there is cognitive dissonance.

We can resolve this dissonance by exploring the contradiction and trying to determine its cause.

The examples I used were the ancient Greek’s fear of irrational numbers and triskaidekaphobia or fear of the number 13.

There are many reasons given for fear of the number 13, but the one that makes the most sense to me is that, although we only see 12 moon phases, the moon actually revolves around the earth 13 times each year.

This is because the earth is orbiting the sun, so that each full moon is in a slightly different position with respect to the earth (but the same in the sun-earth-moon alignment that creates the full moon).

I think that this is why the Catholic church reacted so strongly against the heliocentric theory.  By watching the sky, it seems that the sun, moon and planets move around the earth.

But, if we observe more closely and make some calculations, it turns out that this model doesn’t work.

If we think that the world is one way and mathematics and science give us different information, we can explore and analyze and try to understand the information or we can be afraid of it.

If we don’t have time to explore, analyze and understand, we may end up with fear by default.

Ben Blum-Smith gets at this same idea in his discussion of the impact of mathematical proof.  He points out that if students only ever see examples in which their intuition is correct, they don’t see the benefit of proof.

However, if they see examples (and he lists a few at the above link and a few more here) in which an initial pattern breaks down after it has been established, then students may better understand the benefits of mathematical proof and robust scientific theories.

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There was an interesting article in this weekend’s New York Times about the SAS Institute, a software company in North Carolina.

The company was started in 1976 by four former professors who worked in the agricultural statistics department at North Carolina State University.  The business software they design is made to analyze and interpret massive amounts of digitally generated data.

Their business model is also pretty interesting in that most employees typically work a 35-hour week and the company provides an on-site day care center and medical clinic.  60 Minutes profiled SAS in 2003, but I don’t see this video readily available on the web.

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