Wednesday, July 31, 2013

A different lens

As I wrote recently, I find that some reading and exposure to math and math-related concepts gives a different view of the world.  The philosopher and mathematician Bertrand Russell said that it must have been millenia before humans realized a connection between 2 birds and 2 days.  Philosophy and history are often thought to be fundamental in understanding the world but too often mathematics is overlooked. 

Mathematics is often thought to be cold and unfriendly but lots of history, philosophy and logic which can clarify the world and make life far more understandable are not so warm and cuddly, either.  There are other joys and pleasures in life besides friendship and smiles.

Most people I know had a math curriculum of arithmetic in elementary school, algebra in middle school and geometry and maybe calculus in high school.  Traditionally, calculus was considered the top of the lower part of the curriculum.  Nowhere in the curriculum were math subjects that were invented and used after about 1850.  John G. Kemeny came to the US after getting his doctorate in Germany.  He led the creation of a basically simple book called Introduction to Finite Mathematics, the first book to point intelligent, non-math majors to the many branches of math and associated logic that were pertinent to their studies.  The book is now available free on online at Dartmouth, the college were Kemeny taught.  I love that book.  I had plenty of questions answered by it.

I was part-way through college when it became clear that I had to have a minor.  My major was elementary education, which some experts think is a waste of time and certainly not a subject to study.  I agreed to that major when I found it involved more choice in what to study than the alternative possibilities available at that school: a combo English-history or math-science.  I guessed that math for a minor would give me the least homework and leave me the most freedom to date, read on my own, wrestle, and generally have fun. The best math course I had in college was math of finance, how interest is calculated and mortgage pay-off schedules are created.

Toward the end of college, I read "Men of Mathematics" by Eric Temple Bell.  Really opened my eyes to the humans behind the creation of Western math even though the actual history of our Hindu-Arabic counting system and other important insights and ideas from non-Western countries was not touched on.  The crucially important invention and understanding of zero (if it means nothing, why have it at all?) and related subjects of negative numbers, irrational numbers and complex numbers are discussed in the very readable "Zero" by Charles Seife.

A look at mathematics from the view of its history makes things much clearer and less mysterious.  Often, math is associated with the idea of difficulty but part of that comes from the usual way of deciding if some math is understood.  The most common way of doing that is to give someone a problem which can be solved using the mathematics in question.  Very often, in other subjects, one is asked to explain a concept in one's own words, not solve a problem.  It is true that if something can be applied in the sense of a method or procedure, a knowledgeable student should be able to make that application.  But it is also true that having a firm grasp of a concept can be very satisfying and provide the basis for further curiosity and learning.

Another branch of mathematics is entering its heyday now: statistics and data analysis.  Prof. Hans Rosling of the Swedish Karolinska Institute is delivering wonderful, clear and succinct talks on TED talks and YouTube.  He specializes in revealing statistical information that explains some aspect of the world that you might not have currently up-to-dates views on.

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