Friday, September 30, 2011

You can Count on Asimov

Isaac Asimov is on a short list of my favourite science authors.  The list has two names on it: Arthur C. Clarke and Isaac Asimov.  Both write excellent science fiction (Asimov's "I Robot" and Clarke's "Fountain's of Paradise" are my personal favourites) and both write excellent topical science articles and essays.  While Orson Scott Card writes some compelling sci-fi (Ender's Game is probably my favourite novel of all time), he is not a "popularizer" of science - it is rare to find an author that is skilled in both fiction and non-fiction.

Asimov may have been the most prolific author ever, having published upwards of four hundred pieces.  His direct style in story-telling and, at times, redundant style of communicating in non-fiction does not appeal to everyone, but it does appeal to me.

Asimov's largest volume of work involves the communication of science, but physics in particular.  I just finished reading "Asimov on Numbers," which involves mathematics, but really focuses on, well, numbers.  It is a collection of essays written over a period of many years, beginning in 1959.  Although all articles are between four and five decades old, they have aged well.  The only instances where the book feels old is when population and financial figures are discussed, as the absolute values of both have inflated significantly in the ensuing years.

I learned a lot in reading these essays, mostly about the history of mathematics (very fascinating) and the Earth's geography (which, as it turns out, can be described so well numerically).

Asimov challenges the reader to consider the very act of counting, and note that the ten-based arabic counting system used around the world today is in fact quite arbitrary.  The base of ten is convenient as we have ten fingers, and groups of ten appeal to people (take the ten commandments for example).  In fact, we could have had a different base...perhaps a base of twelve.  In such a case, a number like 18 (in the base ten) would actually be written as 16, since the first digit would represent 12, and 12 + 6 = 18.  This may seem absurd, but computers are perfectly happy using the binary counting system, which uses a base of two.

There is even an essay on the subject of large numbers.  Here, we are asked to ponder the question, "What is the biggest number one might ever need to describe any measurement within our universe?"  I already knew that a googol referred to 10 to the power one hundred.  However, the fact that a twelve-year-old had proposed the number was news to me.  But there are numbers bigger than a googol...I won't mention them though, because that would spoil the fun of reading about them from Asimov (I actually laughed out loud reading this particular essay).

I particularly enjoyed learning about the ancient greeks, such purists when it came to mathematics, that they refused to recognize any geometrical activity that required more than a ruler and compass.  And yes, there are multiple articles about the irrational number known as pi.

Articles centering around geography use numbers to describe large things, like the volume of water on Earth, or the height of our highest mountain peaks.  We are also invited to think about how many electrons can fit in the volume of the universe.  This is a pretty big number (though not quite a googolplex).

I read and write so much about science, but seldom recognize the language with which we communicate it quantitatively: mathematics.  With this in mind, my next posting will touch on my favourite math topic: differential equations.

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