Le mathématique pour le mathématique
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Math for Math’s Sake (What a concept!)
I’m sure you’ve heard of the concept of “art for art’s sake.” That basically implies that the beauty of art is reason enough to pursue it.
The phrase (l’art pour l’art) is generally attributed to Théophile Gautier (1811–1872). He was rebelling against the Idea that, historically, art was used to push some third-party agenda, like some religious, political, or otherwise non-art-related Idea.
It sounds obvious to 20th and 21st century minds that art might not have to serve any purpose other than to enjoy it (after all, almost every child has made a painting or diorama for the fun of it). But for it’s day, l’art pour l’art was a very rebellious and subversive concept.
We haven’t progressed far enough, though, that most people realize that one of the reasons, if not the greatest of reasons, to have an interest in math is for the beauty and romance of math.
Yeah, you read that right. Math, beauty and romance, all in the same breath.
Those who don’t see any beauty or romance in math, or worse, can’t even imagine it, are at the same intellectual stage, as far as understanding mathematics, as those benighted pre-enlightenment minds who couldn’t appreciate nor participate in the arts, except for the glory of the king, the emperor, God, or whatever else they needed to make themselves feel worthy.
Art can serve any purpose you want it to, good or bad. So can math. But the ultimate purposes of both may just be to be - for your personal growth, enjoyment, participation, etc. Both art and math are activities that make a person more human.
James McNeill Whistler wrote :
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“Art should be independent of all claptrap —should stand alone [...] and appeal to the artistic sense of eye or ear, without confounding this with emotions entirely foreign to it, as devotion, pity, love, patriotism and the like.”
You can find out more about this subject at http://en.wikipedia.org/wiki/Art_for_art’s_sake.
Today, in most American schools, math is a “subject,” and only a subject. It is taught for the pure utility of it. To “pass the test,” to “get a job,” or whatever.
We play sports for the fun of it, do art for the fun of it, play music for the fun of it. As soon as they become “subjects” they become a major drag.
As a practitioner of the art of magic, I can attest that playing with numbers can be as much fun and fulfilling as playing with cards can be. It is hypnotic, like that “zone” you can get into while creating art, playing music, playing sports, etc.
A person can only realize this once math is taken out of the realm of “drill and kill and test.” The problem is that very few elementary school teachers have any interest in math, besides as a “subject,” and policy-makers don’t have a clue as to what you can use math for besides bean-counting.
Therefore, to take math out of the drill and kill realm, you usually have to do it yourself, with the help of inspired input. You can best find that in your local library or bookstore. (You could look for it in schoolbooks, but you could also look for diamonds in pigsties, or an honest person in Congress).
The trick is to willingly suspend your disbelief for a short time while investigating new inputs. One good way is to learn a new method for doing some arithmetical operation, and get good enough at it to impress someone else with it. On the way to doing this, you will probably have to practice a bit (without a test hanging over your head!) and that will get you a chance to experience what it is like to be in the “zone.”
A good place is to start is mental multiplication by 11. You can find a good interactive lesson on it at mathmojo.com.
The beauty of math is reason enough to pursue it.
Go see for yourself.
Hotcha!
Brian
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Comment by Khaled
Here’s something I thought up a few days ago. Don’t know how interesting it is.
It came to mind (not sure why), that 81 and 18 add up to 99. This was kind of intriguing since the numbers are similar.
But then I realized there was more to it than that. Both those numbers were not just multiples of 9, but were in fact 9^2 and 9*2 adding up to give 99 (two nines). Chatting with a friend, we wondered: was this a coincidence, or did it hold for higher numbers?
Let’s see:
99^2 + 99*2 = 9801 + 198 = 9999
999^2 + 999*2 = 998001 + 1998 = 999999
Basically, if x is a series of nines, then x^2 + 2x gives a series of nines twice as long.
So I think to myself “This can’t just be a coincidence. What is going on here?”
I came across the answer through the way I had been squaring the numbers. To figure out 999^2, for example, all I did was figure out 1000^2 (1000*1000 = 1000000), find 999*1000 by subtracting 1000, then find 999*999 by subtracting 999. This holds whenever you want the square of an integer given the square of the integer plus 1, as shown by:
(x+1)^2 - x^2 = x^2 - x^2 + x + (x+1) = 2x + 1
But that can simply be rearranged as:
(x+1)^2 - 1 = x^2 + 2x
So, if x is a series of nines, then x^2 + 2x is simply equal to a power of ten, squared, minus one.
Recognizing that the powers of ten always square to a one followed by a series of zeroes, it is clear that subtracting one will give us a series of nines.
And so the trend does hold, for all numbers made up entirely of nines.
Loving the chronicles by the way, and the multiplication method in the previous post. It works quite well for me.