In math, quality is better than quantity

I was unaware that April was Math Awareness Month.

My unawareness is either a terrible missed opportunity to publicize math awareness or a great stroke of luck that I avoided further exposure of my ignorance.

I think the reason math needs an awareness month is that most of modern math is disguised as quantity.  I guess quantity is pretty good as far as it goes. It’s just that when it comes to things most of us really want to know, we are generally more interested in quality. Like when I was trying to impress my wife with how much affection I felt for her prior to marriage, it would have been extremely foolish of me to say, “I love you about six.” 

Yet looking back, that is what I would have had to say if I expected to love her even more after 48 years together. I suspect we are all the way up to, oh, say, eight or nine, depending on how much longer I expect to live.

However, if I were to proclaim any quality today, I would be forced to say 10. Otherwise I would not expect to live that much longer. See? Numbers have their limitations.

Take the number two. Pythagoras (and who am I to argue with him?) thought two was the first number that had sex. You know, two represents male and female, and all sorts of other opposites. Now, right there, numbers get more interesting than just quantity. I think listing all the things that have opposites would be far more interesting and useful than jumping directly into the fact that two follows one, or that two plus two equal four. 

Speaking of adding, did you know the Greeks thought of numbers as squares or triangles? If you add one pebble plus two pebbles you get three pebbles, which can be stacked into a triangle. If you add three plus three you get six, which can also be a triangle of pebbles. Numbers like three, six, 10 and 15 are triangle numbers.

However, if you add one pebble plus three pebbles it makes a square of four pebbles. Numbers like four, nine, 16 and 25 all make squares.

However, if you add any two consecutive triangle numbers you always get a square number. That is why, to this very day, we think mathematics is for squares. And that’s the reason why I like geometry. Geometry has personality. Yes. Square is a personality. 

With geometry, we can almost always tell when something is a good square or a bad one. (Down, boy! Sit! Bad Square!) There are a number of ways a triangle can be a good one: equilateral, isosceles or scalene. One doesn’t confuse parallel and perpendicular.

My wife says I’m not a square, but I do seem to be perpendicular. I’m not sure what she means by that, yet it seems clear. That’s what numbers with personality can do for you. 

I didn’t learn about symbolic numbers until I sneaked a book out of the library and read it under the covers late at night. I hid it during the day under my mattress, although I’m not sure why. My mother was always afraid to come into my room. Yet, somehow, I sensed that I was on forbidden terrain. Within its pages I discovered that bee cells, snowflakes and quartz crystals all have the same six-sided shape. The reason is that six-sided objects are the most economical use of space. There is also a reason plates, pipes and planets are round. Hurricanes and hair curls both unfold as spirals. Coincidence? I don’t think so. 

The numbers from one to 10 are all represented by a geometric shape. Their designs are found throughout the universe. By treating math as only quantity and bookkeeping, we miss out on a lot more interesting personality traits. Quantity pales in comparison to the heptagon, symbol of the sacred virgin.

Gary McCallister, .(JavaScript must be enabled to view this email address), is a professor at Colorado Mesa University.


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