Because I don’t think of math. My life is almost entirely math free. I seldom think of money but when I do I think in terms of math. I look at financial reports. I figure out if the cashier gives me the right change at the store, but never does my math thinking rise above multiplication or division. I see no reason that it should. There are I admit pursuits that require math, but my life rarely crosses path with them. In fact, every once in a while at the end of the day, when I’m turning off my computer in the shack and getting ready to go into the house, I have a sip of Bushmills whiskey, lean back, put my hands behind my head and think
“Another day gone by without algebra.”
I know people will say that math is all around us, that math is essential to so much of everyday life, that we take math for granted, that without math life as we know it would be impossible. And that’s probably true. But I don’t have to think about it, because I have a calculator on my phone that does math for me. And X? I have not solved for X since perhaps the late 70’s. I don’t remember what X was. Do you?
Does math help us develop our brains in some good way? Teach us logic? Have benefits that go beyond coming up with a number that is essential for one thing or another? Probably so. But I seem to be doing all right by virtually ignoring it. Let me give you an example of the depth of my need for math.
I’m building a woodshed slowly, taking on one part of it at a time. I built the foundation by making little concrete posts. I knew how long I wanted it to be and how deep. I built the floor of the woodshed, a platform really, off the ground at a convenient height so I wouldn’t have to bend over so far to pick up logs. I figured I would gap the boards about a half inch to let air flow up and dry the wood. I incorporated posts going up that would later hold a roof and determined how high I wanted it by reaching up and determining how high I could comfortably stack wood. All that was done simply with a tape measure. I did have to calculate how much wood to order for the platform. I took out my I Phone, multiplied the length of the platform in feet by twelve, converting it to inches, and then divided that number by the width of the board plus a half inch for the gap. From that number I determined I could order eight footers and cut them in two so I cut the number in half. It was calculator stuff.
Same thing with the roof. I looked at the posts sticking up in the air, imagined the kind of roof I wanted and how I wanted it to look, and invited John Liebhardt to come to the shack for coffee. John is a carpenter, a neighbor, and a good guy that has done and is doing some more work on our house. I asked him to look at my woodshed project.
“John, I want to build a pitched roof that’s asymmetrical to resemble my shack roof but I’m going to gap boards and cover this one with wood shingles. That could be lighter than a plywood sub roof with asphalt shingles. Think I need to stay with 2x6 rafters on sixteen inch centers?”
“Oh, maybe not. But I’m a fan of staying with sixteen inch centers anyway, because you know then it’s not going to sag and everything will be tied together well. It doesn’t cost that much more to put up a few more rafters. What I would do though, is when you put up your two by lumber on these 4 x 4’s, which you’ll attach the rafters to, is to bolt them on instead of nail them. And I’d do 2x8 facing boards there and 2x6 rafters. Like I say, you could maybe get by with 2x4 rafters on a small structure like this but why do it? Why not build it well and ensure it lasts longer?”
“Yeah, you’re right.”
“And when you know how much overhang and basically how you want that roof I can cut you a couple of sample rafters.”
“I was hoping you would say that.” John did the same thing for the shack rafters.
Cutting rafters, with the bird’s mouth and the proper angle where they join the ridgepole, and stair stringers which result in steps that are equal in height and depth, requires real math. Slope, rise, span. Carpenters used to figure that all out on their framing squares. I worked for a pair of carpenters in high school who did such calculations. Mr. Walsh, the guy of the two who was better at it, would take a piece of scrap board, a pencil, some measurements, his framing square, and go off by himself to figure it out. He liked to sit on the tailgate of his pickup by himself with a cup of coffee. You could see almost see him concentrate. He would usually start by looking over his measurements and sharpening his pencil. Then he would jot some figures on the scrap lumber, consult the square, and do it all again before marking out lines on boards carefully before cutting the pattern board himself.
That’s real math that matters and I readily admit I don’t know how to do it. But fortunately others do. Actually, John tells me there is a computer program that does all that now. The markings on the framing square have pretty much gone the way of the slide rule in countries flush with capacity for computing. Somebody has figured it out for us and shared their knowledge.
After John left my math consisted of adding two feet, a foot at each end for overhang to the sixteen feet of platform the roof will cover, multiplying 18 by 12 to convert that length to inches, then dividing it by sixteen to determine the number of rafters I’ll need. I need fifteen. I should be able to get both rafter slopes out of an eight foot 2x6. Now I know what to order for rafters. Multiply and divide. Calculator.
That may prove to be the most sophisticated math I do the entire year. And it’s been that way for about forty seven years. Even when I had responsibilities to manage big budgets in my work, I found that budgets are built primarily by addition and subtraction. I used to do them on green columnar pads using a calculator from Walgreens and a Dixon Ticonderoga Number 2 pencil. In the eighties I discovered that spreadsheet programs on a computer do a lot better job at those functions than we ever could. I rarely felt math deficient. I still don’t.
I am of course. I was English major. I stopped taking math in high school after I finished geometry in 1967, and I found a way to graduate from ISU without taking (I should say passing) a math course. I am by my wife’s standards, she a math major and retired math teacher, woefully under educated and extremely ignorant of the benefits and importance of higher mathematics. I admit this. However life goes on without it, and I’m happy to report it’s not bad.
There are however the occasional run ins with math majors. My wife doesn’t like to talk to me about math because she is convinced my underlying motivation in having such discussions is to make fun of it, an intent she classifies as evil. I see it as merely mischievous. As a result we don’t have those conversations anymore. I find it safer to have them outside of my marriage.
The other day I was counting the offering at church with my young friend Kevin, a math teacher at the high school. I faced a computer screen while he filled out a deposit slip by hand and gave me information, check numbers and amounts, off checks which I entered into a spreadsheet;. One was a computer check with a big string of zeros at the beginning of its identifying number. He began to read the zeros.
“Kevin, just give me the real numbers. You can skip the zeros.”
“Zero is a real number Dave.”
Oh boy, I thought. Déjà vu. I’ve had this same conversation before. Nothing I say from here on out will make any difference, because math people live in a world of such certitude. I won’t go so far as to use the word smug. Or self righteous either.
“OK. How about just giving me the integers.”
“Zero is an integer too.” I turned and tried to look at him with as little emotion as possible. Zero affect.
“What you want is just the natural numbers. Zero is not part of the natural numbers.”
“Thanks Kev. So how about we just stick with the natural numbers? Given that zero is nothing.”
“And you can’t say zero is nothing either. That’s not entirely true.”
“Yes I can. I just did. It’s nothing to me.”
Kevin began to laugh and I joined him. Kevin was putting me on, but it reminded me once again that math is a foreign language made up not of words but of numbers and symbols. At the very least it’s a unique way of thinking. And it’s thinking I don’t do.
Last night after choir practice, thinking of my nephew Sean and his common core math problem, I engaged Kevin in math talk again. After teaching all day he appeared reluctant to go into common core specifics, shaking his head and looking away sadly, so I simply asked him to go over that number classification thing. That brought sparkle to his eyes. He immediately looked for a pencil and paper. As he did I knew what ended up on the scratch paper I would carry home would not resemble a poem in any way. I have them here on my desk. I can barely make sense of them. I’m afraid I’m going to have to consult my wife.
Kevin began by drawing a big circle. “You start with rational numbers.” He put a capital R just inside the circle. Then he drew circles within circles making concentric rings that resembled the orbits of the planets in our solar system. Inside the next ring he put a capital I.
“A subset of the rational numbers is integers. Within them are whole numbers.” He labeled the next ring as W.
“And finally you get to natural numbers.” He put an N inside the little circle where the sun would be in the middle of Mercury’s tiny orbit around it. Then he began putting equal signs by the letters and within brackets started scribbling numbers and dots.
“Natural numbers begin with one and go to infinity.” N= {1,2,3…}
“Whole numbers begin with zero.” W= {0,1,2,3…} Kevin grew more excited as he went along, because clearly he really knew this stuff and liked explaining it.
“And integers are all the negative and positive whole numbers.” I={-3,-2,-1,0,1,2,3…}
“Those are all subsets of Rational numbers which include, in addition to all these, fractions represented by decimals that repeat. Like 5/6ths as a fraction, which is 0.833333… to infinity.”
“Then” (he drew another circle) “you have all your irrational numbers, which are fractions represented by decimals that do not repeat or end, the most famous of which is Pi.” 3.141592654…. Irrational numbers also come up often when you are using the Pythagorean theorem to figure out triangles.”
At that point Kevin got pretty animated and broke into a free form historical and improvisational Pythagoras rap, which included some fairly strong opinions about the famous old number cruncher.
“You know mathematicians way before Pythagoras knew that theory. But Pythagoras and his followers, who were pretty much of a cult, really, hung his name on it and it’s been that way ever since. I mean it was a break through, and useful as all heck, but he didn’t discover it.”
Talk to a math person for any length of time and sooner or later they’re going to throw in the name of some long ago mathematician they either admire or hate. English majors do the same thing, the way I might mention some old wordsmith like Chaucer.
Kevin looked at his diagram with a certain amount of pride and then drew a big circle around the two circles representing rational and irrational numbers.
“Put them both together and you get what is known as real numbers.”
“What about imaginary number? “ I asked innocently. Imaginary numbers were always the flash point in conversations between my wife and me about math.
“Imaginary numbers? That would be another circle yet. But you don’t really have to worry about imaginary numbers. They all revolve around the square root of negative one, which is I squared =-1.” He scribbled both things on the paper. “ Once in a while they appear in algorithms engineers use, but for the most part they cancel out before the end of the calculation. I mean you have to know what they are, but they aren’t used often in any practical sense.”
I have in the past badgered my wife about imaginary numbers following their mere mention, which resulted in her refusal to talk math further with me. It would go like this. I would say
“And why would you call numbers, any numbers, imaginary? Math is concrete and practical. Saying there are numbers that are imaginary, using imaginary as an adjective for a set of numbers, undercuts all that. It’s like having a subset of the laws of physics that are called ‘laws of physics we just pulled out of our hat’ or something. It’s stupid.”
To which she would reply “Ok. That’s it. I’m done. You don’t want to understand this. You just want to argue.”
OK, so I didn’t always use the word hat, and I probably should stop using the word stupid in that context. But there is something I don’t like about math. You might even say there is something I hate about math. It’s that smug sense of always coming out with one right answer that makes me mad. I try not to take it out on math people but I'm afraid perhaps I do. Life doesn’t have simple answers. Give me a vague passage from a Don DeLillo novel any day. Keep your love for differential equations to yourself.
I didn’t say that to Kevin. We don’t have that kind of relationship. To Kevin’s explanation of imaginary numbers I simply replied
“I see.”
And so Sean, I’m going to write that blog entry on common core math and the problems it is causing students and teachers alike. But I’m going to have to overcome some attitude to get there. I hope you understand.
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