Tag Archives: algebra

Bastard Reasoning

What can be nothing one moment and something the next, yet disappears in the presence of anything? –  Robert Kaplan, The Nothing That Is (59)

IMG_0042 The other day, my fourteen year old son pointed out that life and death are not antonyms, “You can’t have death without life, therefore the opposite of life is not death, it’s nothing.” Nothing, as in, an absence- not even an absence- a void without context- Well, what is that? my other sons and I wondered… I had cause to think on this thought further as I was coincidentally reading The Nothing That Is: A Natural History of Zero by Robert Kaplan.

Zero is neither negative or positive, but the narrowest of no-man’s land between those two kingdoms. (190)

Kaplan takes the reader through the transition of numbers from mere adjectives to nouns in their own right, and then he hits us with the mystery and enigma that is zero. Either Kaplan is an extremely clear and gifted writer or my math skills are far more impressive than I ever knew. Alright, settle down, Jessica, that’s a bit of an overstatement. Maybe. It may be a simple thing for most people to get their heads around why any number to the power of zero is one, but I got through college algebra getting the answers right without knowing what it really meant, but which now, thanks to Mr. Kaplan, I do. The next day, I tried to get my eighteen year old son to appreciate how exciting it was that I actually understand the concept, but he wasn’t up for my enthusiasm at 8 am, if ever.

But I digress-  before Kaplan even gets into what zero is (or isn’t), he gives an account of the possible ways by which it came to be understood at all.

If you favor the explanation that the ‘O’ was devised by the Greeks without reference to their alphabet, its arbitrariness is lessened by noticing how often nature supplies us with circular hollows: from an open mouth to the faintly outlined dark of the moon; from craters to wounds. ‘Skulls and seeds and all good things are round,’ wrote Nabokov. (18)

One of my favorite images from this natural history is the method for computations that the ancient Hindus used: a board covered in sand to mark the numbers, subtractions, and additions as they went along. Kaplan tells us their word for “higher computations” is dhuli-kharma, ‘sand-work.’ But what is most intriguing to me  is the more metaphysical idea that the way in which they expressed zero (mostly as a place-value marker- which was a huge development) was by a simple finger impression, a dent of nothing formed by something…there is something perfectly beautiful in that…

Once zero was an official thing then things got a little complicated. Zero takes us out of the realm of  nouns into travels as a verb and things get a lot freaky. A number to the power of zero is one, but what of zero to the power of zero? How can that equal one and also, zero? What about division? Division is the first clue, in fact, that we have problems comprehending the magnitude and minuscule nature of the slippery zero.

‘Allez en avant et la foi vous viendra,’ said French mathematician d’Alembert: ‘Just go ahead and faith will follow.’ (157)

That math so elegantly sums up all the mystery and power of our universe is something I find fascinating. I love books such as this that make some of that wonder accessible to my rather limited mind.

After all, maybe, like zero, we are all indivisible in our center. Knowing we’re nothing, but only in the context of our absolute something. I kind of love that idea- we are one with zero. Kaplan draws from a gallimaufry of disciplines in  a poetic, profound and valiant attempt to describe zero, that “pure holding apart,” concept to which zero lends and points itself. The poetic justice of taking our psychologically linear perspective and wrapping it around into the perfect symbol- 0, stretches all boundaries of philosophy and meaning: circumference – everywhere; center – nowhere* …by the end of the book I felt as though my skirt had been caught up in the door of a moving car driving around in circles and I was just holding on for my life. When it stopped,  all I could do was smooth the tangents from my shirt, straighten the x-axis of my skirt and say: Kids,  I got nothing, I have no answers.  But whew, that was fun!

Opposites are an illusion of language. Something and nothing, you know, are equally false substantives. (218)

*Sphaera cuius centrum ubique, circumferentia nullibi

**“…space, which is everlasting, providing a situation for all things that come into Being, but itself apprehended without the senses by a sort of bastard reasoning…” Plato’s Timaeus quoted (63)

Alimentary Algebra

My version of a traditional Sicilian Cassata

My middle son and I attend college together. I kind of forced him to take Intermediate Algebra this term as I wanted to make use of the textbook that I had purchased for myself in the fall. It nearly cost as much as the class. Possibly I love the idea of this more than he does, except as I have recently taken the class, I turn out to be an excellent private tutor for him. We have class on Tuesdays and Thursdays. We go early to work on homework in the library and then at noon we head to the cafeteria to have lunch together. I am aware that this is a unique and (for me) wonderful way to spend two days a week. I regal him with all of my “don’t do that” moments of math stupidity, but there is always some mental deficiency to rail against on our drive home.

I have to admit to liking Algebra, an arabic word meaning restoration or, my favorite: reunion of broken parts. A method of reduction and balance is one description I read that appeals to my sense of beauty. I derive a childish pleasure out of reducing, eliminating and balancing the equations. My pencil swiftly crossing out and rewriting with abandon.

Although my son and I are a lot alike, I can see that he “gets” the math more than I do. Sometimes when it gets complicated he wants to, and can, understand the why. I’m interested, but am satisfied in being able to simply apply the rules or formula. This is more revealing of my own limitations than anything else. I try to explain to him my feeling for math: It’s like cooking, I expound, anyone can follow a recipe and if they are literate, get a good result. That is my level of math. But I know that there is a higher level- like when you can simulate a recipe in your mouth before you even cook it, when you know that omitting x and adding y will improve the end result. The improvisational aspects that I can grasp in cooking: I am not there mathematically. I am not saying, if I was so inclined, that I could not get there. I’m sure I could, but these things take time. It took me years to learn to cook at the level of letting the ingredients rather than the recipes lead. I’ll probably never be Emilie du Chatelet, but then again, although I make a mean cassata,  I’m not Jacques Torres either. I’m just trying to press up against the edges of my own mediocrity.

Math with Miss Parker

Every time I open my Intermediate Algebra book to have a gander at the week’s lesson the same thought goes through my head, “What fresh hell is this?!”

Settle down, Dorothy.

I am usually relieved…more shocked really, to I find that I get it.  A few weeks ago I had a glass of wine and began hacking away at my homework. I don’t necessarily advocate drinking and Algebra, but it’s not a bad way to spend a Friday evening. Every time I put the answer into the computer (my class is online) I would scoff, “There is no way that ugly number is the answer.” But, I would be wrong. Wrong in my rightness, as usual. “Nice job!” the program would egg me on. I’d get a sort of sinking feeling; a voice in my head would say, “You don’t really know why that’s right do you?”

No Dottie, I don’t. Shut up.

But I couldn’t stop myself, even though I knew I would have to do it all over again to make sure I was reasonably competent.

It’s the stupid mistakes that kill me: the unforced errors. I am, it would appear, more than a little prone to them. I tried making a deal with the math gods: offering up 1 or 2 answers for every quiz and test I took, “Take them: my gifts to you.” They were mostly appeased.

That is until yesterday.

I had to take a quiz. I decided to take it at the college in the library. I pressed the “I am ready to start” tab: the commitment that small action requires is unnerving. The quiz is timed: once you begin you have to finish. I had had a pretty easy time with the homework, so I was feeling okay even though my day had started out on the wrong track when I ran my son’s ipod through the wash cycle.

No matter, carry on.

It was going swimmingly, a little too easy. I was working on the final problem on the scrap paper in front of me. I looked up to input the answer and a black screen looked back at me. I rose from my seat; so well accustomed to my ridiculous life I was not even slightly perturbed. “Excuse me,” I politely interrupted the librarian in my best sotto voce library-esque voice, “I’m in the middle of a timed quiz and my computer just crashed.”

She had no succor beyond sympathy.

By the time I reached my lodgings, my kind professor had emailed me to say that she had re-opened the quiz for me so that I could finish. In hysteric haste I finished the test and hit, with reluctant finality, “submit.” Half the answers were wrong. Fully half of them. Does an electronic demon possess every computer I touch? I wondered. No, of course not. The demon possesses me and mine alone. I had forgotten that every answer needed to be given in both its positive and negative form. I got all the answers “right,” and yet they were all wrong. Wrong in my rightness. Again.

I went for a walk. About a mile out it began to pour.