Teaching myself arithmetic at sixty-five

Hoping to educate myself and write a book about it, I began to study mathematics at the age of sixty-five, which was five years ago. As a child, I was kicked off the math train in algebra, so I decided to start there and then study geometry and calculus—three of the so-called eighteenth-century disciplines. pure mathematics. I passed algebra and geometry in high school by cheating, not a good life lesson for a teenager, but I never took calculus. I don’t know what it is. It’s less of a theme than a trip, a unique place where girls and boys share secrets.

For two years, I spent my days learning what children learn. I’m going back to childhood not to take anything back but to try to do things differently from the way I did, try to do better and see where it leads. When I hit the wall, I heard a voice saying, “There’s no reason for this. You failed the first time, and you will fail now. Trust me. i see you.

After a while, my studies started to be in two streams. One way is to try to learn algebra, geometry, and arithmetic, and the other way is to stick to the things they introduced me to and lead me to think about. Even though it’s humbling to realize that what I know means nothing to what I don’t know, that’s what keeps me going. I have done the math, to the best of my ability, but the thinking and questions raised continue.

What did I learn? Among other things, while mathematics is the greatest invention of civilization, it has also provoked many unsolved conjectures. Those figures who live in the highest positions in relation to these ideas are unable to correct them. Life is not enough to work.

What else? That math is either true or false. Like writers and musicians, mathematicians generate ideas that do not exist in the physical world. (Anna Karenina is no more true than the imagination about Anna Karenina.) Like other artists, mathematicians have the ability to navigate a world that other people visit. not. For mathematicians, this country has more rules than any other. Moreover, the difference between mathematicians is that they all agree about the things in that world, as they see them, and all mathematicians know the same thing inside, although things are notional. No one, if right, is more right than another. Parts of this world are inhabited, and parts are uninhabited. The regions were visited by only a few people, and the regions were not visible, like dark spots on old maps. The parts that appear to be ephemeral, but also hold true to reality, and are more reliable and permanent than anything in the physical world. Two people who don’t share the same language and don’t understand a word the other says can do math with the other, silently, like thinking.

It is strange how innocent the imaginary world is. This characteristic feature is puzzling, even to mathematicians. Mathematician John Conway once said, “It’s amazing, and I don’t understand it, since I’ve been a mathematician all my life. How can it be there without being there?”

Some of the things I learn are so difficult for me that I feel lost, confused, and stupid. I couldn’t get rid of these feelings, because they accompanied me as a dark companion, an experience that I could shake off only by working harder and, of course, for a short time. alone. There are times when I feel like I’ve made a point that I’m not ready to carry out, but I keep going. I was motivated, in part, by anger and hurt feelings. I got him for math, because I remember his self-satisfaction, his humility, and his bad temper. I was tortured, and I was hurt. I am coming back, with the wisdom of half a century, to knock the smile off the face of the mathematician.

As a child, I was fascinated by mathematics. Although some people are tone deaf, I have wondered if I am mathematically deaf. I enjoy reading about math and thinking about the world it introduced me to, though. Exploring that world as tourism is spreading, and it has changed my mind. What I wrote was, to my surprise, a metaphysical travelogue about a fantasy land. The title is “A Word of God: Teaching Algebra, Geometry, and Calculus at the Edge of Old Age.”

Mathematics, on the other hand, is full of mysteries, and, although I can understand only the simplest things, I am fascinated. The easy part is where the numbers come from. They don’t often appear in job records. In “Chinese Myths,” Anne Birrell writes that the Coiled Antiquity myth, which belongs to “a small ethnic group of southwestern China,” explains “how numbers were made” and “gives the etiological account of the science of mathematics,” but he gave no reason for this statement, and I could find none, so I must take his word for it. Gods and guardians are few in number. Plato, in the “Phaedrus,” says that he heard that there was in Egypt a god named Theuth, who “of arithmetic and calculation, geometry and astronomy, not to mention details and with dice,” but that’s just the old saying. to the gods and making up numbers that I can find, and it is not clear that Plato did not do this. Babylonian, Indian, African, and North American stories and cultures, as far as I can tell, are about more than just numbers. The authors of the creation accounts probably thought of numbers as practical things, like the ax and the wheel, and did not think they needed explanation.

A number is as simple as a letter – both are serial devices – but letters are real and numbers have esoteric meanings. If I write the letter “A,” it’s the letter “A.” It doesn’t represent anything, it is something. If I write “4,” however, it is not “4” as “A” is “A.” “A” is solid, the representation of a sound, but “4” is a symbol,​​​​a word representing a collection. Scaleless and invisible. It can be four cats or four galaxies. I can write “4,” but I can’t say it is it “4,” at least not all the equivalents of “4.” I can display only “4”, by collecting four elements—”AAAA,” for example.

Numbers are used in calculations, which are groupings. Letters changed language from something ephemeral to something tangible, another form of association. Through addition or subtraction or any other mathematical operation, one number can give us another, which letters cannot do, however, unless you think that addition is the same letters to each other touch a word, it is not. . You cannot divide a word by a word, or a letter by a letter. You can’t have a half letter. Or the square root of the letter. Or 3.65 percent of a note. (Just in math, I read somewhere, “A/B” is a mental statement. In agreement, we can change the way we say it, but we can’t change the number number. We can accept “theater” or “theatre,” but with “5 + 7” we can’t do anything about it.

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