the dawn come and flowers grow, even when it’s the middle of the day on a pavement. There’s the Song of Evening, which brings love. So keep your ear open; some day you may hear a piece of the Llano, and you want to be sure to remember it.
I was also going to tell you about how math could be beautiful. No, don’t drum your fingers impatiently on the armrest; someone might see you, and then there would be a great hue and cry: “She can drum her fingers!” and your privacy will be gone. You see, I know about the deadly dullness of math. I mean, who can stand to memorize the Times Tables? I couldn’t! I took an IQ test once, and the problem was all in words, but I immediately saw that it worked out to eight times twelve. Then I had to stop and figure out what that was, while the woman was timing me on the stopwatch. It turned out that that was supposed to be the easy part; most kids couldn’t get that far, but when they did, they knew the answer instantly. Which sort of thing explains why folk never thought I was smart. That, and the way I took three years to master first grade. Yes, I really did! So maybe some day I’ll succeed in memorizing eight times twelve. I wonder if it’s close to the answer for twelve times eight? That would be a nice coincidence! Anyway, arithmetic was the bane of my existence, until about ninth grade, when it changed. I didn’t change, it changed. It quit with the stupid Times Tables, which are called Rote Learning, which is the stuff of idiocy, and started with algebra, which is like a puzzle. If X plus 5 equals your age, what’s X? I’ll bet you can solve that one! You can even use it to solve one of the trickiest riddles ever, which your mother probably encountered generations ago: Mary is 24. Mary is twice as old as Ann was, when Mary was as old as Ann is now. How old is Ann? This is the stuff of fun, if you like brain-buster riddles, which I do.
You can make lines and circles and things on paper with the right X and Y formulae. This is because the answers change. Next year X will be larger than it is this year, because your age will be more. So you can plot a line of all the possible values of X, and you can even follow it back into the past: when you were 4, what was X? What number added to 5 equals your age of four? A minus number, that’s what! Maybe that seems foolish in the real world, but math is a world of its own where strange things can happen. It can be fun making up equations and finding out what pictures they make.
But mainly, it is that math can become very like art, especially with the aid of a computer. You see, a few years ago a man tried plotting an equation—what? No, his name doesn’t matter. He used a complex equation—no, I told you his name doesn’t matter. He made a drawing of all the points that fell inside this equation; the ones that fell outside he ignored. So—oh, all right, his name was Mandelbrot. Now will you listen? He took this complicated formula and used the computer to figure out all the points—and it turned out to be a very strange figure indeed. The main part of it looked like a lady bug, but there were also little lady bugs near it, and they were all connected by curling patterns. When he used colors to mark these patterns, it became beautiful. In fact I would call it art. The patterns keep repeating on smaller and smaller scale, but never quite the same as before, so there’s always something new to find. So this science of figuring out such pictures is called fractals, and this one figure is called the Mandelbrot set (I can’t think why!) and it is considered to be the most complicated object in mathematics—and perhaps also the most beautiful and fascinating. I can look at it for hours, always being amazed. There are patterns like little shells in there, and others like sea-horses, and who knows what else. Maybe your folks have encountered this, and can show you one of those colored pictures in a book. If your mind is anything
I was also going to tell you about how math could be beautiful. No, don’t drum your fingers impatiently on the armrest; someone might see you, and then there would be a great hue and cry: “She can drum her fingers!” and your privacy will be gone. You see, I know about the deadly dullness of math. I mean, who can stand to memorize the Times Tables? I couldn’t! I took an IQ test once, and the problem was all in words, but I immediately saw that it worked out to eight times twelve. Then I had to stop and figure out what that was, while the woman was timing me on the stopwatch. It turned out that that was supposed to be the easy part; most kids couldn’t get that far, but when they did, they knew the answer instantly. Which sort of thing explains why folk never thought I was smart. That, and the way I took three years to master first grade. Yes, I really did! So maybe some day I’ll succeed in memorizing eight times twelve. I wonder if it’s close to the answer for twelve times eight? That would be a nice coincidence! Anyway, arithmetic was the bane of my existence, until about ninth grade, when it changed. I didn’t change, it changed. It quit with the stupid Times Tables, which are called Rote Learning, which is the stuff of idiocy, and started with algebra, which is like a puzzle. If X plus 5 equals your age, what’s X? I’ll bet you can solve that one! You can even use it to solve one of the trickiest riddles ever, which your mother probably encountered generations ago: Mary is 24. Mary is twice as old as Ann was, when Mary was as old as Ann is now. How old is Ann? This is the stuff of fun, if you like brain-buster riddles, which I do.
You can make lines and circles and things on paper with the right X and Y formulae. This is because the answers change. Next year X will be larger than it is this year, because your age will be more. So you can plot a line of all the possible values of X, and you can even follow it back into the past: when you were 4, what was X? What number added to 5 equals your age of four? A minus number, that’s what! Maybe that seems foolish in the real world, but math is a world of its own where strange things can happen. It can be fun making up equations and finding out what pictures they make.
But mainly, it is that math can become very like art, especially with the aid of a computer. You see, a few years ago a man tried plotting an equation—what? No, his name doesn’t matter. He used a complex equation—no, I told you his name doesn’t matter. He made a drawing of all the points that fell inside this equation; the ones that fell outside he ignored. So—oh, all right, his name was Mandelbrot. Now will you listen? He took this complicated formula and used the computer to figure out all the points—and it turned out to be a very strange figure indeed. The main part of it looked like a lady bug, but there were also little lady bugs near it, and they were all connected by curling patterns. When he used colors to mark these patterns, it became beautiful. In fact I would call it art. The patterns keep repeating on smaller and smaller scale, but never quite the same as before, so there’s always something new to find. So this science of figuring out such pictures is called fractals, and this one figure is called the Mandelbrot set (I can’t think why!) and it is considered to be the most complicated object in mathematics—and perhaps also the most beautiful and fascinating. I can look at it for hours, always being amazed. There are patterns like little shells in there, and others like sea-horses, and who knows what else. Maybe your folks have encountered this, and can show you one of those colored pictures in a book. If your mind is anything
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