Has anyone even asked you, after you attended a seminar or class, "so what did you learn," only to have your mind go blank? If so, you just passed the test for being a "normal learner." We all forget most of what we try to learn, even when we can temporarily recall, and use, what was taught. So what makes this happen? This question is what we will explore in this chapter of On Education and Learning.
Why Is It So Hard For Us To Retain Things?
Over the past week, I've continued to look for ways in which we can know for sure we have learned something. Know I've continued to focus my questions on what makes it so hard for us to retain the things we have learned. So what have I come up with so far? To put it mildly, it's complicated. Even so, I have at least found a way to begin to answer this question. Unfortunately, in order to explain to you what I've found, I first need to teach you a bit about what may be the core concept underlying all learning. The idea of fractals.
What makes understanding fractals so hard? Simply this. Fractals, like their cousins, geometric shapes, are the patterns which our minds refer to whenever we try to identify something. Kind of like a basic chart of the visual possibilities. However, unlike geometric patterns, which repeat identically regardless of scale, fractals never repeat identically. In truth, they only repeat almost identically. Which makes them kind of like an "almost geometry."
Oops. Did I just lose you? Let me try again.
Let me begin with what both geometric shapes and fractal shapes have in common. For one thing, they are both shapes. Which is to say, they are both recognizable visual patterns.
And what exactly makes me call them both visual patterns? I call them this because this is what we must learn in order to become able identify things. Everything from kitchen cabinets and the State of California to your dog's gait and your daughter's nose.
OK. So we learn geometric shapes and fractal shapes in order to be able to identify things. So far, so good. This is how they are alike. The question now becomes, so how are these two kinds of shapes different? The answer? They differ in how perfectly they repeat. Let me explain.
Let's begin with the easy one; geometric shapes. With geometric shapes, the basic design which defines them never varies regardless of what we make with this shape. This is why, once you learn to identify a square, you can recognize it for life, no matter how and what it is made of.
In a way then, we can say that "a square is a square is a square." Sort of like Shakespeare's rose. Which means that what makes something "geometric" is that the basic underlying pattern never changes, this despite the fact that we can make an infinite number of square things.
So OK. The basic shape never varies. Not even one iota. The thing to ask is, so what does vary?
Answering this is also easy. With geometric shapes, only the basic underlying pattern never varies. Everything else can vary. In other words, while the "four sides, four equal angles" never varies, the color, size, smell, what's it's made of, the purpose of and so on can all vary. Infinitely, in fact. All this while the underlying pattern never varies. Which is why we can say, "a square is a square is a square."
So what are fractal shapes then?
Start with this. Fractal shapes and geometric shapes are exactly the same. Except for one thing. They differ in how perfectly the pattern which defines them repeats. Thus, as far as the ways in which they can and do occur in the real world, fractals and geometry have a lot in common. They can both vary infinitely in everything from color, size, smell, texture, their purpose, their construction and so on. The difference, then, is in how the basic underlying pattern does or does not vary. With geometry, it never varies. And with fractals, it always varies. But only a little.
In other words, although the basic underlying patterns beneath fractals always vary, to us, fractal shapes remain recognizable. This, in fact, is why we can easily recognize a cloud as a cloud, this despite the fact that no two clouds will ever be the same.
This is also what makes the shapes of clouds fractal rather than geometric. And the shapes of roses and leaves. And the shapes of ocean waves and stock market prices.
It is also what makes some of the things Shakespeare said so amazing. You see, although he never actually spoke about fractals in technical terms, he must have realized that the beauty in our world comes from the way things repeat fractally. Certainly, this is what he must have been referring to when he said, "A rose by any other name . . . " What he was saying was that roses repeat but never identically. Moreover that this pattern of almost repeating but never identically is what makes something beautiful.
Now consider what this means. It means that what makes us see something as beautiful is the degree to which we can see it as fractal. This is why no mere machine can see this kind of imperfection as being the essence of beauty. You see, only in our minds is this pattern recognizable for what it is. Why? Because only we humans can understand what is, in essence, the very nature of our humanity. And the very nature of the beautiful world in which we live.
Fractals. They're amazing.
As for the question I've been pondering this week; what makes it so hard for us to retain the things we have learned. The answer? We retain only those things we have learned to see the beauty in. Translation. We retain only those things we have learned to see as fractals. Everything else, to our minds, is simply geometric. And cold. Or chaotic. And confusing. Especially to us beautifully warm and fractal humans.