Sunday, February 23, 2014

Learning our lessons



Human beings must learn so many things in the course of their lives. That is not what separates from the rest of the animals, however. It’s the level of our self-awareness. Among other things, we learn that we are indeed human – gradually understanding more of what that means.

I have already forgotten so many things. What was it like when I first began to learn about pain and fear, for example? Oh these things are not unique to humans among the species of living beings, but we do become aware of them in some unique ways.

I am thinking now of a little girl that I know. She smiles easily. She also put on a face to go with the words when she said that it was sad that the puppy they were taking care of along with their own puppy had to go back to its family.

And then the other night I heard that she was in a top bunk and a ceiling fan struck her and bloodied her nose. That’s all I know really. But I imagine the pain, maybe more than a little fear, the shock of happily playing one moment and then blood. These are the things that we learn about.

And I’m sure that she will be okay, for now, and I - roughly ten times her age - I am okay, for now.


The times tables were easy. Reading and writing. I learned these basics when I was about her age.

Hurt and loss are much harder lessons. I can bear to think about a bloodied nose. Two times two is four. But no calculator I know about can work out to my satisfaction some of the suffering I have experienced or seen in others.

It gets to be a little like working with imaginary numbers. In math, the only way to think of numbers such as the square root of -1, for example, is with your imagination. And even then, the concept isn’t clear. But yet you can work with such numbers. A man named Benoit Mandelbrot has done some amazing things with these imaginary numbers. Now in this age of fast computers, you can readily see how an infinite series called the Mandlebrot Set (a series  that includes these imaginary numbers in an equation with the results then plotted on a graph  and visualized on your computer screen) will produce some of the most intricate and beautiful patterns that you can see.

And I have also seen people work with pain with amazing results. Some answers have been suggested, but I’m afraid this problem still needs more work. Still there is no escape, hurt is one of the elements of life.

I can’t understand why it must be that children so young must begin these lessons so early. But I suppose that with time so short and with even more complicated problems ahead, humans simply must begin learning about life when they are very young.

But not about pain every day or very moment. There should also be time for children and all of us to go out and play and laugh. There are things to learn about pleasure, too. Life is intricate and sometimes beautiful.

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Two places to start exploring the Mandelbrot set:

Zooming in to infinity with musical accompaniment:

More about the math and some explanation - as well as a gallery of images:

You don’t need to understand the mathematical language to appreciate this, but effort will be required if you wish to learn how this all works. But if you take this basic formula and plug in a succession of complex numbers which includes the imaginary number – the square root of -1 – and plot the result on a graph, you will get the amazing fractal patterns unfolding on your computer screen. Of course, it’s more complicated than I’m describing, but it starts with this formula:  zn → zn+1 = zn2 + c. You should start by looking at the pictures.

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