to sing with the understanding
There's been a convergence of themes in my life recently. First of all, Catherine and I just had our 1,123rd day of knowing each other. The Eleventy-leventh day was fun, but of course the 1,123rd is our Fibonacci day. (Actually, real Fibonacci numbers would be 987 or 1597, but, taken separately, 1, 1, 2, and 3 are the more well-known.)
Second, I was just reading a rather one-sided interview with Benoit Mandelbrot, in which he looks back over his life as this rambling series of curiosities, to which he can only now ascribe a shape. What a brilliant man, and a kindred soul, recognizing as he did and does the beauty of numbers and their relationships.
And, third, for a few weeks now I've been haunted with a phrase from the writings of St Paul. Everyone recognizes his great rhapsody on love from his letter to the Corinthians: "Though I speak with the tongues of men and of angels, but have not love.... Love bears all things, hopes all things, believes all things.... And the greatest of these is Love." But on the next page there's a little rhapsody on the mind that very few know. It culminates with a phrase I've loved for a long time:
I've inscribed that line on the doorposts of my life. It says so much about who I want to be. Most people don't even recognize the idea of singing with the understanding. Our culture creates dogfights between the heart and the mind, stacked so that the heart always triumphs, as if it had to.
Ah, but the brain has its passions, of which passion knows nothing.
When I think of singing with the understanding, I think of the guys who developed the remarkable Graphing Calculator for Macintosh computers. Their story itself is worth knowing, and the product itself is gloriously worth seeing. It's exactly the sort of thing that Mandelbrot would appreciate: indeed it's the sort of thing he paved the way for, turned on as he was with how things looked. You can come up with an equation like this:
and know that it's a simple prescription for a surface, but when you actually see it, rendered and painted, it becomes something else entirely.
It becomes easy to imagine that you could come up with an equation that would produce the Rocky Mountains, and another the Himalayas. And, from there, who couldn't wonder about the great creator of all this, the developer of phi, whose sorcery brought into existence the properties called — well, what were they called, for millennia, for eons, until just a moment ago when Mandelbrot decided to call them "fractals"? Yet there they were, nameless to us lower creatures, shaping our existence.
Who couldn't fall in love with such a creation? Who couldn't desire to leap among the numbers and letters, to whale-leap through the naked cosmos? I will sing with the spirit, and I will sing with the understanding also.
Second, I was just reading a rather one-sided interview with Benoit Mandelbrot, in which he looks back over his life as this rambling series of curiosities, to which he can only now ascribe a shape. What a brilliant man, and a kindred soul, recognizing as he did and does the beauty of numbers and their relationships.
And, third, for a few weeks now I've been haunted with a phrase from the writings of St Paul. Everyone recognizes his great rhapsody on love from his letter to the Corinthians: "Though I speak with the tongues of men and of angels, but have not love.... Love bears all things, hopes all things, believes all things.... And the greatest of these is Love." But on the next page there's a little rhapsody on the mind that very few know. It culminates with a phrase I've loved for a long time:
I will sing with the spirit, and I will sing with the understanding also.
I've inscribed that line on the doorposts of my life. It says so much about who I want to be. Most people don't even recognize the idea of singing with the understanding. Our culture creates dogfights between the heart and the mind, stacked so that the heart always triumphs, as if it had to.
Ah, but the brain has its passions, of which passion knows nothing.
When I think of singing with the understanding, I think of the guys who developed the remarkable Graphing Calculator for Macintosh computers. Their story itself is worth knowing, and the product itself is gloriously worth seeing. It's exactly the sort of thing that Mandelbrot would appreciate: indeed it's the sort of thing he paved the way for, turned on as he was with how things looked. You can come up with an equation like this:
sinxy + .5cos2x + .33sin3y + .25cos4(x+y)
__________________________________________
1 + | sin5y + .5cos6x + .33sin7y + .25cos8x |
and know that it's a simple prescription for a surface, but when you actually see it, rendered and painted, it becomes something else entirely.
It becomes easy to imagine that you could come up with an equation that would produce the Rocky Mountains, and another the Himalayas. And, from there, who couldn't wonder about the great creator of all this, the developer of phi, whose sorcery brought into existence the properties called — well, what were they called, for millennia, for eons, until just a moment ago when Mandelbrot decided to call them "fractals"? Yet there they were, nameless to us lower creatures, shaping our existence.
Who couldn't fall in love with such a creation? Who couldn't desire to leap among the numbers and letters, to whale-leap through the naked cosmos? I will sing with the spirit, and I will sing with the understanding also.
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