Brocken Specter
I pushed the shower door open this morning and played with the arc of water droplets falling off the far edge of the door onto my bath mat. By pushing with a steady, even pressure I took pleasure in controlling the uniformity of the arc that drew itself on the mat. That’s probably the same pleasure that Jackson Pollock felt when he dripped paint onto canvas. There’s something pleasurable about creating a design on a surface without coming into direct contact with it. In a way, photography is like that. If I photograph a landscape, the subject is the dripping water, and the light sensor is the bath mat.
But I digress. Once I saw the arc forming, the pivot point of the door reminded me of a compass, which got me thinking about the arc in terms of degrees. A circle is an arc of 360 degrees, but what is the minimum degree of arc you need to know in order to calculate the circle’s radius and, by extension, its circumference?
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| Glory with Brocken Specter |
Although I love questions like that, I have very little patience for finding their answers. I searched the internet in the hope of finding an easy answer, and I guess I did, because I found out it’s not possible. You can’t calculate the radius with the degree of arc alone because you also need what they call the sector angle.
The sector angle is formed by two radii extending from the center of the circle to each end of the arc, like a slice of pizza. The arc length is equal to the radius times the sector angle. I was trying hard to remain patient as I encountered these mathematical terms until I saw that you have to convert degrees of arc into radians, a term I was not familiar with despite the fact that I used to ride a Yamaha Radian motorcycle.
I almost stopped my line of inquiry at this point, but I found the conversion of degrees to radians as easily online as I could have found the conversion of dollars into yen. Enter “convert degrees to radians” into a Google search bar if you don’t believe me.
As you’ll see, each degree of arc is “worth” 0.0174533 radians (a radian equals pi divided by 180; not so tough after all).
But we’re still stuck with the fact that you need two of three numbers to calculate the third number. So I thought of a new question: Couldn’t you draw straight lines that just touch the ends of each side of the arc and converge in what would be the center of the circle?
I couldn’t do it in my head, and I feared I was treading close to calculus or something, so I set a nickel down on a piece of paper and used a pen to draw part of a circle. I looked at the arc and used a bookmark to draw a straight line past both ends of the arc. Sure enough, the lines converged on a point and created a slice of pizza, but was the point of intersection actually the center of my circle?
To find out, I set the nickel back down and drew the rest of the circle.
Long story short, the point was not in the center. Not even close.
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| Glory Photographed With Polarizing Filter |
By this time I realized I had spent an awful lot of time following my curiosity into a mathematical dead-end. But at least it was time enjoyably spent.
Similarly, I recently went to see the Joan Mitchell show at SFMOMA. I do not consider myself a fan of abstract art, and my artist wife was braced for the possibility that I might not like the show. One of the cool things about art, though, is that it can affect you in a way that leaves you speechless.
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| Sandhill Cranes & Waning Crescent Moon |
You could walk past a Joan Mitchell painting, or even a whole room full of them, glancing at them one by one before moving on to the next, and be confirmed in your suspicion that abstract art was useless. But the minute you stop wandering and actually plant yourself in front of one of these paintings, you get sucked in by its power.
Waves of light reflect off the paint and enter your eyes, triggering a cascade of neuronal impulses that converge on the point in your brain where your soul resides, producing more electrochemical cascades that release an emotion that spreads through your being like a drop of ink dispersing in a glass of water. What that emotion is, I can’t exactly say. I guess it’s a kind of awe. Whatever it was, it was deep and powerful, and I felt amazed and grateful for having experienced it.
The show continues until January 17, 2022.
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| Crane With Rising Sun |
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