I’ve been watching The Art Assignment since it started but this is my first attempt at actually making art. I’m a mathematician, so when I saw this week’s video I started thinking about how I haven’t seen most of the tools and ideas that are so central so my work. So I started thinking “what would an integral look like?”

I decided to attempt to draw one. I used a pencil and unlined 8.5 by 11 paper, because that was how I did all my problemsets in college.

I started by drawing the symbol representing an integral, but it was inadequate to articulate the concept, so I spun out into graphical, and symbolic representations of what an integral is.

So much of mathematics is a useful fiction. Math is a story mathematicians tell each other to make sense of the world. This art assignment helped me explore this sometimes uncomfortable aspect of my chosen field of study.

We talked about how integrals will tell you the “area under a curve.” Look up above where we drew a trapezoid to find the area under the curve. A little bit of the trapezoid is actually over the curve though, so it’s not exactly the right area. But it’s close. If we want to get closer, why not use two trapezoids? Then we can add their areas together. Great, how about four trapezoids? Even better, but still a little bit off because the top of a trapezoid is straight, and the curve is curved.

With an integral it’s like you make the trapezoid width Δx infinitesimally small, in which case it becomes dx. Then you add up an infinite amount of them, so you’ve used the smallest trapezoid size possible. This gives you the true area under the curve.

Lost in a sunset; transfixed by the play of moonlight on a crystal dark pond which possesses no bottom; floated out of self and time in the enraptured emrbace of a loved one; caught and held still-bound by the crack of thunder echoing through mists of rain. Who has not touched the timeless?
—  Ken Wilber
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