But there is a difference, not accounted for.) A small arc of parabola looks much like a small arc of circle. (An alternative interpretation is to treat the path swung by the end of the pendulum as though it were part of a parabola, instead of the section of circle that it really is.

But I wanted to know when that difference was accounted for, and it never was. This approximation is quite good, if the angle is small, as you can see from comparing the sine of 0.01 radians to the number 0.01. To do this you have to approximate the sine of the angle the pendulum bob with the angle itself. I remember struggling in high school physics, in the modeling a pendulum’s swing.

But it happens in analytic mathematics too. You expect this from numerical mathematics, yes. Things we know not to be right, but which we know are not too far wrong. This and other essays mentioning Wallace the Brave are at this link.Ī thing that creates a problem, if you love this too closely, is that much of mathematics builds on approximations. Will Henry’s Wallace the Brave for the 8th of August, 2022. It’s a wonderful sense of security, even when you get past that childhood age where so little is in your control. Not just coincidentally right, but right for all time. If you follow these knowable rules, and avoid calculation errors, you get results that are correct. I imagine everyone feels this appeal of mathematics, arithmetic particularly. Will Henry’s Wallace the Brave for the 8th opens the theme, with Rose excited to go to mathematics camp as a way of learning more ways to be right. That’s a common impulse among people learning mathematics, that drive to have the right answer. The handful of comic strips I’ve chosen to write about this week include a couple with characters who want to not be wrong.

Read wallace the brave