What is Nerd Sniping
In XKCD 356, reproduced below, we are introduced to the idea of nerd sniping, which is the act is the act of presenting a particular type of person with an interesting puzzle/problem that causes them to drop everything else they are doing to work on it. It’s called nerd sniping, but I’ve seen it happen to most creative people, from artists to engineers to mathematicians. As I was putting together a problem set for my undergrads, I looked at one of the problems and started to play around with it. Tweaking the underlying differential equations, visualizing the new results, tweaking it some more, visualizing it some more, looking up and realizing I’d just spent my entire morning playing with this one system of equations. I had just nerd sniped myself. Being completely honest, this is a semi-regular occurrence. Usually, after throwing away a day’s productivity on these tasks, I end up forgetting about these “projects” and going back to work on the tasks that I should have been doing all along. Instead, I’m going to share some of the more interest ones in shorter-form posts titled Nerd Sniping Myself.
Source: https://xkcd.com/356/
The Initial Problem
I was going over stationary points and linearization with my undergrads, and so I created a problem set for hem to work on to apply the skills they had learned. One problem was designed to show them that the linearization of non-linear systems is not informative in all situations. To do this I used the following dynamical system
Linearization predicts that the stationary point, located at the origin, is marginally-stable, however, the higher-order terms that we ignore in the linearization, cause it to be unstable! In order to show this to my undergrads, I ended up numerically integrating 500 points an equal radius away from the stationary point.
The Final Product
Multiplying the first equation by -1 ends up stabilizing the system, which gives you the following
By increasing the radius of the initial points, and correspondingly increasing the figures axis, you get the following, very relaxing gif.
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