Silly math

In Jank in Teams, I employed a method of sharing mental models that I call “silly math.” Especially in surroundings that include peeps who love (or at least don’t hate) math, these can serve as a simple and effective way to communicate insights.

For me, silly math started with silly graphs. If you ever worked with me, you would have found me me at least once trying to draw one to get a point across. Here I am at BlinkOn 6 (2016! – wow, that’s a million years ago) in Munich talking about the Chrome Web Platform team’s predictability efforts and using a silly graph as illustration. There are actually a couple of them in this talk, all drawn with love and good humor by yours truly. As an aside, the one in Munich was my favorite BlinkOn… Or wait, maybe right after the one in Tokyo. Who am I kidding, I loved them all.

Silly graphs are great, because they help convey a sometimes tricky relationship between variables with two axes and a squiggle. Just make sure to not get stuck on precise units or actual values. The point here is to capture the dynamic. Most commonly, time is the horizontal axis, but it doesn’t need to be. Sometimes, we can even glean additional ideas from a silly graph by considering things like area under the curve, or single/double derivatives. Silly graphs can help steer conversations and help uncover assumptions. For example, if I draw a curve that has a bump in the middle to describe some relationship between two parameters – is that a normal distribution that I am implying? And if the curve bends, where do I believe nonlinearity comes from? 

Silly math is a bit more recent, but it’s something I enjoy just as much. Turns out, an equation can sometimes convey an otherwise tricky dynamic. Addition and subtraction are the simplest: our prototypical “sum of the parts.” Multiplication and division introduce nonlinear relationships and make things more interesting. The one that I find especially fascinating is division by zero. If I describe growth as effort divided by friction, what happens when friction evaporates? Another one that comes handy is multiplication of probabilities. It is perfectly logical and still kind of spooky to see a product of very high probabilities produce a lower value. Alex Komoroske used this very effectively to illustrate his point in the slime mold deck (Yes! Two mentions of Alex’s deck in two consecutive pieces! Level up!) And of course, how can we can’t forget exponential equations to draw attention to compounding loops?! Basic trigonometry is another good vehicle to share mental models. If we can sketch out a triangle, we can use the sine, cosine, or tangent to describe things that undulate or perhaps rise out of sight asymptotically. In the series, I did this a couple of times when talking about prediction errors and the expectation gradient.

Whatever math function you choose, make sure that your audience is familiar with it. Don’t get too hung up on details. It is okay if the math is unkempt and even wrong. The whole point of this all is to rely on an existing shared mental model space of math as a bridge, conveying something that might otherwise take a bunch of words in a simple formula.