Getting a slow start to the new year here, but thought I would begin with commenting on the graph above. It’s a slide from a website which I’ll leave unnamed, but which I suspect news junkies out there could easily figure out.
If you take a look at the graph, its intent is clear: the more it snows, the more we hunker down and watch endless hours of Netflix.
But it says a bit more than that. The first thing that struck me looking at the graph was that “Inches of Snow” was on the Y-axis and “Hours of Netflix Watched” was on the X-axis This seemed counterintuitive to me. Typically in math, the dependent variable is placed on the Y-axis and the independent variable on the X-axis. This graph had it backwards. Rather than implying that the number of hours of Netflix-bingeing depended on the amount of snow outside, it was saying the reverse, i.e. the amount of snow outside depended on the amount of Netflix watched.
Then I thought: “Whatever. This independent/dependent variable stuff is really important when talking about functions, but maybe this graph is just correlating two variables, in which case it really doesn’t matter what you put on which axis.”
Which would be fine except that an exponential model relates the two variables. What that means is that for every fixed number of hours you watch of Netflix, the snow level is going to double, triple, quadruple, etc. To illustrate, suppose the model in the graph is represented by the rule y=2x.
x = 1 hour Netflix, y = 21 = 2″ of snow
x = 2 hours Netflix, y = 22 = 4″ of snow
x = 3 hours Netflix, y = 23 = 8″ of snow
x = 4 hours Netflix, y = 24 = 16″ of snow
x = 5 hours Netflix, y = 25 = 32″ of snow
As you can see, for every hour of Netflix watched the amount of snow doubles. After ten hours, there would be 1024 inches on the ground, just over 85 feet of snow! If this were the case, Earth would resemble the ice plant Hoth and watching video-streaming sites would be punishable by a 1,000 lashes with a wet noodle :-P.
Simple fix for this humorous slide: switch the labels of the axes. Not only will the original intent be properly communicated, the graph will make mathematical sense too.