You are doubtless familiar with ordinary *<x, y>* coordinates that you would use to plot something on graph paper. That way of plotting thing was developed by René Descartes. So they call them Cartesian coordinates.

But that’s not the only way of plotting things. Another way is to describe the location of a point as a distance from the middle, and the direction to go (typically given as an angle). This system is called Polar coordinates. We traditionally use *r* as the distance (like radius) and θ as the direction. So instead of *<x, y>* we use *<r, θ>.*

Now look at your keyboard. The middle is right between G and H. So lets make that the origin of our polar system. If we start θ as going East at zero degrees, then H might be <1,0°>, J is <2,0°>, K is <3,0°>. We might find Y at <1,80°> or so. Got it?

OK, so what I’ve noticed is that my typos on my phone keyboard all have to do with not going far enough away from the center. I’ve got the right direction θ, but not the right distance *r**.* My *r* is always too small, as though I multiplied it by a number less than 1.

Hence the *r* of my typo is some number (k) multiplied by the right *r*. And that number (k) is less than one.

Homework: plot the duration of each nap you took reading this incredibly boring blog entry, against the time that nap ensued, in polar coordinates.

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And not one reference to how this is all to be blamed on the Polar Vortex? : )

Sounds like you are very close to eliminating typos via mathematics, thereby bringing your distate for math errors into a wonderful harmony with those who are bugged by grammar errors.

Touché! For those of you keeping score at home, walt is referring to this tweet of mine: https://twitter.com/alfageeek/statuses/436695078950563840