What’s the joke here? AFAIK radians in fact do allow one to calculate the number of square degrees of sky.
We’re used to talking about angles as measured in degrees, and we’re used to talking about angles as measured in radians, which are considered to actually be dimensionless. It also feels natural to speak of a circle with a dimensionless radius, but even though it follows logically from all of that, it’s still never done to refer to dimensionless quantities other than angles in degrees.
It’s like measuring torque in joules. Sure, you can, and there’s nothing actually invalid about it, but nobody actually does it, and so it just looks wrong.
And yet a sphere does have a surface of approximately 41,253 square degrees. So is it that the example given just isn’t the proper way to go about it, or what?
Logically, how many degrees would the radius of a non-unit circle have?
Depends on how non-unit it is. A circle of radius 2 would be 114.6 degrees, and so on.
There’s a site dedicated to working through Randall’s always brilliant, sometimes nebulous comics.Here’s the one that treats this comic.