I never know which cartoons will strike a chord.
But judging by the bizarre and amusing commentary that flooded my Twitter mentions after posting this one, it struck a real chord. Among badly drawn math cartoons, it was like the chord at the start of “A Hard Day’s Night.”
This cartoon’s strange Sean Carroll meets Lewis Carroll mash-up (heady astrophysics + total illogic) prompted so many questions that I feel compelled to provide a series of FAQs and responses.
What, exactly, are you smoking?
Only the bargain-priced hallucinogen of pure mathematics.
You’re wrong! You’re wrong on the internet! The day isn’t a circle. It’s a spiral, ending in a different place than it began.
First: not a question.
Second: Sure, let’s go with that. After all, you begin at 12am on one date, and end at 12am on a different date. In terms of polar geometry, you’re at same angle, but you’re more distant from the origin. So it’s not crazy to say that our days are a tremendous spiral, with the Big Bang at the center.
(Okay, it is crazy, but it’s not crazy crazy.)
Still, this isn’t a solution; it’s a greater paradox! After all, the radius of a spiral is continuously growing. This suggests that each day is longer than the previous one!
Why, then, do we experience each day as identically 24 hours? Are we traversing the spiral at a faster and faster rate? If so, does this explain our occasional feelings of nausea as we rocket through time?
(This is what happens when you ask a non-question. Ask a question, get an answer; ask an answer, get a boatload of questions.)
If you’re imagining the day as 2D, why not go further? Why not a 3D sphere?
Aha! Perhaps the full day is measured not in square hours, but cubic hours, because the 24 hours that we traverse are merely a great circle on the exterior of a sphere. Trippy thought, my friend.
But why not go even further? Couldn’t the day be a hypersphere, or a 4-sphere in 5-space, or a 100-dimensional sphere in 110-dimensional space?
To explain the circularity of the day, we need to posit a second dimension. But once you arbitrarily posit a third, it seems there’s no reason to stop. Which is perhaps a reason for stopping at 2D.
Also: who says the 24 hours must be a great circle? If the day is spherical, perhaps we are circling near the pole. It’s like we’re flying around the earth at the latitude of Greenland. If so, we could experience a longer day merely by moving towards the equator.
What exactly is a square hour?
Dude, I wish I knew.
Perhaps a hint lies in our measure of acceleration. We measure speed in miles per hour, and so we measure acceleration miles per hour per hour, i.e., “miles per square hour.”
Thus, the day’s “area” can be thought of as a distance, divided by an acceleration. But after that, I’m stumped.
Further Carroll-ian insights (of either kind) will be appreciated.