The Sun should turn his watch back too

He’s reporting for duty too early!

Today, Sunday Nov. 2, is clock-change day in America, and another phenomenon involving Time and clocks and the Sun falls at the same date – almost. On November 3 the equation of time will be at its maximum for the year.

What the hell – I mean what on Earth – is the equation of time?

Our days are all 24 hours long. That’s 1440 minutes, or 86,400 seconds – precisely so, in this era of atomic clocks. (Or 60,480 of my heartbeats, less precisely.)

And our days are defined as the time from noon to noon, that is, from when the Sun crosses the meridian to when it next crosses the meridian. The meridian is the line that passes over your head and down to the south point on your horizon.

But that is an average, the mean day. Noons are not precisely 1440 minutes apart, because the Sun moves at a slightly variable rate around our sky. What is really happening is that the Earth, while rotating about constantly, is moving at a slightly variable rate around the Sun because of its slightly varying distance from the Sun; and there is another factor which is harder to explain (I’ve tried to on page 33 of Astronomical Calendar 2015, not to my own complete satisfaction), to do with the way the Earth leans.

Supposing that you had a watch set to the exact mean time for where you live – ignoring your difference in longitude from the middle of your time zone, and certainly ignoring the one-hour distortion imposed by the summer clock-change law – then you could be timing the Sun as it arrives each day at its highest, over the south point on your horizon – casting due northward its shortest shadow. It should have been arriving there at 12, but since September it has been early, at first by a little, then by an increasing amount, until tomorrow it will be early by 16 minutes and 28 seconds. The Sun will cross that high point in the sky and start downward for another 16 minutes before the bell of the nearby church (which also happens to be on true mean time) chimes noon.

Hearing that, the Sun fiddles with its wristwatch and, realizing it shouldn’t be in such a hurry, will gradually become less early at its meridional appointment, until on Christmas Day it will be exactly on time. But it will go on slowing down; it’ll start being a late Sun.

Is there any connection between tomorrow’s equation-of-time date and today’s clock-change date, other than their near coincidence? Not really. The other equation-of-time extreme, when it is at minimum, will come on Feb. 11, which isn’t very near to the next clock-change date on March 8 (March 29 in Europe). Both are consequences of our seasons, the March and September equinoxes, but the clock-change’s connection is crude, the equation-of-time’s subtle.

“Equation” is a funny word. It doesn’t rhyme with “nation”: it’s the only English word (in the dialects I’m aware of) in which the -tion ending is pronounced not with sh but with the voiced phoneme as in measure or beige.

And why is the equation of time an equation? Couldn’t it have been called something like the correction or adjustment or smoothing of time? Yes, that was what the word did mean, back when earlier astronomers were figuring it out. To “equate” meant not that you said that it was equal but that you made it equal: you changed something to bring it into equality with something else. By subtracting 16 minutes from the actual time when the Sun crosses the meridian, you bring it back to identity with the time when it ought to.

The “apparent” (that is, the observed) time minus the equation equals the mean time.

As for equations in the now dominant and very powerful sense, I remember that when I was first around scientists I asked them why everything was expressed in equations, and they tried to explain. I’m convinced now, though it’s still possible to wonder whether the brains of some other form of life would conduct their mathematical reasoning in something other than equations. And then there are the equations in our programming languages, or what are written in the form of equations but are really replacement statements. I’ve written hundreds of lines of the type of:

A = A + 1

which are obvious lies.