Where the Sun Stands Decides the Moon

The Hook

The first sentence of this chapter says something that should stop you. There are two mean rates of progress with regard to the moon. Two. Not one moon moving at one average speed, but two separate averages, each with its own daily figure, each needing to be tracked from its own starting point, because the moon is riding on something that is itself riding on something else.

And then, after four halachot of pure arithmetic, the chapter ends somewhere nobody would predict. Before you may use the moon’s mean for anything, you have to look up and find the sun. Depending on which constellation the sun is standing in, you add half a degree to the moon, or a quarter of a degree, or you leave it exactly as it is, or you take a quarter or a half away. The correction to the moon is a function of the sun. The chapter does not explain why. It simply tells you to do it, and then tells you what you now hold.

Two Moons, Two Rates

Here is the picture the Rambam is drawing. The moon revolves in a small orbit that does not encompass the earth. That small orbit is itself carried around inside a larger orbit that does encompass the earth. So there are two motions happening at once, and they are motions of different things. The progress of the moon within its own small circle he calls the mean within its path. The progress of the small circle itself, riding around the earth in the large one, he calls the moon’s mean.

Each gets its own number. The moon’s mean advances thirteen degrees, ten minutes and thirty-five seconds in a day. The mean within its path advances thirteen degrees, three minutes and fifty-four seconds. Six minutes and forty-one seconds of arc apart, per day. On any single night the difference is invisible. Over a hundred days it is more than eleven degrees, better than a third of a constellation, which is the difference between a calendar and a rumor.

The Rambam then does what he always does with numbers he expects you to actually use, which is to multiply them out for you in advance. Ten days of the moon’s mean: one hundred thirty-one degrees, forty-five minutes, fifty seconds. A hundred days, once you have thrown away the whole circles: two hundred thirty-seven degrees, thirty-eight minutes, twenty-three seconds. A thousand days. Ten thousand days. Twenty-nine days, which is the length of a lunar month and therefore the figure you will reach for most often. A regular year. And then, almost impatiently: following these guidelines, you can multiply these figures for any number of days or years you desire.

Then he does the same for the mean within its path, a parallel table with different numbers, ten days at one hundred thirty degrees and thirty-nine minutes exactly, and so on down. Two ladders, side by side, running at slightly different pitches. Everything in this chapter depends on your not confusing them, and nothing in the layout of the page protects you from confusing them. That is not carelessness. The Rambam warned three chapters earlier that these matters are deep and abstract and not to be treated lightly. He meant it as a description of the reader’s obligation, not as an apology for the material.

The Numbers He Hands You

Then the anchor. At the fixed starting point of all these calculations, Wednesday night, the third of Nisan, 4938, the moon’s mean stood at one degree, fourteen minutes and forty-three seconds, in the constellation of Taurus. At that same instant, the mean within its path stood at eighty-four degrees, twenty-eight minutes and forty-two seconds. Two positions, one moment, one moon.

And the Rambam says, plainly: since you know the rate of progress and you know the position at the starting point, you can calculate the position on any date you desire, exactly as you did with the sun. That is the whole method. A known place, a known speed, and a count of the days between. There is no observation in it anywhere. A man in a dark room with a wax tablet can tell you where the moon’s mean will stand on a night nine centuries from now.

Which is a good moment to notice what the word mean is doing here. A mean is not a place. It is a fiction, an average, a smoothed-out version of something that does not actually move smoothly. The moon in the sky is never precisely where its mean says it is. The Rambam is completely unembarrassed by this. He builds the entire structure of the calendar on a number he knows is not the truth, because the number that is not the truth is the only one you can compute, and the truth gets derived from it later.

The Emendation That Looks Elsewhere

Now the turn. After calculating the moon’s mean for the beginning of the night you want, the Rambam says, focus on the sun and see which constellation it will be in at that time.

And then eight bands. Sun between mid-Pisces and mid-Aries: leave the moon’s mean alone. Between mid-Aries and the beginning of Gemini: add fifteen minutes. Between the beginning of Gemini and the beginning of Leo: add thirty. Between the beginning of Leo and mid-Virgo: add fifteen. Between mid-Virgo and mid-Libra: leave it alone. Then the whole thing runs backwards down the other side of the year, subtracting fifteen, then thirty, then fifteen, until you are back at mid-Pisces where you started.

Look at what has just happened. You have spent the entire chapter computing a lunar quantity from lunar rates and a lunar starting point, and the last operation performed on it is governed by a body you were not tracking at all. A student holding the moon’s mean in Libra will feel the pull to consult the Libra clause, because Libra is the word in front of him. The clause is not about the moon in Libra. It is about the sun in Libra. The number you correct and the number that tells you how to correct it belong to two different bodies, and only one of them is written on your worksheet.

And then the last halachah of the chapter tells you what you are holding, and it is characteristically modest. The figure that remains after these additions or subtractions, or when the mean was left alone, is the mean of the moon approximately twenty minutes after the setting of the sun. He names it: the mean of the moon at the time of the sighting. Still a mean. Not the true position, not where anyone will actually see it. He has spent a chapter of arithmetic and one strange correction to arrive at a better average, timed to the moment a witness would be standing outside looking west.

The Unifying Principle

The chapter is built on one move, made three times. Every quantity here is defined by its relationship to something outside itself.

The moon within its small orbit means nothing until you know where the small orbit is. The small orbit means nothing until you place it against the earth. And the moon’s mean, computed to the second, still cannot be used until you turn around and find the sun. There is no self-contained number anywhere in this system. Every figure is a figure with respect to something else, and the moment you forget the something else, your arithmetic keeps working perfectly and stops describing anything.

This is the reason Chassidus has always found so much in the moon. The Alter Rebbe returns constantly to the fact that the moon has nothing of her own. What she shows is the sun’s, received and given back at whatever angle she is standing. Her waxing and waning is not a change in the sun and not a change in her substance. It is a change in relationship, in how much of what is always fully there she happens to be facing. A body whose entire visible history is a record of an alignment.

The Lubavitcher Rebbe would press this further into the Jewish calendar itself. Israel counts by the moon, and the sanctification of the new month was the first commandment given to the nation as a nation, and the moon was chosen precisely because she disappears. The point was never the light. The point was that something can vanish completely and be new three nights later without ever having been replaced. And the correction in our chapter says something quieter alongside it. Even the moon’s own bookkeeping is not settled by the moon. Where the sun stands changes what her number means.

Modern Application

Everyone has a worksheet. Everyone has a column of figures that is internally consistent, carefully maintained, and computed from a starting point they no longer examine. The hours worked, the money set aside, the effort put in, the reasonable account of what kind of person you have been this year. None of it is dishonest. Most of it is arithmetically correct.

The Rambam’s instruction is to stop before the last line and look at the sun. Not to redo the figures. The figures are right. To ask what they are being measured against, because the same number means one thing in one season and something else in another, and nothing on the page will tell you which season you are in. The Baal Shem Tov taught that everything a person encounters is placed in front of him deliberately and is addressed to him. That is exactly the operation being demanded here. The correction never arrives from inside the column. It arrives from outside the column, from something you have to deliberately turn and look at.

And there is the other half, which is the mercy in it. What you end up with, after all the work, is still only a mean. The Rambam labels it as such and hands it to you anyway. You are not going to compute your way to the true position tonight. You get a well-founded approximation, timed to twenty minutes after sunset, good enough for the man walking out to look. Not everything has to be exact to be usable.

The Closing

What is striking about this chapter is how little it hides. The Rambam tells you the moon has two means because the geometry demands two. He tells you the earth is not at the center of the orbits that encircle it. He tells you the number you finish with is an average and names it as one.

He does not tell you why the sun’s constellation should shift the moon’s mean by half a degree. He simply instructs you to look. There is a kind of intellectual honesty in that which is easy to miss, because it looks like an omission. It is not. It is a man handing over a working method and declining to dress it up as a complete explanation.

You can hold a number that is perfectly computed and still not know what it is worth, because its worth was never inside it. Turn and find the sun. That is the last instruction of the chapter and it is the strangest one, and it is the only step in the whole procedure that requires you to stop looking at what you were working on. Everything up to that point was arithmetic. That step is attention. And the number it produces is not the truth about the moon. It is the best account of her anyone can give at the hour someone is finally going out to look.