The Moon Does Not Know

The Hook

At the end of the longest technical stretch in the Mishneh Torah, the Rambam stops and quotes the Sages. The sun knows the time of its setting; the moon does not know. He offers it as an explanation, and what it explains is arithmetic. He has just finished a procedure with four longitudes in it, three separate corrections, a table of twelve constellations, and a rule that reverses itself halfway around the sky, and he wants you to understand that the complexity is not his. It is the moon's.

Chapter seventeen is where every calculation in the preceding chapters is finally spent. You do not compute the position of the moon here. You already know it. What you compute is whether anyone standing in Eretz Yisrael that night will be able to see it.

The Two Halves of the Sky

He begins by asking for three figures, the true position of the sun, the true position of the moon, and the position of the head of the moon's orbit, all for the hour of the sighting. Subtract the sun's position from the moon's and you have the first longitude, the distance between them. From the head and the moon you derive the first latitude, and you note whether it is northerly or southerly. Then comes an instruction that reads like housekeeping and turns out to be the hinge of the chapter. Be careful with regard to these two symbols, the first longitude and the first latitude, and have them at hand for later calculations.

Now the shortcuts. If the first longitude is nine degrees or less, the moon will certainly not be seen anywhere in the land, and there is nothing more to calculate. If it is more than fifteen, it will certainly be seen. Between nine and fifteen you have to do the work.

And then, immediately, the trapdoor. When does the above apply? When the true position of the moon falls between the beginning of Capricorn and the end of Gemini. If the moon is in the other half of the sky, between the beginning of Cancer and the end of Sagittarius, the numbers are different. Ten or less and it will certainly not be seen. More than twenty-four and it certainly will. Between ten and twenty-four you calculate. A man who memorized nine and fifteen and never read the next paragraph will declare a moon certainly visible at sixteen degrees when the actual threshold in that half of the sky is twenty-four, and he will not have made an arithmetic error. He will have used a real rule in the wrong hemisphere.

Then the first correction, and the reason for it, which the Rambam gives plainly. The true position of the moon is not the place where the moon will actually be sighted. There is a small difference in both longitude and latitude, and it is called the sighting adjustment. Twelve constellations, twelve values, from thirty-four minutes in Libra and Scorpio to a full degree in Taurus. The longitude adjustment is always subtracted. The latitude adjustment is subtracted if the latitude is northerly and added if it is southerly. What you have now is the second longitude and the second latitude. Where the moon truly is has been quietly replaced by where a person would see it from.

The Arc That Has to Be Built

The next correction is the strangest and the most beautiful. Because the moon fluctuates slightly in its orbit, a portion of the second latitude has to be set aside. How large a portion depends on where the moon sits in the sky, and the Rambam runs through the whole circle: two fifths, one third, one fourth, one fifth, one sixth, one twelfth, one twenty-fourth, and then, in one narrow band from the twenty-fifth degree of Gemini to the fifth of Cancer and its counterpart opposite, nothing at all, because at this point the moon does not fluctuate at all from its orbit. Then the fractions climb back out the other side in mirror image. The portion is called the circuit of the moon.

Where the circuit goes is where the chapter sets its second trap. Northerly latitude means subtract it from the second longitude, southerly means add it, but only for the half of the sky from Capricorn to Gemini. In the other half the opposite is true, and northerly now means add. Same figure, same sign of latitude, opposite operation, and the only thing that decides it is which side of the sky the moon happens to be on. The result is the third longitude. And if the moon is in the band where there is no fluctuation, there is nothing to set aside, and the third longitude is simply the second, unchanged.

One more adjustment by constellation, and this one is proportional rather than fixed. Add a sixth, add a fifth, add a sixth again, leave it alone, subtract a fifth, subtract a third, depending on where the longitude falls. That gives the fourth longitude. Then the last step, and here the instruction from the opening of the chapter comes due. Return to the first latitude, the one you were told to keep at hand, and set aside two thirds of it. Add that to the fourth longitude if the latitude is northerly, subtract it if southerly. What remains is the arc of sighting.

Nine degrees or less and the moon cannot be seen. More than fourteen and it cannot be hidden. Between the two the Rambam gives five bands, and every one of them sends you back to the beginning. Arc between nine and ten, and the moon is seen only if the first longitude is thirteen degrees or more. Arc between ten and eleven, first longitude of twelve. Between eleven and twelve, first longitude of eleven. Between twelve and thirteen, ten. Between thirteen and fourteen, nine. The whole apparatus of adjustments and circuits and fractions produces a number that cannot be read on its own. It has to be laid against the raw distance you measured before any of the corrections were made.

Friday Night, and Who Said It

He then works an example, and it is worth following once. Friday night, the second of Iyar. The sun stands at seven degrees nine minutes of Taurus, the moon at eighteen degrees thirty-six minutes of Taurus, with a latitude of three degrees fifty-three minutes, southerly. Subtract and the first longitude is eleven degrees twenty-seven minutes. Taurus costs a full degree, so the second longitude is ten degrees twenty-seven minutes. The latitude adjustment for Taurus is ten minutes, and because the latitude is southerly it is added, giving a second latitude of four degrees three minutes. The moon is in the eighteenth degree of Taurus, so a quarter of that is set aside, and the circuit is one degree one minute. Southerly, in the Capricorn half of the sky, so the circuit is added, and the third longitude is eleven degrees twenty-eight minutes. Taurus adds a fifth, two degrees eighteen minutes, and the fourth longitude is thirteen degrees forty-six minutes. Two thirds of the first latitude is two degrees thirty-five minutes, subtracted because southerly, and the arc of sighting is eleven degrees eleven minutes.

Eleven and eleven falls in the band that requires a first longitude of eleven or more, and the first longitude was eleven twenty-seven, and so the moon will be seen. The margin is twenty-seven minutes of arc. That is the whole distance between a month that begins tonight and a month that does not.

Then the chapter turns, and the last two paragraphs are unlike anything around them. He explains that all this labor was an attempt to present a method that comes close without requiring extremely complicated calculations, and that the trouble is in the object, not the method, because the moon has major incongruities in its orbit. And he closes by telling you where the reasoning comes from. The rationales belong to astronomy and geometry, concerning which the Greeks wrote many books. The texts written by the sages of Israel in the age of the prophets, from the tribe of Yissachar, have not been transmitted to us. And since these matters can be proven in an unshakable manner, the identity of the author, be he a prophet or a gentile, is of no concern. We do not rely on the individual who made these statements. We rely on the proofs he presented and the reasons he made known.

The Unifying Principle

The chapter is built on a single structural insight, and it is not astronomical. Almost every step in it is conditional. Subtract or add, depending. Set aside a fourth, or a twelfth, or nothing, depending. Use nine and fifteen, or ten and twenty-four, depending. There is nearly nothing here that is simply true. There is a great deal that is true given where you are standing and which half of the sky you are looking at.

The Alter Rebbe's account of ratzo v'shov in Tanya, the running out and the returning, describes the soul's motion as inherently two directional, never resting at a fixed value, always either reaching or coming back. A person who expects his inner life to hold a steady reading will misread every one of his own measurements. The Rambam has written the astronomical version of that. He does not apologize for the additions and subtractions. He explains that the object being measured behaves this way, and that any method that refused to oscillate would simply be wrong more often.

The Baal Shem Tov taught that a descent is for the sake of an ascent, that the disappearance is part of the mechanism and not an interruption of it. The moon is the standing illustration, and this chapter is what it costs to take that seriously. If the moon merely vanished and returned, one table would do. The reason there are five bands of sighting limits and twelve constellations of adjustment is that the disappearance is never quite the same twice, and the calendar of the Jewish year is anchored to a body that will not repeat itself.

And the last paragraph is a teaching in its own right. The Rebbe returned often to this Rambam, that we do not accept a proposition because of who said it but because of the proofs presented and the reasons made known, and that a truth demonstrated by a gentile astronomer is not on that account foreign to Torah. It is placed here deliberately. Having asked you to trust a procedure of extraordinary intricacy, on which the dates of every festival depend, he tells you exactly where he got it and invites you to check.

Modern Application

The instruction that governs this chapter is the one about the two symbols. Be careful with them and have them at hand. The first longitude is used in the third paragraph and again in the last, and between those two moments it is corrected, adjusted, fractionally reduced, and renamed four times. Every intermediate figure is legitimate and every one of them is a working number. If you reach the final comparison and reach for the version you have been carrying, the one that has been through every refinement, you will compare the wrong thing and you will get an answer that looks entirely reasonable.

Most of us do this with our own accounts. The reason a person took a job, or married, or moved, is the first longitude. Then come the adjustments, all of them honest: what it turned out to require, what other people understood it to mean, what became defensible at dinner parties. Years later, asked why, he produces the fourth longitude, and it is a real figure, and it is not the one the question was asking for. The original is still written on the sheet. He was told at the outset to keep it at hand.

And there is the reversal at the boundary of the sky, which is the humbler lesson. Northerly means subtract in one half and add in the other. A person who has learned a genuine rule, and applied it faithfully for years, and then moved into a different half of his life, will keep applying it. The rule is not wrong. The rigor is not fake. It is simply that the Rambam wrote a second sentence, and the second sentence begins with the words, when does the above apply.

The Closing

This chapter arrives on the third of Elul, with the moon a thin sliver just past its own renewal and the year narrowing toward the one night in the calendar when the moon is deliberately hidden at the moment of judgment. Everything in these seventeen chapters exists so that a court could look at the sky, hear two witnesses, and say the word that starts a month.

The sun knows the time of its setting; the moon does not know. Read as a complaint it is a note about orbital mechanics. Read the way the Rambam sets it down, at the end of everything he built to compensate for it, it is closer to a description of what he has been doing for seventeen chapters, which is to take something that does not keep steady time and refuse to give up on knowing where it will be. He did not make the moon regular. He made it findable, and then he told you whose proofs he used.