The Night the Counting Starts From

The Hook

There is a certain kind of Torah chapter that people skip, and this is one of them. It has almost no stories in it and no arguments and no ethics. It has numbers. Twenty nine days, twelve hours, 793 units. Three hundred fifty four days, eight hours, 876 units. Two days, sixteen hours, 595 units. The Rambam works through them with the calm of a man who expects to be checked, and if you are reading quickly your eye slides right off the page.

Do not let it. This is the chapter where the Jewish calendar stops depending on eyes and starts depending on arithmetic, and the Rambam knows exactly how large a thing that is. He has just spent five chapters on witnesses walking into a courtyard and saying what they saw in the western sky. Now he sits the court down before the witnesses ever arrive and has it calculate, in the manner of the astronomers, whether the moon could possibly be seen tonight at all. And the strangest part is not the mathematics. It is where the mathematics begins. Every molad the Rambam will ever compute, for any month of any year in either direction forever, is reached by adding to a single starting figure: the conjunction of the first year of creation, Monday night, five hours and 204 units after nightfall. Nobody was standing there. There is no witness to that one.

An Hour in 1080 Pieces

Begin with the unit, because the Rambam does something unusual here. He tells you why he chose it.

Day and night together are treated as a fixed composite of twenty four hours, twelve of light and twelve of darkness, which he is careful to say is an average rather than a fact about any particular day. Then he divides the hour into 1080 parts, and rather than simply announcing the number he gives his reasoning: this number was chosen because it can be divided in half, into fourths, into eighths, into thirds, sixths, ninths and tenths, and each of those fractions still contains many whole units. He picked a unit of time for its hospitality to fractions.

Consider what that means. Nature did not hand anybody 1080. There is no astronomical fact that makes a chelek the right size. The Rambam chose a ruler whose marks are close enough together, and spaced by a number generous enough in its factors, that almost nothing you want to say about time falls between the lines. Split an hour three ways and you get 360 whole parts. Split it eight ways and you get 135. Split it ten ways and you get 108. The remainders that would plague any coarser unit simply do not appear. This is a man designing a measuring instrument for a system that has to run without correction for thousands of years, and his first design decision is to make sure the fractions come out whole.

With the unit in hand the constants arrive. The mean interval between one conjunction of sun and moon and the next is twenty nine full days, twelve hours of the thirtieth day, and 793 units of the thirteenth hour. Twelve of those months make an ordinary lunar year of three hundred fifty four days, eight hours and 876 units. Thirteen of them make a leap year of three hundred eighty three days, twenty one hours and 589 units. And a solar year is three hundred sixty five days and six hours, which exceeds the ordinary lunar year by ten days, twenty one hours and 204 units. Chapter one told us the drift was about eleven days. Here we are told what it actually is, and it is not eleven.

The Remainder, and How the Day Slips

Then the Rambam takes each of those figures and does something to it that is worth pausing over. He divides out the sevens and throws them away.

The lunar month, counted in weeks, leaves a remainder of one day, twelve hours and 793 units, which he writes as 1-12-793. The ordinary year leaves 4-8-876. The leap year leaves 5-21-589. And he explains why he is discarding all those whole weeks in a sentence that quietly tells you what the entire chapter is for: the purpose of our calculations is not to know the number of days, but rather to know on which day of the week, and at what hour, and after how many units, the conjunction will take place. Nobody needs to know how many days have passed since the beginning of the world. Everybody needs to know which weekday it will be.

So the arithmetic becomes almost trivially simple. You have a molad; you add 1-12-793; you have next month's molad. You have a year's molad; you add its remainder; you have next year's. Carry 1080 units into an hour, twenty four hours into a day, and cast out sevens as you go. He says you may follow this method month after month for eternity, and then year after year for eternity, and the word keeps returning like a drumbeat.

He gives one worked example, and the example is more slippery than it looks. Suppose the conjunction for Nisan falls on Sunday, five hours and 107 units after sunrise. Add the monthly remainder of one day, twelve hours and 793 units. The units come to 900, comfortably short of 1080, so nothing carries. Twelve hours added to five hours after sunrise lands you five hours after nightfall, which in the Torah's reckoning is no longer Sunday at all but already the beginning of the next day. Then add the whole day. And the Rambam's answer, which many a student has gotten wrong, is Tuesday night, five hours and 900 units after nightfall. Not Monday. The twelve hours quietly walked you across a boundary before the day you were adding ever got counted.

That is the sort of detail that separates a person who has memorized the constants from a person who understands the system. The numbers are easy. The day changes underneath you while you are adding.

Nineteen Years, and What Will Not Come Out Even

The last movement of the chapter is the machzor, the cycle of nineteen years containing twelve ordinary years and seven leap years, and here the Rambam again refuses to simply assert. He shows you why nineteen.

Add up twelve ordinary lunar years and seven leap years, with all their hours and units, carrying properly, and the total comes to nineteen solar years of three hundred sixty five days and six hours each, with a difference of only one hour and 485 units. Nineteen years of two calendars that fundamentally disagree, brought into alignment with an error smaller than a morning. That is why the cycle is nineteen and not some other number, and the seven added months fall in the third, sixth, eighth, eleventh, fourteenth, seventeenth and nineteenth years of it.

But look at what he does with the leftover hour. He prints it. He could have rounded, or said the cycles agree, or left the residue for a commentary. Instead he tells you the exact size of the disagreement that remains after all this labor, and then he gives you the remainder of a whole cycle, two days, sixteen hours and 595 units, so that you can step from one nineteen year cycle to the next and, adding cycle to cycle, reach any year that has ever been or will be. The system is not presented as perfect. It is presented as honest about its own imperfection and workable anyway.

And the whole edifice rests on 2-5-204. The molad of the first year of creation, Monday night, five hours and 204 units after nightfall. Every Rosh Hashanah of every century is that figure plus a great many additions. It is the one number in the chapter that was not measured, not observed, not testified to. It is received.

The Unifying Principle

Put the pieces together and the chapter says something that a chapter of arithmetic has no business saying. A people that had been told to look at the sky is now told how to know what the sky is going to do, and the knowledge does not come from looking. It comes from a remembered beginning plus faithful addition.

The Alter Rebbe, in Shaar HaYichud VehaEmunah, insists that creation is not an event in the past but a continuous act, that the letters of the divine word are renewing every existing thing at every instant, and that if that word were withdrawn for a moment the thing would not decay but simply never have been. Read chapter six with that in your ear and the structure changes. The Rambam is not describing a clock that God wound up and left running. He is describing a count in which every single month must be added by hand, one day, twelve hours, 793 units, again and again, month after month for eternity. The calendar does not coast. It is renewed one addition at a time from an origin that never stops being the origin.

The Baal Shem Tov taught that no leaf turns without the specific intention of Heaven, and that the smallest details of the world are the places where providence is most exact rather than least. Somebody once asked why the Torah should care about a unit as small as a chelek, one part in 1080 of one hour, when no human being can feel such a thing pass. The answer this chapter gives is that the small units are precisely what makes the long count survivable. Coarse measurement accumulates error. It is the chelek, unfelt and unnoticed, that keeps the festivals of the year five thousand from drifting into the wrong season. What you cannot perceive is holding up what you can.

And the Sfat Emet, on the word chodesh, points out that it does not mean month; it means renewal. Which makes the arithmetic here a strange kind of theology. The Rambam has taken a word that means the sudden reappearance of a sliver of light and turned it into an operation of addition, and he has done it without losing the meaning. The renewal is still real. It is simply guaranteed now, computable now, available to a Jew standing in a place where nobody has seen the sky in weeks.

Modern Application

Everyone has some practice that once ran on inspiration and now has to run on arithmetic. It began because you saw something, and for a while the seeing was enough, and then the seeing became intermittent and you had to decide what to do about that.

The usual instinct is to wait. To not learn tonight because nothing is stirring. To not daven with any seriousness because the sky is cloudy this week. And the Rambam's answer, offered without a word of exhortation, is a table of constants and an instruction to add. He does not tell the court to feel more. He tells it to reckon like an astronomer, so that it will know what it is looking at when it finally does look. The calculation is not a substitute for the sighting. It is what makes the sighting intelligible.

There is something freeing in that. You do not have to see the moon tonight to know where you are in the month. You have an origin, you have a constant, and you have the discipline of adding one more interval. Some months that is all a person has, and the Rambam is telling you, in the driest possible register, that it is completely sufficient. The month will begin whether or not you were moved by it.

And then the honest hour and 485 units. Even the best cycle we have does not come out perfectly even, and the Rambam writes the leftover down instead of hiding it. A life arranged around a Torah calendar is not going to come out perfectly even either. The residue is not a sign that the system has failed. It is a number you are allowed to know.

The Closing

What lingers about chapter six is how much trust is buried inside its dryness. A whole nation's festivals depend on a figure for a conjunction that occurred before anyone existed to observe it, transmitted, added to, and added to again, month after month for eternity. Nobody can verify 2-5-204. It is the axiom, and the entire structure is built out from it in one direction only, forward, by addition.

An hour was cut into 1080 pieces because 1080 divides cleanly, and because a system meant to run for thousands of years cannot afford remainders it does not understand. That is the whole spirit of the chapter. Choose your unit so that almost nothing falls between the marks. Write down the error that is left over anyway. Anchor everything in a beginning you received rather than one you witnessed, and then do the addition, one day and twelve hours and 793 parts at a time, without waiting to be inspired by it. The month will come. Your only job was to know which day it lands on.