Where the Leftover Hours Go

The Hook

A lunar month is twenty nine days, twelve hours, and seven hundred ninety three parts of an hour. No calendar ever built can hand you seven hundred ninety three parts of anything. So the Rambam does the only honest thing available to him. He throws the remainder out of every single month, and then spends the rest of the chapter tracking exactly where it went.

Because it does not vanish. That is the whole point. Chapter eight of Kiddush HaChodesh is about a system that refuses to lose what it cannot hold.

No Month Begins at Noon

Start with why the remainder is a problem at all, because it is not obvious that it should be.

The Rambam has already established the true length of the lunar month. Now he adds a rule that has nothing to do with astronomy. Rosh Chodesh cannot begin in the middle of a day. You cannot have a morning that belongs to Av and an afternoon that belongs to Elul. The verse speaks of a month of days, and the Oral Tradition reads it exactly: you count the days of a month, you do not count its hours.

That single ruling creates every complication that follows. If months could begin at any hour, the calendar would be trivial. You would mark the moment the moon comes around and move on, and every month would be precisely as long as the moon made it, down to the last part of an hour. Instead the Rambam has committed himself to whole days, which means every month is either twenty nine days or thirty, and both of those are wrong. Twenty nine is short by twelve hours and change. Thirty is long by nearly the same. There is no correct option. There is only a choice about which direction to be wrong in, and then an obligation to remember by how much.

If the month were exactly twenty nine and a half days, he says, the whole thing would resolve beautifully. Six full months, six lacking months, three hundred fifty four days in a lunar year, repeating forever. It is only those seven hundred ninety three parts, the surplus over the half day, that accumulate into hours and then into days and then wreck the symmetry, so that some years carry more full months than lacking ones and other years the reverse.

So the calendar is not a description of the moon. It is a negotiation with the moon, conducted in whole days, with a running balance nobody is permitted to forget.

The Ten Fixed and the Two Free

Now watch what the Rambam does with the thirtieth day, because it is the hinge of the whole system.

The thirtieth day is always Rosh Chodesh. Always. If the month is lacking, the thirtieth day is Rosh Chodesh of the coming month and that is the end of it. If the month is full, the thirtieth day is still Rosh Chodesh, since part of it is fit to be Rosh Chodesh, and yet it is simultaneously counted as the completion of the month that just ended. Then the thirty first day is Rosh Chodesh as well, and that is the day the coming month is actually reckoned from. That is the established day.

So some months have one day of Rosh Chodesh and some have two, and the second day of a two day Rosh Chodesh is really the first day of the new month, while the first is really the tail of the old one. This is what it looks like when a system honors a remainder it cannot spend. The extra day is not deleted and it is not fully promoted. It is held in both places at once.

Then the Rambam fixes the year. Tishrei is always full. Tevet is always lacking. From Tevet onward they simply alternate, one full and one lacking, all the way down. Tevet lacking, Shevat full, Adar lacking, Nisan full, Iyar lacking, Sivan full, Tammuz lacking, Av full, Elul lacking. In a leap year the first Adar is full and the second is lacking. Ten months, decided permanently, in advance, with no reference to any particular year.

Which leaves exactly two months undetermined. Marcheshvan and Kislev. Sometimes both are full, and the year is called a year of complete months. Sometimes both are lacking, and it is called a year of lacking months. Sometimes Marcheshvan is lacking and Kislev is full, and the year is said to proceed in order.

Stop and look at which two months got the job. Tishrei cannot move; it is crowded with Rosh HaShanah and Yom Kippur and Sukkot. Nisan cannot move; it holds Pesach and it anchors the spring. Sivan has Shavuot, Av has the ninth, Adar has Purim, Tevet has the tenth, and Kislev has Chanukah beginning on its twenty fifth. But Marcheshvan is the one month in the Jewish year with nothing in it at all, and Kislev's obligations do not begin until nearly its end. The system placed its flexibility exactly where the year is emptiest.

That is not a coincidence and it is not merely convenient. A calendar carrying a remainder has to have somewhere to put it, and it put it in the room with nothing else in it.

Reading a Year From Two Weekdays

Then the Rambam hands over a piece of arithmetic so small it looks like a parlor trick, and it tells you the shape of an entire year.

Find the weekday on which Rosh HaShanah falls this year. Find the weekday on which it falls next year. Count the days between them, excluding both of those days themselves. Two days, and the year is lacking. Three, and it proceeds in order. Four, and it is complete.

And then, immediately, the sentence that separates the people who learned the chapter from the people who memorized it. When does the above apply? When the year in question is an ordinary year. A leap year runs on entirely different numbers. Four days between means lacking, five means in order, and six means complete.

The same count of four days means the fullest possible year in one case and the emptiest in the other. Nothing in the arithmetic tells you which. You have to know first what kind of year you are standing in.

He works an example, and it is worth doing with him. Rosh HaShanah on Thursday, an ordinary year, next year's Rosh HaShanah on Monday. Friday, Shabbat, Sunday. Three days between. The year proceeds in order. If next year's falls on Tuesday instead, that is four days and the year is complete. Then he closes with a small set of signs to check yourself against, because he knows perfectly well you will get it wrong. Rosh HaShanah on Tuesday, and the months always proceed in order, ordinary year or leap year alike. Rosh HaShanah on Shabbat or on Monday, and they never do. Rosh HaShanah on Thursday, and if the year is ordinary its months cannot possibly be lacking, while if it is a leap year they cannot possibly proceed in order.

Notice that these signs are not shortcuts. Each one is true only inside its own kind of year, and the Rambam sets them down side by side so that you will have to hold the distinction or fail.

The Unifying Principle

Here is what the chapter is actually about.

There are two ways to handle a measurement that will not come out even. You can round and forget, which is what most systems do, and accept that you will drift until somebody eventually notices and resets everything by force. Or you can round and remember, which costs you a permanent apparatus, and means every year has to be individually diagnosed, and means nobody can know when Chanukah falls without first knowing what weekday Rosh HaShanah lands on the following year.

The Rambam chose the second, and he chose it for a reason that is not astronomical. The festivals are appointed times. If the calendar drifts, the appointed time stops being the appointed time. So the remainder has to be carried, and carrying it is expensive, and the expense is paid by two ordinary months in the depth of autumn that agree to be different lengths depending on what the rest of the year needed.

The Alter Rebbe taught that a person must live with the times, meaning with the portion of the week that is being read, and the Rebbe repeated it constantly and pressed it further, that the Jewish calendar is not a container the year sits inside but something a person is meant to be inside. Read chapter eight that way and it stops being arithmetic. The remainder that Marcheshvan and Kislev absorb is the year admitting out loud that it does not come out even, and refusing to pretend otherwise.

The Baal Shem Tov taught that wherever a person's will is, there the person is entirely. The court that fixes the months does something like the inverse. It decides where the year's will is, which parts of it are fixed and cannot bend, and which part will do the bending. Tishrei will not bend. Nisan will not bend. Marcheshvan, which asks nothing of anybody, will.

And the Sfat Emet, on the renewal of the moon, teaches that the new month is not a replacement of what waned but a restoration of it, the same moon, returning. The Rambam has built a calendar in which nothing is ever discarded. Twelve hours and seven hundred ninety three parts are shaved off every single month, and not one of them is thrown away. They are held, accumulated, and eventually paid out in whole days in Marcheshvan and Kislev, sometimes years later, in a month nobody was watching.

Modern Application

You have a remainder too.

Every commitment you have made is stated in whole units. The hour you promised. The day off. The visit, the practice, the amount you said you would give. And none of it comes out even. There is always the piece that would not fit into the shape you agreed to, and the ordinary way of handling it is to round and forget, which works well enough for a while and then one day you look up and everything has drifted and you cannot say when it started.

The Rambam's alternative is more work, and it is the only one that holds. Decide in advance what cannot move. Tishrei is full, Tevet is lacking, and that is settled before the year begins so that nobody has to argue about it in the moment, under pressure, with a reason ready. Then designate, deliberately, the place where the slack will live. Not wherever slack happens to fall. A named place, chosen because it is empty, whose actual job is to absorb what the fixed parts could not.

Most people do this backward. They leave the important things flexible, because the important things are the ones with give in them, and they hold the line on the trivial ones, because the trivial ones are easier to be rigid about. Then the drift shows up exactly where it does the most damage. Kislev is permitted to run twenty nine days or thirty. Yom Kippur is not up for discussion.

And then the arithmetic, which is the part I would keep. You cannot know what kind of year you are in until you know whether it is a leap year. Four days means one thing in an ordinary year and the opposite in a leap year, and the number by itself will tell you nothing while sounding completely certain. Before you read your own evidence, know what kind of season you are standing in. The same amount of tiredness means something different in a hard year than in an easy one. The same silence from a friend. The same setback, the same doubt, the same slow week. The count is identical and the reading inverts, and the Rambam wrote the warning into the middle of the halachah for precisely this reason. When does the above apply? Ask that first.

The Closing

There is something almost tender about Marcheshvan.

It is the only month in the year with nothing in it. No festival, no fast, no obligation that belongs to it alone. If you were designing a calendar to impress somebody you would have given it something. The Rambam gives it a job instead, and the job is to not be a fixed length. To be twenty nine days in one year and thirty in another, depending on what the rest of the year could not carry.

That is not nothing. That is the thing that keeps Pesach in the spring and keeps the appointed times appointed. The whole enormous machinery of the fixed calendar, the parts of an hour and the postponements and the signs to check yourself against, comes to rest on two quiet months in the autumn that are willing to be different lengths.

We spend most of our attention on the fixed months. That is where the festivals are, and that is where we can see ourselves being counted. But a year is not held together by its fixed points. It is held together by whatever is willing to absorb the difference between what was promised and what actually arrived, and to do it without announcement, and to do it again next year in the other direction if that is what is needed.

The moon takes twenty nine days, twelve hours, and seven hundred ninety three parts. The calendar says twenty nine days, or thirty. The difference has to live somewhere. The Rambam's answer, worked out across ten halachot of arithmetic, is that it lives in the emptiest room in the house, and that the emptiest room in the house is therefore the one holding everything up.