The Starting Point You Are Allowed to Move

The Hook

Fifty nine minutes and eight seconds. That is the whole opening of the chapter, and it is the mean distance the sun travels in a single day, in twenty four hours, measured against a circle of three hundred and sixty degrees. From that one number the Rambam builds everything else. Ten days, nine degrees and fifty one minutes and twenty three seconds. A hundred days, ninety eight degrees, thirty three minutes, fifty three seconds. A thousand days, and now the number has been around the circle twice and he gives you only what is left over, two hundred and sixty five degrees and change. Ten thousand days, and the leftover is a hundred and thirty six.

Then, without announcing that anything has changed, he does something a book of law has no business doing. He plants a flag on a specific Wednesday night in the spring of the year 4938, tells you exactly where the sun stood at that moment, and instructs you to count from there to any day you please. And a few lines later he adds that if you would prefer to plant the flag somewhere else, the beginning of a nineteen year cycle, the beginning of a century, a day in the distant past, you may, and the path is well known. Why should the place you begin counting from be a matter of choice?

Fifty Nine Minutes and Eight Seconds

Read slowly and the chapter is doing something unusual with numbers. The Rambam is not proving anything. He is furnishing a workshop. Here is the daily rate. Here is what it comes to over ten days, a hundred, a thousand, ten thousand. And then, generously, he tells you to build the rest yourself. If you want tables for two days and three days and four days up to ten, make them. If you want twenty and thirty and forty up to a hundred, make them. All of it becomes obvious once you know the distance for a single day.

But two of the figures he insists you have ready, and the reason he gives is the key to the entire chapter. Prepare the mean distance for twenty nine days, and for three hundred and fifty four days, which is a lunar year of ordinary months, what he calls a regular year. Why those two? Because there are twenty nine full days from the night the moon was sighted in one month to the night it may be sighted in the next. No more and no less. Every month, the same gap. And he says outright why he is telling you: our sole desire in these calculations is to know when the moon will be sighted.

That sentence should be held up to the light. The entire astronomical apparatus, the degrees and minutes and seconds, the tables, the leftovers after casting off the circle, exists to answer one small human question. On the thirtieth night, can the moon be seen from Jerusalem, so that a court can honestly receive witnesses. He gives the monthly figure, twenty eight degrees thirty five minutes and one second, and the yearly one, three hundred and forty eight degrees fifty five minutes and fifteen seconds, and every one of them is in service of a court sitting in a room waiting for two men to walk in.

The Point That Moves Once in Seventy Years

The second half of the chapter introduces something stranger. In the orbit of the sun there is one point at which the sun stands furthest from the earth, and the same is true for the other six of the seven. That point is called the apogee, and it does not stay still. It rotates, uniformly, about one degree in seventy years.

Sit with the scale of that. A degree is a small thing in the sky. Seventy years is most of a human life. And the Rambam, who has just told you the calendar we actually use could be taught to a schoolchild in a few days, stops and builds a table for this too. Ten days, a second and thirty thirds. A hundred days, fifteen seconds. A thousand days, two minutes and thirty seconds. Ten thousand days, twenty five minutes. Twenty nine days, four seconds and a fraction. A regular year, fifty three seconds. He is tabulating a motion so slow that a man could watch for his whole life and never see it happen. He tabulates it because it is real, and because leaving it out would make everything downstream slightly wrong.

And then the flag. All reckoning begins from the eve of Thursday, the third of Nisan, the year 4938 from creation. At that moment the sun's mean position was seven degrees, three minutes and thirty two seconds in Aries, and its apogee was twenty six degrees, forty five minutes and eight seconds in Gemini. From there the method is simple enough to say in a breath. Count the days from the starting point to the day you want. Look up the distance for those days. Add it to the starting point, accumulating each unit separately. That is the mean position. He works one for us, a hundred days out, the eve of the Sabbath on the fourteenth of Tammuz that year. Ninety eight degrees thirty three minutes fifty three seconds, added to seven degrees three minutes thirty two seconds, gives a hundred and five degrees, thirty seven minutes, twenty five seconds. The sun is in Cancer, having completed fifteen degrees and standing in the sixteenth.

What comes next is the most honest sentence in the chapter. Sometimes the figure holds at the beginning of the night, and sometimes it holds an hour before sunset, and sometimes an hour after. He says so plainly, and then tells you not to worry about it, because the slack will be taken up later, when the moon's mean position is calculated. He is handing you an instrument and telling you exactly where it is loose and exactly where he tightens it. A man who was hiding the seams would not have mentioned them.

A Starting Point of Your Own Choosing

The chapter ends by dissolving the very fixity it just established. Follow this procedure for any date you want, he says, even a thousand years from now. And if you would rather establish a different starting point instead of the one we have chosen in this year, a year that begins a nineteen year cycle, or a year that begins a new century, you may. And if you want a date in the past, or one many years in the future, the path is well known. He even gives you the raw material for it: a year of full months is one day longer than a regular year, a year of lacking months one day shorter, and a leap year runs thirty days longer, or thirty one, or twenty nine, depending on its months.

And the last move is the one that stays with me. Just as you may add the distance forward from the starting point to reach any future day, you may subtract it backward and reach any day that has already happened. Once you have that date, he says, you can use it as a starting point. The past is not sealed. It is computable. Stand anywhere, do the arithmetic, and you can say where the sun was on a night nobody recorded.

The Unifying Principle

What holds this chapter together is not the sun. It is the relationship between a rate that never varies and an origin that is chosen. The rate is not up for discussion. Fifty nine minutes and eight seconds, every day, since before anyone was counting and after everyone has stopped. The origin is entirely up for discussion. The Rambam picked a Wednesday night in 4938 because he had to pick something, and he tells you so, and he offers you the freedom he took.

The Alter Rebbe, in Shaar HaYichud VehaEmunah, presses the point that the world is not a thing that was made once and left running. The letters of the ten utterances are standing inside every creature at every instant, and if they withdrew for a moment the creature would not slow down, it would not have been. What looks from below like unvarying regularity is, from above, a continuous act of beginning. That is the sun of this chapter exactly. Its perfect constancy is not inertia. It is something being said again.

The Baal Shem Tov taught that a leaf turning over in the wind is turning because it was seen and wanted, that providence reaches all the way down to the smallest motion. Here is the Rambam building a table for a point that moves one degree in seventy years, a motion no observer will ever catch in the act, and refusing to round it away. And the Rebbe returned constantly to the teaching that teshuvah done out of love does not merely cancel what a person did; it reaches back and turns the deliberate failures into merits. Set that beside the last lines of the chapter. You may subtract the mean distance from the starting point and determine the position for any past date, and then take that date as your new starting point. The arithmetic runs backwards. So does repair.

Modern Application

Most of us experience our own lives as irregular. Some stretches move fast and some barely move, and we conclude that the underlying rate is erratic, that we are erratic. The previous chapter already gave the correction: the unevenness we measure comes from standing somewhere that is not the center of the circle. This chapter adds the second half. The rate is fine. What you are entitled to reconsider is the point you decided to count from.

People carry epochs. The year something broke, the day a thing was said, the age by which it was supposed to have happened. Everything afterward gets computed as a distance from that. The Rambam, in a chapter about the sun, quietly rules that an epoch is a convenience and not a fact. You may establish another date as the starting point. A new cycle. A new century. Tonight. Nothing about the motion changes, and nothing about the past is denied, because the same arithmetic still reaches back and tells the truth about where you were. You are simply permitted to count from somewhere else.

The Closing

The Sfat Emet reads the first commandment given to Israel as a nation, that this month shall be for you the head of months, with weight on the two small words, for you. The reckoning of time was handed over. Not the motion of the heavens, which was never anyone's to adjust, but the counting of it, the deciding of where a month begins and when a year is full. A people that had been living inside somebody else's calendar was given its own starting point, and the first thing it was asked to do with freedom was to count.

One chapter, and the whole argument is inside a single number. Fifty nine minutes and eight seconds, unwavering, indifferent, going on above a court that is only trying to work out whether two men will see a thin curve of light tonight. The rate is not yours. The starting point is. And on any day you choose, you may set the flag down again, run the count forward into a future you will not live to see, and run it backward into a night nobody wrote down, and find that the sun was exactly where it should have been the whole time.