The Intricacies of the Jewish Calendar

Judy Callahan: So, each day of Elul, we have been hearing the call of the shofar alerting us to the approaching New Year.  Tonight, we officially enter the High Holiday season with Selichot. It’s our one late Jewish service all year. In many communities, it’s actually even held at midnight. And it’s when we really seriously begin reflecting on the year to come.

Now, last time, pretty much at the same time last year, we kicked off our Sinai and Synapses program, which was an 18-month grant from a project that feels it’s important to bridge the religious and scientific communities, to create a world that is scientifically grounded and spiritually uplifting. The specific program of our grant was “The Intersection of Judaism and Science: Coexisting Searches,” and we began with a wonderful lecture from the president of Caltech, Dr. Thomas Rosenbaum. And throughout the year, we have explored medical ethics with a panel led by Dr. David Snyder and Rabbi Elliot Dorff. We looked at Torah and archeology with Dr. Christine Garroway. We questioned the relationship of free will, and what is built into our brains, with Dr. Liad Mudrik from Israel. And we spent Shavuot with Dr. Victor Zlotniki, Dr. Bonnie Buratti and Rabbis Jason Mann and John Carrier as we examined the relationship with Jewish Halacha and the changing technology that was developing during COVID, and how we balance those things.

Tonight, we are honored to have Albert Hayden with us. Bert works as a navigation systems engineering specialist for the Aerospace Corporation in El Segundo, where he analyzes the performance of GPS and other global navigation satellite systems. He served in the U.S. Air Force for eight years, four of them working on a space-based infrared system. His interest in the Jewish calendar, and calendars in general, is tied to a lifelong interest in both history and astronomy. It is also tied to his work on navigation systems, which must address many of the same timing and Earth-orientation phenomena that affect calendar design. In addition to his engineering work and studies, he has studied Biblical Hebrew and Aramaic at the graduate level, is an active student of the Hebrew Bible in Jewish history, and holds a Master of Science in Electrical Engineering and a Master of Arts in Theology. Like many of us, I always look to see if the holidays are early or late in any given year – spoiler alert: all the High Holidays next year don’t start until October. And we all forget that Rosh Hashanah actually is always on the same day. It’s on the first of Tishrei. So I’m now happily turning this over to Bert, who can explain to us why, if it’s always on the first of Tishrei, and why is it never on the same day?

Bert Hayden: So thank you so much, Judy. I really appreciate — that was a wonderful introduction. I’m so glad that Judy said all those kind words, because I was going to start off and explain: why would a navigation engineer be someone to talk to you about a calendar? And what many of you may or may not know is that the navigation systems that we depend on for our phones to work, for the banking system to work, in order to get ourselves from point A to point B, actually depend upon precise timing systems. GPS satellites are essentially just orbiting ensembles of clocks, and that is how it works. And my interest, as Judy said, in the calendar began when I became a navigation engineer a couple decades ago, working for Sperry Marine Systems. At that time I was not working so much on GPS, but on the Voyage Management Systems. They used GPS, and it was there that I came to understand the role of the stars and astronomy in navigation. And that really drew me into to a greater interest in calendars.

So I want to talk to you tonight about two things, because we can think about a calendar in different ways. And so yeah, there’s sort of a technical view. So I decided that what I would do is I’d take a look and see: what does a popular source say about what a calendar is, because we’re going to talk about calendars? If we’d answer what a calendar is, when I took a look I saw Wikipedia, the first sentence was “a calendar is a system of organizing days.” This is a very sort of a bland way of thinking about it. But it’s the very technical view of it. And then this is done by giving different names to their divisions, whether it’s organizing them into months, months into years, years into decades, and so forth. This is a technical view.

But there’s also a social view of calendars. And this is a quote from Sacha Stern. Dr. Stern is a professor at the University College of London; he’s written several books on the calendar, on the Jewish calendar. He wrote Calendar and Community, which is a very good book. And in fact, when I started to think about the topic of this presentation, I kind of wanted to do a review of his book, but then I realized I only had an hour and I wasn’t about to go through the entirety of the book. But I would highly recommend it to you if you have the desire to read through highly technical material on the past. But Dr. Stern, he’s an expert on the Jewish calendar, and he’s an expert on calendars from antiquity in general. And this is what he says:

“The calendar is far more than a functional, utilitarian device for the organization of social life. As a shared conception of time, or of the flow of human and natural events, which it assumes (for example) to be structured and recurrent, the calendar contributes to a certain perception of reality, and hence, to socially shared worldviews. Calendars have often been invested, indeed, with ideological meanings that transcend the temporal organization of society and assume sometimes cosmic significance.”

And this, like I said, is a much more expansive view of what a calendar is, and it is ultimately where I want to go tonight, because I want to make the argument – and I think that Dr. Stern is making the argument as well – that the Jewish calendar is more than just simply a way of organizing time. It’s actually something that has inside of it sort of implicitly within it, Jewish identity, and that the Jewish calendar is a way in which we reinforce and support our identity as Jews.

So the first thing is about that technical view is, it’s talking about “What is a day?” All right, it’s saying this –  it’s saying that the calendar is a way of organizing days. And this brings us to a logical question, the natural question, which is: “What is a day?” Now, this may seem obvious, but there are actually three possible options that we could talk about, of  “What is a day?”

At least in the context of a calendar, one possibility, which is how the Ancient Egyptians reckon the day, which is morning to morning. Now, you may say “Well, you know, the Egyptians reckon the the day from morning to morning, but you know, we as Jews don’t do that. We do it from evening to evening.” But there’s actually evidence within the Torah that somebody, somewhere in our past, actually thought of the day as being morning to morning, and we say that every Shabbat, if you say kiddush, “va’y’hi erev, va’y’hi voker, yom hashishi” if you actually start off with the full thing, you go here, right. And that comes from the creation account in Genesis Chapter 1. “And then there was evening, and then there was morning.” And if you remember the creation account, you’ll remember that within it, it starts off with God doing something. God is doing all kinds of things. And then he says something – something happens, “And then there was evening, and then there was morning.” And then the day is reckoned. And so sort of implicitly within that is this idea that there’s stuff that happens, and then there’s night, and then the day is complete in the morning. So there is evidence for that.

There’s also another concept of the day – midnight-to-midnight. You know, this is the way the Romans reckon the day, and it’s the way people still, in the modern world, generally reckon the day, midnight to midnight. You might say, “Well, is there evidence for that? You know, did we ever reckon midnight to midnight?” And here’s the question: when did we leave Egypt? We left Egypt in the middle of the night. And there are other places in the Torah that talk about “Well, what day did we leave?” The 15th of Nissan, not the 14th, when the Korban Pesach sacrificed the sacrificial offering. So there’s some support for a midnight-to-midnight day. But overall, what we have within – and you really do have support. I quoted the Gemara, in which it talks about, “There’s one Rabbi who said ‘Hey, you know, the day is evening to evening, and why is this?’ Well, it’s because when you read in the Book of Leviticus about Yom Kippur, it says that from evening to evening, from the evening of the ninth to the evening of the 10th, you will keep your fast.” You will shabbat your Shabbat, right. You will Shabbat your shabbaton. And that really does demonstrate that we have an evening-to-evening day.

And people say, “Well, wait a second, it says ‘from the evening of the ninth day.’” And this is something that you have to remember, that within the Torah, when it says Yom, when it says “day,” it usually means “daytime.” Sometimes it means a day, a 24-hour day as we understand it, but oftentimes, and usually, it means “day” as in “daytime.” So for instance, with the Flood, you have something like “40 days and 40 nights.” So when it says that we will reckon Yom Kippur from the evening of the ninth until the evening of the 10th, it’s talking about the evening of those days. So at the evening that ends the ninth day of the month, the seventh month, which is Tishrei – and yes, it is the seventh month, I’ll get to that in a second – until the evening of the 10th. That’s how you reckon it. And the Gemara says, “Yeah, that’s why our day is evening to evening.”

And this is actually the most compelling view, but I just want to bring up the fact that there are other possibilities that Biblical scholars bring up. But as a professor of mine once said, “You know, scholars dispute everything because that’s what they do for a living.” So what is a day? We’ll start off with the Jewish day, which is evening to evening. But how do we organize those days? Well, almost every calendar organizes the day according to the cycle that I have displayed up here. I pulled this image off of a NOAA website. It takes, of course, the heliocentric view, with the Earth orbiting the sun rather than the sun going around the Earth. But we have to understand that from the view of calendars and the people who developed calendars, it’s the sun that goes around the Earth, not the other way around, right, because they’re thinking from the perspective of someone who’s living on the Earth.

But this is what we have. The Earth goes around the sun, and because of the tilt of the Earth – which is relatively stable, it wobbles back by meters, and of course, for those of us that know, it also precesses over thousands of years – but over the scale of a year, the earth’s spin axis pretty much just points just off the direction of Polaris. And because of that, as the Earth is rotating around the sun, the different regions of the Earth receive differing levels of sunshine and sunlight, and this results in the seasons, as we understand it. And most calendars are trying to align themselves to this solar cycle. There is a major exception, which is the Muslim calendar, which will probably explain for you, if you ever wonder “Why does Ramadan always seem to be happening at a different time of year – you know, last year it was happening at this time, and now it’s happening at another time?” The reason for that is because the Muslim calendar is a purely lunar calendar, and it makes absolutely no correction to fit to the solar cycle. And I’ll kind of explain why that happens in a second.

So here I’m pretty much saying, “Hey, you know, the solar motion is actually pretty simple.” I know a lot of you are going to sit down and say, “Oh no, it’s not.” I know that the Earth’s orbit is eccentric. And yes, I completely agree, there’s little wobbles. But compared to something like the motion of the moon, this is pretty stable. And we have just, you know, a tropical year, which is the year of the seasons, which is about 365 days – 365.24. So about a quarter-day. And that’s the reason why, in the Julian and the Gregorian calendars, which are solar calendars, you get this extra day once every four years. But also because of that slightly-off-of-a-quarter, it doesn’t always happen, and you have to have not one every 100 years, and then one every 400 years.

So we come to lunar motion. I was looking for a nice grab somewhere online to kind of describe the difference between solar motion and lunar motion, and the best one that I found was actually from a comic. The comic had a bunch of other items in it that weren’t true, but these four are actually. And you see that you’ve got four things up there. You’ve got nodal procession, apsidal procession, phase, and distance. And what is meant by this? Well, the node of an orbit – and I know I’ve got people from JPL here who are going to – like, you know this far better than I do.

But the node of an orbit – there are actually two nodes. There’s the ascending node and the descending node. What does that mean? Well, as something is going around the orbit has some kind of inclination relative to the equator, or some kind of reference, usually the celestial equator, which is just the Earth’s equator projected out into the celestial sphere. And where the orbiting body is going up is called the ascending node, and where it is going down is called the descending node. And when it talks about nodal procession, it’s talking about [how] that orbit and where that node is changing. It’s rotating around. And so the moon’s orbit is doing that absolute procession that has to do with the axis. Because orbits aren’t perfectly circular, and the moon’s orbit is definitely not perfectly – it’s nearly circular, but it’s not perfectly circular, and actually is kind of flexing back and forth at all times. It’s also moving around. And it’s so that that ellipse that describes the Earth, the moon’s orbit, is just going around too. And so there’s that motion.

There’s, of course, phase. And the reason that I kept phase in there, up there, is because it’s important to understand that people don’t observe phase. Like we, people living here on on the surface of the Earth, are not observing things like, what is the “What is current true anomaly of the moon?” or something like that. What we’re observing is what is the phase of the moon. Is it a new moon? Is it a full moon? Is it a half moon? Something like that. And that’s what is actually important to calendars, because things like the Jewish calendar and the Babylonian calendar are based on the observation of the lunar crescent. And then, of course, I just put in the distance there.

So what’s the major message that I’m trying to send with this slide? The major message I’m trying to send is that the moon’s orbit is a lot more complicated than the sun. It’s moving around, and so it changes. So the period from one new moon to another new moon, or from one full moon to another full moon, is actually changing month to month. In terms of full fixed days, that means that a lunar month can either be 29 days or 30 days. So if you’re trying to devise a calendar that is based upon lunations – that is, a calendar that is starting whenever the moon is new – the length of your month is always going to be changing. It’s going to be somewhat unpredictable. And for those of us that pay attention to the Jewish calendar, we know that there are 29-day months and there are 30-day months, and we also know that when there are 30-day months, that we end up getting to Rosh Kodesh, two days in Rosh Kodesh. And why is that? It’s because in ancient times, they would always double it up just in case, you know, we know that it might show up in 29 – well, then maybe they might declare it the next day. So you would end up having two Rosh Kodesh. And they sort of made this official as part of what it is.

Now I put down there the Halachic Molad. And you’ll see that it is almost exactly the same figure that Norton gives for the period of the synodic month, which is the phase-to-phase month. And that’s actually the number that is given by Rambam in the Mishnah Torah. It’s the one that is used to reckon the Jewish calendar. And it’s actually very, very accurate.

So this creates a problem. And the thing is that the Jewish calendar is tied to the seasons. The principal reason for the calendar is to fix the time of the festivals. And the festivals are agricultural festivals, so they’re seasonal. They’re tied to the solar year. They’re tied to the position of the Earth in that orbit around the Sun. And so we have up here – so for instance, with Pesach, that it says “shamor et chodesh ha aviv,” so “Keep the month of the Spring and do Pesach to Hashem, your God, because in the Kodesh Ha’Aviv you went out, or Hashem took you out – your God took you out from the land of Egypt at night. That’s Deuteronomy 16:1.

And so when it says to keep the month of Aviv, this is not a reference to a name of a month. Chodesh Ha’Aviv is not the name of a month. Aviv, when you see the word — Aviv is a description of a state of barley, and barley in the field. And it’s not quite ready to be harvested – it’s not ripe yet. But it is in a certain state – ready, you know, getting ready to be to be harvested. Or actually, it is ready. And so when it is, it’s Aviv. And the justification — how do we know this? It’s because when it talks about the plague of hail in the book of Exodus, it talks about how the barley was not yet Aviv. So it wasn’t destroyed when the plague of the hail came. So Aviv is not a description, it’s not a month, it’s not a name of a month, it’s a description of a state of barley.

This Hebrew verse here, I was discussing the Omer of the first wheat at Shavuot that is offered at that period in time – again, this is agricultural. And then of course, Pri Etz Hadar, which is a reference to etrogim, which have to be brought at Sukkot. So because the harvest of fruit is associated with Sukkot, what we have here is that the Torah festivals are in fact agricultural festivals.

Okay, so but we have again this problem –  the Jewish calendar has to be solar in the sense that it’s a seasonal calendar, it’s an agricultural calendar. But a tropical year does not divide into an integer number of synodic months. What is a synodic month? The synodic month, as I said before, is the phase month. It’s the time from successive phases. So a new moon to a new moon. So if you’re trying to create a calendar that’s both a solar year, and also has these lunar months within it, if you get 12 months, you’re only going to get up to 354 days on average. And so you’re going to fall short. And that’s why, when Judy’s talking about why, if Rosh Hashanah always falls on the first of Tishrei, why is it always changing? It’s because if you’re reckoning 12 lunations, you’re going to fall short of 365 days. And so it will slowly come back to you within any kind of solar calendar, like the Gregorian calendar, which is sort of the official day. And as I said, it’s short of a tropical year by about 11 days – 10.8 days.

So that’s the problem – what are the potential solutions? Well, one potential solution is to just have a solar calendar with fixed months. And there are examples in ancient times. So for instance, the Ancient Egyptian calendar is a well-known solar calendar from ancient times that consists of 12 months of exactly 30 days, to get 360 days. And then to bring it up to 365, you just throw in an additional five epochal […] days that are not associated with any particular month, and you get 365 days. And then it’s essentially a solar calendar.

Now of course, it’s not quite the length of a tropical year. So the Egyptian calendar was famous in ancient times, and even modern times, for slowly slipping through the seasons, like the Muslim calendar, just not quite as seriously. But yeah, that’s one potential solution to this problem. It was more or less stable.

Then you also have the Julian/Gregorian calendar, which, with the exception of the leap day that is given in February, it also has a calendar largely of fixed months that do not change from year to year. But there’s another solution: the lunar-solar calendar solution, which makes use of what I’m calling the Babylonian cycle, but is also known as the Metonic cycle, from the name Meton of Athens, who introduced it into the Athenian calendar in the year 432 BCE. And the Metonic cycle of the Babylonian cycle is based on the fact that if you have 19 tropical years – so those are the seasonal years I’m talking about, the tropical years are the seasonal years, the length of year that it takes to go from one vernal equinox to another, from one beginning of Spring to another, in the Northern Hemisphere, at least – if you take that, 19 years, that’s about 6939 days plus some change. And if you have 235 synodic months, again, that being the month from New Moon to New Moon – if you take those 235 synodic months, you get about the same number of days, it’s just off by a little that really amounts to about one additional day every 218 years. So it’s not too bad. But what it results in is a rule that if you have seven additional synodic months every 19 tropical years, you’ll only end up with this difference of two hours. And like I said, that amounts to about one day every 218 years.

So this, the fact that you could have two solutions, both, potentially, a solar calendar and a lunar calendar, raises the question: well, was there ever a Jewish solar calendar? You know, I kind of brought up that there is some hint of a solar calendar in the creation account itself. And in fact you also have some hint that it actually was maybe even an Egyptian calendar for other reasons that I’ll talk about, but Dr. Stern, in his book Calendar and Community, he brings up that well, we know that at least that the Jewish calendar has been lunar since the first century CE, and that this is well established. And why is that? There are just too many sources that say that the Jewish calendar is lunar, whether that’s Josephus – Josephus was a historian of the first Jewish Roman War, and he also wrote the Antiquities, which was an attempt to write out the full history of the Jewish people from the earliest times on up to the first Jewish-Roman War, which, if you’re not aware of it, is the war between the Jewish people in Rome that ultimately led to the destruction of the Second Temple of Bet Ha-Mikdash in 70 CE. But Josephus – who was actually a kohen, and he was also a general in that war – ultimately wrote these books, and so Josephus attests to the fact that the Jewish calendar in the first century CE was in fact a lunar calendar.

Philo, who was a Hellenistic philosopher, who was Jewish, but he also was very Hellenistic – he lived in Alexandria, he wrote many books on philosophy that are heavily influenced by the Greeks. But he also attests to the fact that the Jewish calendar in the first century CE was lunar. But they’re also, if you look at rabbinic and also Christian sources, they all attest to the fact that the Jewish calendar, from the first century CE on, was lunar.

There is also some evidence, but we also have to understand that the further you go back in time, the harder it is to find solid evidence – but there’s also other evidence that the Jewish calendar was lunar. And one of those things is that the Babylonian month names came to be attributed to the Jewish months. Almost all of the month names that we now use in the Jewish calendar are of Babylonian origin, whether they’re Adar, or… The sole exception is Cheshvan, Marcheshvan, which is of Persian origin. But aside from Marcheshvan, all the other names are essentially identical to the names within the Babylonian calendar. And prior to the Persian period – so up here, we’re seeing books like Zechariah, Esther, the First Maccabees – prior to these First Maccabees would have been about the time of Hasmoneans. It’s in Greek, it was originally written in Hebrew, but it’s in Greek. Esther Zechariah dates to the time of Darius the First, so that would be the late 6th Century BCE. So this is very back in time. But he’s using the names of Babylonian months as Hebrew months. And the fact, if you’re making an equation between the Babylonian calendar and the Jewish calendar in such a manner, this tends to imply that they’re comparable. And if they are comparable, this would imply to the Jewish calendar is lunar.

You also have the Passover Papyrus, and I give you both the museum number there and the the publication numbers. TAD refers to Aramaic documents – it’s by both Ada Yardeni and Bezalel Porton. “Cowley” refers to Aramaic documents from Elephantine. A papyrus was a command in an Aramaic document issued by an official under Darius II, who is an accumulated Persian king to the Jewish community. That elephantine  is an island in the Nile River and it’s all the way at the southern border of Upper Egypt at the first Cataract. And there was a group of Jewish mercenaries that lived there during the Persian period who defended the southern border of the Persian Empire in Egypt. And about 416 BCE or so, they were given an order by Darius II to observe Pesach. And within that Passover Papyrus, it says you should be keeping it in the month of Nisan, which of course was a reference to the Babylonian month, but it’s also the month that we now call Nisan, that we keep Pesach in as well. And so this, again, suggests that even that far back, that the Jewish calendar was a lunar-solar calendar.

But there’s also other evidence that you had solar calendars. And it’s these sorts of apocryphal, deuterocanonical books, their Works, principally – what motivates people to see the potential of a Jewish solar calendar is actually documents found at Qumran, different calendrical documents that talk about a solar calendar.

So Dr. Stern, in the first chapter of his book Calendar and Community, deals a lot with this, saying, “Well, do these cylindrical documents that talk about a solar calendar being used by the Jews at Qumran – is this evidence that there was in fact a solar calendar?” And like I said already, you also have a morning-to-morning day that’s mentioned in the The Genesis creation account, and that matches what’s in the Egyptian calendar. You also have, in the Flood, that it endured for five months of exactly 30 days, which also suggests the Egyptian calendar.

So there’s a question of “Was there a solar calendar?” My argument would be no, that the evidence is pretty strong that the the Jewish calendar, from time immemorial, has been lunar-solar. There may have been some use of a solar calendar for administrative purposes, but really, the evidence for a solar calendar is actually really limited, and isn’t very convincing. It’s usually associated with marginal groups or with stories like the Flood or the Creation. So the Jewish calendar has been lunar-solar. And it has to find some kind of solution, and then, because of that, we have to find some kind of solution to the lunar- solar problem. How do we deal with the fact that 12 lunar months is only 354 days, and falls about 10 to 11 days short of a solar year, the tropical year, from season to season?

So the solution that is actually implemented within the Jewish calendar is the 19-year cycle that was first evident in the well-understood Babylonian calendar. Now, I mentioned before that this cycle is also called the metallic cycle. And so I have two arrows up there, and the purpose of this arrows is to kind of show you where the Babylonians finally figured out the 19-year cycle and where Meton introduced it into the calendar at Athens. Now, what is this table? This table comes from a book called The Babylonian Chronology, which was published in the 1950s by Richard A. Parker and by Waldo Dubberstein, both of whom were scholars of the ancient world. But what they did is they went through and they looked at all of the evidence for the Babylonian calendar, which is actually extremely well-attested.

The Babylonians were really kind of very, or just they were – we have to be very grateful to them, because without the Babylonians we would have almost no certain knowledge about ancient chronology in the Near East. But because they existed, because Babylonian astrologers existed, we have a lot of knowledge about exact chronology within the ancient Near East. And the reason is that the Babylonians had this passionate belief that the destinies of governments, of kings and nations, were all in the stars, and they were very exact about it. So they made very exact measurements of the positions of various stars. And because they were so convinced that it was explaining events that were going on in politics, they also recorded – they tied these astronomical observations to political events going on at the same time. So we actually have very good data that enables us to tie political events within the ancient Near East that are recorded within Babylonian documents with actual times.

But we also have within the various documents from Babylon – we have evidence of when they actually added months to fix the slow divergence between the lunar calendar and the solar calendar. And because what you have to do is that, as the lunar calendar is moving back about 10 to 11 days every year, once you get to about two or three years, you’ve got to push it forward with an additional month. And this is what we do when we have an additional Adar, about once every two to three years.

The Babylonians, of course, were aiming at something different than what the Jewish calendar aims at, because the Jewish calendar, in theory, is aiming to put Pesach right after the vernal equinox. Because of that command that we saw, that command from Exodus and the command from Devarim, from Deuteronomy, to keep Pesach in the month of Aviv, in the month of basically the month of Spring, which came to be interpreted as the month of the vernal equinox. That what we’re aiming at, but the Babylonians were actually aiming at having both to have Nissan immediately after the vernal equinox, so that Nissan would begin with the first new moon right after the Vernal Equinox, and Tishrei would begin with the first new moon, right after the autumnal Equinox, the September equinox. And so they were trying to match up both of them.

And so they they they developed this 19-year cycle by experimenting over years. And so you can see that it’s kind of confused at first. They’re not really sure where to put the months in order to achieve these additional months that are required by a lunar-solar calendar. They’re not quite sure where to put them. But then they ultimately settle in about here, where they’re putting they’re putting an intercalary Addaru. Each one of these letters represent an intercalated month within that 19-year cycle. And you can see that once you get here, they’ve got one at three, they’ve got one at six, they’ve got one at eight, nine – excuse me, 11. They’ve got one at 11. They’ve got one there at 14, 17 and 19. And that is the same cycle is now used within the Jewish calendar. And they figured that out about that period of time.

But you’ll notice that there’s a really important difference between what is being done here in the Babylonian calendar, and what we do in the Jewish calendar. And that difference right there is that intercalary Ululu, which is essentially just the Babylonian name for we now say Elul, for the current month. And the reason for that is that they intercalated an Elul from time to time because they’re trying to keep the association between what they call Tashvitu and what we call Tishrei. They’re trying to keep that month aligned with the autumnal equinox as well. But we ditched that for an important reason, and I’ll explain that.

And that’s the chief difference. And the reason for that is because in the Torah, the numbers, as I said before, the months are only numbered. You only have you know, that Pesach occurs in the first month, Sukkot occurs in the seventh month, Yom Kippur occurs in the seventh month – yes, it is the seventh month. So Rosh Hashanah, even though you know it’s Rosh Hashanah, Rosh Hashanah actually never appears in the Torah. It’s always called “yom teruah,” and it’s the first day of the seventh month, because – and I’m going to get into this in a second – within the concept of the Torah, there is sort of this idea of the holiness of seven. So you have the seventh month as the holiest month, and that’s where all the big holidays are happening, but because there are two calendars, actually four calendars, within the Jewish system, that are mentioned in the Mishnah, but there are at least two calendars that we keep. And there’s the religious calendar, which determines the time of the festivals, which begins in Nisan. And then there’s the civil calendar, which begins with Rosh Hashanah. And that’s, of course, why we call it Rosh Hashanah. The only time that Rosh Hashanah has ever mentioned within the entire Tanakh is actually in the 40th chapter of Ezekiel. But it probably refers to a month, and not to the actual day.

But as I’ve already stated, you know, there’s a bunch of places where people think that we have month names – like, you know, Aviv. But again, like I said, that has nothing to do with an actual name of a month. Within Chapter Six of Kings, you also have Ziv and Bul, there’s also Eitanim, which is not up here. But those are all Phoenician. And like I said, the the main thing is that there have to be six months between Pesach and Sukkot.

But other than that, we have the same leap years as the Babylonian calendar. The critical main difference is the phase. Why do I say that again? It’s because the Babylonians are trying to aim for aligning the first and the seventh months with both equinoxes, and we’re not doing that. And just as a fun fact here, since someone asked me at one time about the Chinese calendar, the Chinese calendar is also lunar. And the big difference what they’re trying to do is they’re trying to put their new year at the second lunar month after this winter solstice, December Solstice.

There are some very technical rules about the postponement of Rosh Hashanah. And you know, this gets this gets beyond – this just sort of deals with some different things. Like for instance, you can’t have Yom Kippur on that on that falls before Shabbat or after Shabbat. And also you can’t have Hoshana Rabbah fall on Shabbat. But something that to focus on here is all the sevens that exist within the the Jewish calendar. And what we see then is that there’s the seven-day week – it’s the period ending in Shabbat. We have seven days of matzah, we have seven days in the sukkah, we have the counter of Omer, which occurs for seven weeks ending in the 50th day, which is Shavuot – which, if you do the math, is actually about one-seventh of a lunar year. A lunar year is about 354 days. Divide that by seven, you get something that’s very close to 50. So there’s one-seventh. Also, you have the sabbatical cycle and the Jubilee count, which also includes seven. So there are a lot of sevens. And this kind of comes back to the idea that Dr. Stern was talking about, that calendars are not just mechanical ways of organizing days, but they also have like a deeper social significance. And I think that the sevens is kind of starting to capture this in the sense of, you know, there’s something going on here, because these do not actually have any astronomical connection with astronomy at all.

So: seven is special. This is actual data that I did from research of Biblical numbers myself, but you can see that what you have here is two things. You have the frequency of the first number of the numbers that are within the Bible – so what does this mean? So like, if you have 100, its first number is 1. If you have 2,369, its first number is 2. And so on and so forth. And there is a statistical law called Benford’s Law, which talks about what is the expected distribution of these first numbers, given  if you have a large enough set. And you can see Benford’s Law, right here, is what you would expect for the numbers. And you’ll see that seven stands out. I have accounted for non-numerical meanings of one and two in this data, but seven does, in fact, stand out. And you’ll also see the other thing is that eight and nine are depressed. But seven actually has a lot of significance.

Seven’s significance is not tied simply to calendars, to days, to systems of months or anything like that. It occurs in a lot of places. For instance, when Jacob is approaching Esau, he bows seven times. When the priest is trying to purify something in the Mishkan or in the temple, he sprinkles it with blood seven times. So seven appears in a lot of different places. When Avraham makes his Covenant, he sacrifices seven lambs. So seven occurs in all places. and it doesn’t seem to have any sort of astronomical explanation. And as for the depressed values of eight and nine, that’s because there’s a real strong tendency in the Hebrew Bible to round numbers. So if you get eight or nine and you they’ll tend to round it up you have 800, 900, you’ll round it up to a thousand or something like that. So seven is indeed special.

Okay, so let’s go back and talk about the significance of Shabbat. So there’s two perspectives on Shabbat that are given within the Torah. One is given within Sh’mot, and the other one is given in Devarim. The one in Sh’mot makes Shabbat into a memorial of the creation, right. You know, “ki sheshet yamim asah Adonai et hashamayim v’et ha’aretz et hayam,” and everything in it, right. And so it’s spoken of as being a memorial of the creation. So that’s one way of thinking about Shabbat. Then there’s a second way instead, for Devarim, in Deuteronomy which is Shabbat as a memorial of our slavery in Egypt. And what is the significance here? It says right here, in Devarim it says so you know you’re going to keep Shabbat, and you’re going to “Remember that you were a slave in the land of Egypt and the Lord your God freed you from there with a mighty hand and an outstretched arm; therefore the Lord, your God has commanded you to observe the sabbath day” (Deuteronomy 5:12-15). This is the JPS translation.

And the point here is that Shabbat is meant to memorialize our slavery in Egypt — not so much our slavery in Egypt. What I really should say is it’s meant to memorialize our liberation from slavery, because what really is going on with the number seven is that it solemnizes things. Why does Jacob bow seven times as he’s approaching Esau? He does it seven times in order to demonstrate that he truly is humble. He does it seven times, just like the seven lambs are sacrificed, because it affirms that Covenant. Why does the priest, why is the Kohen within the Mishkan, or within the Temple, sprinkling the altar seven times with blood? It’s because it solemnizes the act. Why do we dwell in a sukkah for seven days? Because it solemnizes the act. it’s not because we actually dwelt in a sukkah for seven days – we probably dwelt in sukkot for many far more days within the wilderness than just seven. But the act of dwelling in a sukkah for seven days solemnizes it. And so by having Shabbat, what you’re doing is you’re not solemnizing work, you’re not solemnizing being – you’re more than something that is just a laborer.

The same thing also occurs in a cycle that is sometimes the you know some people are aware of some people aren’t aware of, which is the Shmita, or the Sabbatical year. Shmita is the the Hebrew word for “release,” and it’s used because in the book of Devarim, the main thing that occurs during the seventh year is the release from debts. So this – you’ll see this in, say, contracts from the ancient times. They talk about shmita, [and it] can actually mean the conclusion of the contract itself, or it could just mean a release of some kind. Sh’mita means “the release.” But it also was associated with the cessation of agriculture, and principally with the liberation of Jewish lives, there was a liberation every seventh year. There was also the liberation of the Year of Jubilee. But again, we see that the significance of seven, and we also see the sort of significance of reminding us of our liberation from Egypt.

So we have talked about two things from a technical perspective: the Jewish calendar is a lot like other lunar solar calendars. That 19-year cycle that I was talking about is going to appear in practically every lunar-solar calendar that you have, because it’s determined by the science, it’s determined by the relationship between the lunar cycle and the solar cycle. And so it’s pretty much the same. But from other aspects of the Jewish calendar, we have – like I was bringing up here the importance of these sevens,  that we see the seven days of Shabbat, the seven months from Nisan to Tishrei, the seventh of the year that is the Omer, count the seven-year cycle of the Shmita, and in fact, the seven sh’mitas that ultimately come up to the Jubilee. We have in there are a lot of reminders, and within the Torah itself is just a reminder of our Liberation from Exodus.

And the reason why I would say that this ultimately comes back to Jewish identity is because you know Judaism is, essentially, was traditionally a legal system. What it was, at the core of Judaism, was a legal system with religious characteristics. This was the view of Menachem Elon, who was a president of the Supreme Court of Israel. But the point is that we have a legal system, and the basis of that legal system, the core idea of that legal system, is really sort of ethical values that develop out of our ancestral tradition of liberation from slavery in Egypt. And so you can see that yes, there’s the technical aspect – we can have the technical view of the calendar – but we also need to expand that to see the social view of the calendar. There’s a lot of features of the Jewish calendar that ultimately should remind us of our tradition of liberation from Egypt, and the ethical values that then inform the legal system that really is at the core of Judaism. And that concludes my brief – presentation, I say “brief” all the time. [Applause]