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In the two previous articles about Jewish time we discussed how todays time concepts make no sense without the light which only the Torah can shed on the topic, and why the Jewish people are commanded to keep a year comprised of both the solar calendar and the lunar one. If you haven’t read the previous blogs yet – I humbly suggest that you check them out first. In this article I would like to give a general overview concerning the formulation of today’s Jewish calendar. The main source that I use for this is the amazing book Sha’arim le Luach ha’Ivri written (by hand) by one R. Sa’ar Shalom. I also owe a debt of gratitude to haRav Shai Valter from whom I learned a course on the topic as well. First off: if you are a lover of math – Kiddush ha Chodesh is the topic for you (to learn in-depth, not just as an overview). Second: the topic of Kiddush ha Chodesh is fundamental to almost all Jewish observance. This is because all of the months get their sanctity based on their beginning, yet their beginning was given over into the hands of the great sages, those with the semicha (ordination) of Moshe Rabbenu, to establish. Unfortunately, there are no Rabbi’s today with that type of semicha. Meheira yiboneh Beis haMikdash! It is due, in part, to this fact that the Luach that we follow today was created in the first place. With that in mind – let’s jump right in! The only “given” that we have on this topic is that which the Torah and our sages, ob”m, tell us and that is the following. For as long as Jewishly possible the way that the Jewish calendar worked was that it was entirely up to the establishment called the Sanhedrin, the largest judicial body of the Jewish people. More specifically it was in the hands of the Head of the Beis Din. Rosh Chodesh began precisely when the Beis Din said, “It is Holy (mekudash, in Hebrew)”. Not before. The problem is that a lunar month is a riley beast   insomuch as the precise amount of time from the beginning of the new moon until it returns to that exact point is exactly 29.5 days and 793 chalakim out a possible 1080 chalakim in an hour[1]. Because of the general length of the lunar cycle it makes sense that over the course of 2 months one should be comprised of 29 days and the other of 30. (Of course, YOU are welcome to keep a 29 ½ day month if you want to… (just kidding!)) However, because of the remainder, which is constantly adding up, a discrepancy slowly builds up which requires handling to balance out the seasons (as we discussed in Jewish Time 2). (This in addition to the 11-day difference between the lunar and solar calendars). In any case as a result of the above discrepancies no one was ever sure (until the proclamation of Beis Din was made) whether or not this month would be only 29 days or 30. The procedure, as described in Tractate Rosh haShanna, in the Rambam Laws of the Sanctification of the Moon, in the Shulchan Aruch Orach Chaim 428 and others, was that a minimum of two witnesses, having seen the new moon, would come to the Beis Din in Jerusalem (or wherever it was after the destruction), to give the necessary testimony upon which the Beis Din relies (or doesn’t) to establish today as Rosh Chodesh (the New Month). If the witness’s testimony pans out and the Beis Din accepts it, the Rosh Beis Din gets up and pronounces “Mekudash, Mekudash”. By doing this they establishe day 30 as NOT part of last month, but rather as the BEGINNING of THIS month. This seemingly “simple” act has tremendous repercussions. It is as a result of this act that defines what day of the month Yom Kippur comes out on. As a result of this it is established what day Pessach falls on, with all of the severities that are tied to their observance. Directly connected to this statement is how we will deal with a child, born on Rosh Chodesh who does some form of transgression of the Torah’s laws. For we only punish an adult, not a child. As a child can only become an adult if he has reached his 13^th birthday, or a girl on her 12^th birthday, if TODAY isn’t Rosh Chodesh, guess what? He’s not an adult and neither is she! There are many ramifications to the day of Rosh Chodesh indeed. That is an amazing power and a tremendous ability that was given over into the hands of our great Rabbi’s! Many of HaShem’s own commandments only become relevant due to the decisions of the great Beis Din. It is for this reason that we “sign off” in the mussaf (additional prayer) beracha (blessing) of the shmoneh esrei[2] “He Who sanctifies Israel and the times”. Israel is mentioned first because it is on our authority that the moadim, the festivals, are determined. We are truly HaShem’s partners in running the world to some extent. The only exception to this rule is the kedusha, (sanctity) of Shabbos, (the Sabbath day), as it’s sanctity is almost as old as time itself. This is because it received its own kedusha directly from HaShem on the seventh day of creation. It was, is, and will always be kodesh without any regard for our ideas in this matter. But Shabbos is a topic for a different day, be”H. Getting back to Kiddush haChodesh. The problem with this system is that if there IS NO SANHEDRIN, or no Rabbi with the special semicha of Moshe Rabbenu then the whole thing kind of fails. Take today, for example. We have none of that. So, if there are no Rabbis who sanctify the new moon, how do we know which day is Rosh Chodesh and thereby which day/s are the festivals? In reality, without the Rabbis – you can’t solve this problem. If the system were left to its own devices we would be in serious trouble! We would forever keep two days of Rosh Chodesh and of the festivals and the problems would compound further as every so often an extra month would have to be added in order to preserve the festivals in their proper seasons. With no central authority to establish this every Jewish community around the world would make their own decisions and the result would have been that all of the separate communities would disappear into chaos as they would keep Pesach at different times, Rosh haShanna and Yom Kippur at different times and more. Despite having the same written Torah, in all other regards the communities would become so different they might as well have been keeping two different ones! Enter Hillel the Second/ Rav Yitzchak Nafcha (the blacksmith) / a vague generation during the later generations of the Babylonian Talmud/ times of the Geonim. Somewhere during the first couple hundred years of the last 2000 years the institution called the Jewish Calendar was created. I don’t mean to say “invented”. I mean to say, “was put into use”. From the sources it seems quite clear that there has always been a Jewish tradition concerning the mathematics involved in the balancing act that needs to be done to insure the security of the lunar-solar calendar. The Gemara in Tractate Rosh HaShanna clearly states (daf (page) 25a) “Thus I received from my father’s father’s house: the length of the (median) new moon can never be less than 29 (full) and one half (=12 hours) days (or 29.5 days), two-thirds of an hour (+ (2/3 x 1080 chalakim) in an hour) and 73 chalakim”. For a grand total of 793 chalakim in an hour, which translates into 793/1080= 0.73425 of an hour, or, when divided by 24 (hours in a day) =0.03059. For a grand total of 29.53059, which is precisely the amount arrived at by NASA after tracking the moon with lasers[3]. This clearly isn’t an arbitrary number, but part of a masorah from Moses at Sinai[4]. In addition, the Gemara describes all sort of criteria which was utilized to establish when to add an additional month of Adar, otherwise known as Ibbur haShanna. However, this, by itself, isn’t enough, as the Sanhedrin was capable of pushing off the month of Nissan, (the month following Adar, in which Pesach falls), for other reasons as well. In light of this, if they didn’t have a deeper mathematical knowledge of calculations of the solar and lunar years, unchecked this would lead to a great imbalance in the cycle of the lunar-solar year as Rosh Chodesh would start to fall out during the full moon. As long as the Sanhedrin was functioning all of the above information could be utilized successfully in order to establish a functioning Jewish society, as well as a unified one. But that eventually came to an end. So now what? Obviously, we were capable of utilizing the mathematical formulae in order to balance out the year. However, by itself this doesn’t help because, like all mathematical equations, many of the integers are elastic. We needed the single equation that would work for all Jews everywhere, thereby unifying the Jewish people in our observance of all time related Torah issues. As the time that we are discussing is the Talmudic Period, we therefore must realize that the center of the Jewish world at the time was in Babylonia, in Bavel. However, at the same time there still was a significant Jewish community living in the land of Israel. Please remember that for the first 200 or so years both the Babylonian and the Jerusalem Talmud’s were still being written. Even afterwards, during the Geonim period, there were Jewish communities and personalities who lived in Israel and it remained a source of Torah law and customs as well. It seems that historically there were many instances where these two major communities were at odds with each other. Not only did they do Simchas Torah (the celebration of finishing the public reading of the 5 Books of Moses) at separate times, with Bavel finishing the Torah on a yearly cycle, (which is the common practice among all Jews today), and Israel on a three-year cycle, (in Israel they celebrated Simchas Torah only once every three years), but in many regards, they had differing minhagim (customs) as well. Including the formulation of the yearly calendar. Now, we are not ones to care so much about local customs, nor do we mind differing opinions, but we can’t do different moadim. We cannot have the Jewish people celebrating the festivals at different times. That wouldn’t be a straw. That would be the PIANO that not only broke the camel’s back, but totally mushed the entire camel into something wholly unrecognizable. It is quite easy to figure out, based solely on the lunar calculations, by how much the year changes each year. After all, if every month there is an extra 2/3^rd’s of an hour and 73 chalakim[5], “extra”, meaning that it isn’t really “balanced” by the calendar, that means that over the course of one year there is an extra 793/1080 chalakim x 12 months = 9516/1080=8.81 hours added per year. This in addition to the 11 (on average) day difference between the lunar and solar calendars. This means that over the course of 3 years, on average, there is a 34 days difference between the lunar and solar calendars. This NEEDS to get balanced out. Even if we add one month of 30-days every 3 years, it still leaves a remainder of around 4-5 days that need to be dealt with. In addition: to which month will we add days to in order to balance out these extra days? How will this affect the lunar calculations in real-time with the actual lunar patterns? After all, we can’t let our calculations “get away” from the actual moon! So, over the course of many years the following 4 dechiot, (“pushes”, meaning times that we “push off” the day of Rosh Chodesh based on the calculations alone), were created: לא אד”ו ראש, meaning that Rosh haShanna cannot fall out on days 1,4 and 6 of the week, otherwise known as Sunday, Wednesday and Friday. מולד זקן, meaning that if the molad (calculation of the median time) for Rosh haShanna falls out after noon time – Rosh haShanna is pushed off to the next day (assuming it’s not אד”ו, as stated previously. Then it is pushed off even more). ג’ ט’ ר”ד בשנה פשוטה, meaning that during a peshuta year (meaning a year with no second month of Adar) if the molad of the month of Tishrei, (i.e. of Rosh haShanna) falls out on a Tuesday (the ג of גטר”ד) after the 9^th hour (the ט of גטר”ד, which is after 3 AM, as the Jewish day starts from nightfall) and 204 chalakim (the ר”ד of גטר”ד) then Rosh haShanna gets pushed off until Thursday (as it cannot fall on אד”ו, including Wednesday, as stated above). Lastly: ב’ ט”ו תקפ”ט, meaning if the molad of Tishrei falls out on a Monday (the ב of בטותקפ”ט) after 15 hours (the ט”ו of בטותקפ”ט, around 9 am) and another 589 chalakim (the תקפ”ט of בטותקפ”ט) Rosh haShanna gets pushed off until Tuesday. The purpose of all of these “pushes”, in addition to solving several halchick issues, such as certain festivals falling out on Shabbos or Sunday, for example, is also to create a balance in the calendar. Not only between the median calculations around the moon and the actual lunar cycle, but also for the sake of making a well-balanced calendar. One which “only” allows for a possible 3-day yearly imbalance fluctuation, instead of a much greater one. It is due to these dechiot that our calendar is comprised of anywhere between 353-355 days in a “regular” year or 383-385 days on a “leap” year, when we add an extra month to balance out the lunar-solar calendar. It was surrounding the formulations of these dechiot that many discrepancies and arguments “erupted” among the Jewish people over the centuries during the times of the Talmud and Geonim periods[6]. The most famous of which was the argument of Rav Sa’adia Gaon (of Bavel) and Ben Meir (of Israel). Their argument was about the last of the two dechiot and was a source of bitterness for the Jewish people. Due to Rav Sa’adia’s greatness the people all turned to Bavel’s guidelines, thereby insuring the unity of the Jewish calendar for all time since. The final formulation of the calendar is one that allows for an extra month to be added 7 times over the course of a 19-year cycle to balance out the base lunar-solar discrepancies. From this the acronym גו”ח אדז”ט was created, to let us know that the 7 “leap” years are years 3 (ג), 6 (ו), 8 (ח), 11 (א), 14 (ד), 17 (ז), and 19 (ט) are leap years. This unifies the “leap” years among all Jews everywhere. The fluctuation of the years by 3 days allows for all of the “little” discrepancies to be balanced out as well. This is done in a unified way by establishing that all of the months’ work on a cycle of first “missing” months (called chaser in Hebrew, i.e. a 29-day month) and a “full” (maleh month of 30-days) cycle with the exception of the months of Cheshvan and Kislev, (the second and third months of year, which are the eighth and the ninth months in the Torah), which are “swing” months. Meaning that they can either both be 29 (making a 2 days discrepancy, or a 353/383-day year) or 30 days (adding 2 days, for a 355/385-day year), or one 29 and the next 30 (giving the median year of 354/384 days). Obviously, there is a lot more to say on the topic, but as overviews go – this is as basic as it gets. It should be HaShem’s will that just as the Jewish people have become unified in our observance of the moadim in order to do His will – so, too, should He help us to become, once again, a unified people in our desire to live a life of meaning and purpose, full of His Torah and Mitzvos! Chag Sameach! [1] Which translates into another 44 minutes and 3 1/3 seconds. [2] The three times daily, and four times on Shabbos and Yom Tov prayers. Otherwise known as the “eighteen benedictions”. (This even though in the regular daily Shmoneh Esrei there are 19 Berachos. A topic for a different time). [3] http://eclipse.gsfc.nasa.gov/SEhelp/moonorbit.html [4] There are many sources that trace the “Sod ha’Ibbur”, (the Secret or Society of the “impregnation” of the months) all the way back to Adam. See, for example Pirkei d’Rabbi Eliezer chapter 8 and Megillat Evyatar. The book Pesikta d’Rav Kahane parsha 5 says that it was given to Moses at Sinai, and this is also the opinion of Rav Sa’adia Gaon, Rabbenu Chananel and others. All we know for sure is that the ability to balance out the moadim was available to the Jews throughout the generations. It seems clear from the sources that the actual formulation of the calendar was developed later, as we will see. [5] As the extra half a day is “easily” balanced out by having one 29-day month and one 30-day month. [6] In this matter see the portion of the letter of the Geonim to Ben Meir, brought in the book Sha’arim le Luach ha’Ivri on page 28 and also on page 29 the explanation behind the argument between Ben Meir and Bavel.