Bavli Rosh HaShanah 20b

About 30 years ago I was the leader of a gemara sheur in Houston TX, going through masekhet Rosh Hashanah with Rashi. On daf 20b, as pointed out by Tosafot, Rashi's explanation is contrary to physical reality (I managed to explain Rashi by assuming a flat Earth, putting the Moon at an altitude of about 125 miles, and putting the Sun at an altitude of about 35,000 miles), so I devised my own explanation.

Here is the sugya:

אמר שמואל יכילנא לתקוני לכולה גולה אמר ליה אבא אבוה דרבי שמלאי לשמואל ידע מר האי מילתא דתניא בסוד העיבור נולד קודם חצות או נולד אחר חצות א"ל לא אמר ליה מדהא לא ידע מר איכא מילי אחרנייתא דלא ידע מר כי סליק רבי זירא שלח להו צריך שיהא לילה ויום מן החדש וזו שאמר אבא אבוה דר' שמלאי מחשבין את תולדתו נולד קודם חצות בידוע שנראה סמוך לשקיעת החמה לא נולד קודם חצות בידוע שלא נראה סמוך לשקיעת החמה למאי נפקא מינה אמר רב אשי לאכחושי סהדי אמר רבי זירא אמר רב נחמן כ"ד שעי מכסי סיהרא לדידן שית מעתיקא ותמני סרי מחדתא לדידהו שית מחדתא ותמני סרי מעתיקא למאי נפקא מינה אמר רב אשי לאכחושי סהדי

 Here is a translation to English, from Sefaria, except that:

1.  I changed "midday" to "hatzot", which is what it says in the original (חצות). "Hatzot" can mean either midday (noon) or midnight.
2.  I crossed out the parts of the interpolated explanation that assume that "hatzot" means "midday".

Shmuel said: I am able to fix the calendar for the entire Diaspora without witnesses. Shmuel was an expert on the movement of the celestial bodies and on the principles governing leap years and additional days added to months.

Abba, the father of Rabbi Simlai, said to Shmuel: Does the Master know the meaning of this statement, as it is taught in a baraita dealing with the secret of addition, which discusses calendric calculations: Differentiate between when the molad occurred before hatzot and when the molad occurred after hatzot? He said to him: No, I do not know what this means. He said to him: Since the Master does not know this, there are probably other matters that the Master does not know, and therefore you must not establish a calendar, relying upon calculations that were made based on faulty or insufficient knowledge.

As for the meaning of this obscure baraita, when Rabbi Zeira went up from Babylonia to Eretz Yisrael, he sent back a letter to his colleagues in Babylonia: In order for a day to be sanctified as the New Moon, it is necessary that both the night and the day be of the new month. That is to say, the molad must occur before the beginning of the night.

And this is what Abba, the father of Rabbi Simlai, said: The baraita means as follows: They calculate the molad; if the molad occurred before hatzot, so that there are at least six more hours left of the day, it is known that the moon will be visible close to sunset. If, however, the molad did not occur before hatzot, so that there are fewer than six hours left of the day, it is known that the moon will not be visible close to sunset.

The Gemara asks: What is the practical difference that this statement makes? In any case, the court is dependent upon the testimony of witnesses. Rav Ashi said: This information is used to refute the witnesses, as if the witnesses claim that they saw the new moon at a time when it was not visible according to the calculations, they are clearly false witnesses.

Rabbi Zeira said that Rav Naḥman said: For twenty-four hours the moon is covered, i.e., not visible. This occurs between the last sighting of the old moon and the first sighting of the new moon. For us, in Babylonia, it is not visible for six hours of the old moon and eighteen hours of the new; for them, in Eretz Yisrael, it is not visible for six hours of the new moon and eighteen hours of the old.

The Gemara asks: What is the practical difference that this statement makes? Rav Ashi said: It is used to refute the witnesses, as if they testify that they saw two moons, the old and the new, within a single twenty-four hour period, they are certainly false witnesses.

 I also crossed out "faulty or" because "faulty" is being mean to Shmuel. Abba's point was that the Sanhedrin has criteria in addition to astronomical criteria that might lead it to declare the first day of a new month one or two days different from what a purely astronomical calculation would indicate. As is stated in the mishnah at the top of 25a, a new month starts when the Sanhedrin says it starts, no matter what the Moon is doing.

The baraita is a rule of thumb that the Sanhedrin used to verify testimony about the sighting of the new crescent Moon.

According to Wikipedia the Moon is invisible, around the time of new Moon, for between 1.5 days (36 hours) and 3.5 days (84 hours). If the time from the last possible visibility of the old crescent Moon to the first possible visibility of the new crescent Moon is 36 hours then the time from the molad to the first possible visibility of the new crescent Moon is half of 36 hours, i.e., 18 hours. Then the hatzot in the baraita can't be noon on the day that the new crescent Moon will be visible at sunset, because the new crescent moon won't be visible until sunset of the following day. The next candidate for hatzot-hood is the preceding midnight. If the baraita is based on the assumption that the new Moon is invisible for 36 hours, then the rule of thumb makes sense. If the molad is before midnight then the time to the next sunset is more than 36/2=18 hours and the new crescent moon will be visible. If the molad is after midnight then the time to the next sunset is less than 18 hours and the new crescent moon won't be visible. "The night and the day being of the new month" means "most of the night, plus the following day, are after the molad.

That explains the baraita. We still need an explanation of Rav Nahman's statement. Rav Nahman can't really mean that the new Moon is invisible for 24 hours because that invalidates the baraita. If the new Moon is invisible for 24 hours then the time to which the molad should be compared is sunrise (24/2=12 hours before sunset), not noon or midnight.

The explanation I gave in Houston was that Rav Nahman's 24 hours is a possible discrepancy between observations of the first new crescent Moon (and also the last old crescent Moon) in Babylonia vs. Eretz Yisrael. Usually, observers in Babylonia and in Eretz Yisrael see the last old crescent Moon at sunrise on the same day, and see the first new crescent Moon at sunset on the same day. About 1/36th of the time, the last observation of the old crescent Moon is a day earlier in Eretz Yisrael than in Babylonia, and the first observation of the new crescent Moon is a day earlier in Eretz Yisrael than in Babylonia. Rav Nahman's point is that, in addition to knowing all the Sanhedrin's criteria for declaring the first day of a new month, someone who wants to predict the calendar needs to be aware of the possibility of observational discrepancies between Babylonia and Eretz Yisrael.
The longitude of Jerusalem is 35.2 degrees east. The longitude of Baghdad is 44.4 degrees east. So the difference in longitude between Babylonia and Eretz Yisrael is about 10 degrees, and the time in Eretz Yisrael is about 40 minutes behind the time in Babylonia.

For simplicity, suppose that the molad is at midnight halfway between Babylonia and Eretz Yisrael. Then the molad is at 00:20 in Babylonia and at 23:40 in Eretz Yisrael. Also for simplicity, suppose that sunrise in both places is at 06:00 and that sunset in both places is at 18:00. The sunrise immediately before the molad was 18 hours and 20 minutes before the molad in Babylonia and 17 hours and 40 minutes before the molad in Eretz Yisrael, so the old crescent Moon was still visible in Babylonia but no longer visible in Eretz Yisrael. The sunset immediately after the molad will be 17 hours and 40 minutes after the molad in Babylonia and 18 hours and 20 minutes after the molad in Eretz Yisrael, so the new crescent Moon will be visible in Eretz Yisrael but not yet in Babylonia.
Rav Nahman's description of the 24 hour delay before the new crescent Moon is visible in Babylonia is the 18 hours of the "new moon" from the molad until the next sunset, when the new crescent Moon is not yet visible, plus the 6 hours of the "old moon" back to the previous sunset. His description of the 24 hour pause in the visibility of the old crescent Moon in Eretz Yisrael is the 18 hours of the "old moon" from the last sunrise before the molad, when the old crescent moon was no longer visible, until the molad, plus the 6 hours of the "new" moon from the molad until the next sunrise.

30 years ago I had neither the time nor the ability to look for classical explanations of the sugya other than Rashi's, but I had heard that the sugya was somehow connected to the definition of the halakhic dateline. Now I am retired and there is Internet. At HebrewBooks.org I found the book ישועות כהן - קו התאריך. Chapters 3-6 of that book explain the ways that four Rishonim (the Kuzari, HaRav Zerahya Halevi (Ba'al HaMaor), Rabbi Shimon ben Tzemah Duran (the Tashbetz) and Ra'avad) get the dateline from our sugya. All four systems are problematic. All four Rishonim agree that the dateline is 90 degrees east of Jerusalem, but to do that they need to define "us" as observers at or near the dateline, not in Babylonia. In addition, their values for the time that the new Moon is invisible (48 hours for Kuzari, Ba'al HaMaor and two of Tashbetz' three explanations, 24 hours for Tashbetz' third explanation, and 12 hours for Ra'avad) are inconsistent with the baraita.

 While writing the above, another explanation of Rav Nahman occurred to me. Rav Nahman accepts at face value the reading of the baraita as saying that the new crescent Moon might be visible in Eretz Yisrael at sunset if the molad is before noon, but he knows from his own observations that the new crescent Moon isn't visible in Babylonia until 18 hours after the molad. His conclusion is that the new Moon is invisible for 24 hours, but for some reason those 24 hours are partitioned differently around the molad in Eretz Yisrael than in Babylonia.

Under either explanation of Rav Nahman, what his statement has to do with verifying testimony about sighting the new crescent Moon is: be careful about using astronomical data from Babylonia to invalidate testimony about sightings in Eretz Yisrael.

At Age 3 My Grandmother Was A Socialist Agitator In Czarist Russia

True story.
She saw people marching outside with red banners, so she pulled the red tablecloth off the kitchen table and ran out into the street with the tablecloth and joined them. Her parents had to pick her up from the police station.

Where Did Monotheism Come From?

Judaism introduced two revolutionary ideas to the ancient world. The first was monotheism: there is only one God, Who created the universe and Who expects some kind of level of moral behavior from the people He created. The second was abolition of human sacrifice. (I have read that the Hindus abolished human sacrifice about the same time as the Jews; but casual googling gives me the impression that human sacrifice has died out gradually among the Hindus, starting around 500 BCE, and has persisted sporadically into modern times.)

So where did monotheism come from?

The following sentence is phrased to try to convince even people who don't believe in an Abrahamic religion. The traditional narrative of the ancient Israelites, as recorded in Genesis, is that their ancestors came from Mesopotamia in the early second century BCE and that those ancestors worshiped a single God.

I also assume that David Ulansey is headed in the right direction about Mithraism. You can see his take on Mithraism here and here. Briefly, Mithraism was a (sort of) monotheistic mystery cult that was popular in the Roman Empire until it was suppressed by the Christians. The earliest date claimed for evidence of the existence of the cult is 67 BCE. The Mithraic god was Mithra, the god of heaven.

The central image of Mithraism was the "tauroctony", an image of a man killing a bull.

To understand Ulansey's take on Mithraism, you need to know what the precession of the equinoxes is. The first two Google hits on "precession of the equinoxes" are to the Brittanica.com article and the Wikipedia article. Start with the Brittanica.com article first because it is much more concise than the Wikipedia article. Then skim the Wikipedia article for whatever interests you there. If you are having trouble visualizing what is going on, try this video. (You can also try YouTube but beware of videos with agendas.)  Briefly, the Earth's axis wobbles, with a period of about 26,000 years. As a result, the zodiacal constellation in which the Sun rises on the first day of Spring keeps changing. For about the past 2000 years, the Sun has been rising in Pisces on the first day of Spring, and we have been in what the astrologers call the Age of Pisces. Between about 2200 BCE and the year zero, during the Age of Aries, the Sun rose in Aries on the first day of Spring. Between about 4400 BCE and 2200 BCE, during the Age of Taurus, the Sun rose in Taurus on the first day of Spring.

Ulansey's thesis is that the tauroctony shows Mithra the god of heaven killing Taurus to usher in the Age of Aries.

The precession of the equinoxes was discovered by the Greek astronomer Hipparchus in abut 125 BCE. Ulansey proposes that sometime in the following 50 years or so someone, presumably somewhere in the Mediterranean basin, invented a new mystery cult based on Hipparchus' discovery, with the name of the (only?) (main?) god of the cult being borrowed from the Zoroastrian pantheon to make the cult sound exotic.

My problem with that foundational hypothesis is: Why a bull? Why not a ram? In about 100 years the vernal equinox (the point in the zodiac where the sun is on the first day of Spring) is going to move from Aries to Pisces. Wouldn't it be more to the point to depict the Master of Heaven as ushering in the Age of Pisces?

I propose that what eventually became Mithraism started more than 2000 years before, in The Theological Crisis of the 24th Century BCE. I conjecture that during the Age of Taurus Mesopotamian priest-astronomers developed an elaborate (poly)theology, one of whose essential components was that the vernal equinox has to be in Taurus. In the 24th century BCE these priest-astronomers saw to their horror that the vernal equinox was continuing to move west through Taurus and in about 100 years or so would move into Aries. To some of the priest-astronomers, this could only mean that the gods they had been worshiping were mere servants of a Master God Who dwells outside the observable universe and Who directs the affairs of the universe through His servants. Of course, these heretics had to keep their heresy secret.

This conjecture also addresses some of the other weaknesses in Ulansey's theory that have been identified by his critics. For example, Shepherd Simpson wrote:

Prof Ulansey argues that the characters are constellations and that the constellations shown are those which lay on the Celestial Equatorduring the period between about 2000 BC and 4000 BC - his dates for the Age of Taurus. This, he argues, is how the tauroctony is able to depict a particular moment in time: owing to the Precession of the Equinoxes, the constellations which lie along the Celestial Equator change slowly with time, so a particular constellation list indicates a particular time period.

...

Finally, the other question which arises is - even for a skilled astrologer - would it have been possible at the time to calculate which constellations would have been on the Celestial Equator during the Age of Taurus? To say the least this would have been an impressive feat! We have no indication that this was possible, nor any indication that any astrologer of the time ever attempted or achieved such a task.

 The heretical priest-astronomers didn't need to calculate anything. They just had to look up at the sky to see which constellations were on the celestial equator.

Several centuries later, some of the heretics migrated (fled?) west to the shores of the Mediterranean. Some of the migrants were the ancestors of the Israelites. The other migrants kept their heresy entirely secret until the precession of the equinoxes was rediscovered and published by the unbelievers and it was no longer necessary to preserve total secrecy.