Happy Birthday Tomorrow, Galileo

Galileo Galilei in a 1636 portrait by Justus Sustermans.

Tomorrow, February 15th, is a special day. It is the birthday of Galileo Galilei, who was born in Pisa on that day in 1564. Among his many achievements were his careful observations of the Earth’s moon, the identification of four of Jupiter’s moons, and the discovery that Venus, when observed through a telescope, has phases, just like that of our own moon. The only reasonable explanation of this was that Venus orbited the Sun, and not the Earth. And just like that, the geocentric model of the universe in which everything revolved around the Earth, came to a grinding halt.

Galileo’s Jewish Connection

Galileo taught astronomy to anyone who would listen, including Jews, and his most important Jewish student was Joseph Solomon Delmedigo who was born in Candia on the Island of Crete in 1591. At the age of fifteen Delmedigo left for Italy, where he enrolled in the University of Padua. For seven years there he studied astronomy, mathematics, natural science and medicine, and was taught by none other than Galileo Galilei, who was soon to become famous for both his observations of the planets and his clash with the Church.

When Delmedigo graduated he traveled to Lublin, Vilna, and Livona, where he spent much of his time working as a physician. He ultimately settled in Amsterdam where he published his Sefer Elim, a long book (it runs over four hundred pages) that deals with philosophy, science, mathematics, and astronomy.

“Galileo my Teacher” from Delmedigo, Sefer Elim, Amsterdam 1629. 148.

In this book Delmedigo outlined the reasons he accepted the Copernican model of the universe. In addition to explaining all of the theoretical support for the heliocentric model, he cited experimental evidence. If the planets revolved about the Sun and were illuminated by it, the amount of light that they reflect would depend on their location and distance from the Earth. And this is precisely what Delmedigo and his famous teacher had observed through the telescope. 

My teacher Galileo observed Mars when it lay close to the Earth. At this time its light was much brighter than that of Jupiter, even though Mars is much smaller. Indeed it appeared too bright to view through the telescope. I requested to look through the telescope, and Mars appeared to me to be elongated rather than round. (This is a result of its clarity and the movement of its rays of light.) In contrast, I found Jupiter to be round and Saturn to be egg-shaped.

This glorious passage reminds us that religiously observant Jews were sometimes at the very cutting edge of the new astronomy. How many could claim to have been instructed by the great Galileo himself?

But don’t get carried away

The historian Andre Neher (d. 1988) viewed Joseph Delmedigo as a fearless trailblazer whose goal was not only to influence his own community, but also the Catholic Church itself. In a paper published in 1977 he wrote:

When Delmedigo published Elim in 1629, he used the term “Rabbi” in speaking of his teacher Galileo. Rabbi Galileo! Was this not something of a challenge directed to the inquisitors in Rome who were then preoccupied with Galileo and who were not to let him go until his death in 1642? Free Galileo, Delmedigo seems to be saying, or release him to us; in the midst of our Jewish community, he will not be subjected to any trial, we shall not require him to make any retraction, we shall welcome him and honor him like a Rabbi in Israel!

Well, not quite. As I have written elsewhere, this account is linguistically, historically, and conjecturally incorrect. In the first place, although the term used by Delmedigo to describe Galileo was indeed the word rebbi, in this context, it means “my teacher,” and not “my rabbi.” By translating it in this way Neher was able to support his claim that the Jews were open, receptive, and respectful to new ideas emerging in astronomy; but the linguistic reality (and much else besides) does not bear this out.

Secondly, in the years prior to the publication of Sefer Elim in 1629, Galileo had not become the “preoccupation” of the Inquisition. The work that led to the trial by the Inquisition, Dialogue Concerning the Two Chief Systems of the World, was not published until 1632. And so Neher’s claim that Delmedigo was writing a message to release Galileo is chronologically incorrect. Finally, the notion that the Jewish community would not punish one of their own for expressing antinomian views is inaccurate. It was, after all, in Amsterdam itself, the city in which Delmedigo’s books were published, that the Jewish community excommunicated Spinoza in 1656 on account of “the horrible heresies which he practiced and taught.” Although Neher’s assessment of Delmedigo as challenging the Inquisition on behalf of Galileo was not accurate, it he was certainly correct in noting the important role that Galileo must surely have played in the education of the young Jew Joseph Delmedigo from Crete, who grew up and became the first Jewish Copernican.

A selection from the Talmudology Library Galileo Collection

Want more Galileo-related Talmudology posts? Try Jews and their Telescopes, available here.

[A repost, obviously, because it was also his birthday last year.]

Chagigah 12b ~ Rabbinic Cosmology and Rabbinic Allegory

To the naked eye, the terrain of the Earth varies quite distinctly; in some places it is fairly flat, while in others it is mountainous and irregular. Standing and looking out over the sea, the water appears perfectly smooth and continues as far as the eye could see. What is beyond that was often unknown in the ancient world, and what supported the Earth itself could only be ascertained from reading the Bible. Of the few sages whose cosmology is known to us, one of the most important was Rabbi Yose ben Halafta. Born in Lower Galilee some time in the middle of the second century, Rabbi Yose was a student of the famous Rabbi Akiva, and he went on to establish a rabbinic court in his hometown of Zippori (Sepphoris). Although most of his teachings were legal in nature, he also addressed the geographic locations of both the Earth and God in the universe on today’s page of Talmud:

חגיגה יב, ב

תַּנְיָא, רַבִּי יוֹסֵי אוֹמֵר: אוֹי לָהֶם לַבְּרִיּוֹת, שֶׁרוֹאוֹת, וְאֵינָן יוֹדְעוֹת מָה רוֹאוֹת. עוֹמְדוֹת, וְאֵין יוֹדְעוֹת עַל מָה הֵן עוֹמְדוֹת. הָאָרֶץ עַל מָה עוֹמֶדֶת — עַל הָעַמּוּדִים, שֶׁנֶּאֱמַר: ״הַמַּרְגִּיז אֶרֶץ מִמְּקוֹמָהּ וְעַמּוּדֶיהָ יִתְפַלָּצוּן״. עַמּוּדִים, עַל הַמַּיִם — שֶׁנֶּאֱמַר: ״לְרוֹקַע הָאָרֶץ עַל הַמָּיִם״. מַיִם, עַל הֶהָרִים — שֶׁנֶּאֱמַר: ״עַל הָרִים יַעַמְדוּ מָיִם״. הָרִים, בְּרוּחַ — שֶׁנֶּאֱמַר: ״כִּי הִנֵּה יוֹצֵר הָרִים וּבוֹרֵא רוּחַ״. רוּחַ, בִּסְעָרָה — שֶׁנֶּאֱמַר: ״רוּחַ סְעָרָה עוֹשָׂה דְבָרוֹ״. סְעָרָה, תְּלוּיָה בִּזְרוֹעוֹ שֶׁל הַקָּדוֹשׁ בָּרוּךְ הוּא — שֶׁנֶּאֱמַר: ״וּמִתַּחַת זְרוֹעוֹת עוֹלָם״

It is taught in a baraita: Rabbi Yose says: Woe to them, the creations, who see and know not what they see; who stand and know not upon what they stand. He clarifies: Upon what does the earth stand? Upon pillars, as it is stated: “Who shakes the earth out of its place, and its pillars tremble” (Job 9:6). These pillars are positioned upon water, as it is stated: “To Him Who spread forth the earth over the waters” (Psalms 136:6). These waters stand upon mountains, as it is stated: “The waters stood above the mountains” (Psalms 104:6). The mountains are upon the wind, as it is stated: “For behold He forms the mountains and creates the wind” (Amos 4:13). The wind is upon a storm, as it is stated: “Stormy wind, fulfilling His word” (Psalms 148:8). The storm hangs upon the arm of the Holy One, Blessed be He, as it is stated: “And underneath are the everlasting arms”(Deuteronomy 33:27), which demonstrates that the entire world rests upon the arms of the Holy One, Blessed be He. 

It is of course entirely reasonable to suggest a metaphoric explanation for this cosmology and to suggest that this talmudic discussion not be taken literally. This approach would seem to be supported by an opposing cosmology suggested by those who take issue with Rabbi Yose’s picture:

וַחֲכָמִים אוֹמְרִים: עַל שְׁנֵים עָשָׂר עַמּוּדִים עוֹמֶדֶת, שֶׁנֶּאֱמַר: ״יַצֵּב גְּבוּלוֹת עַמִּים לְמִסְפַּר בְּנֵי יִשְׂרָאֵל״. וְיֵשׁ אוֹמְרִים: שִׁבְעָה עַמּוּדִים, שֶׁנֶּאֱמַר: ״חָצְבָה עַמּוּדֶיהָ שִׁבְעָה״. רַבִּי אֶלְעָזָר בֶּן שַׁמּוּעַ אוֹמֵר: עַל עַמּוּד אֶחָד, וְצַדִּיק שְׁמוֹ, שֶׁנֶּאֱמַר: ״וְצַדִּיק יְסוֹד עוֹלָם״ 

And the Rabbis say: The earth stands on twelve pillars, as it is stated: “He set the borders of the nations according to the number of the children of Israel” (Deuteronomy 32:8). Just as the children of Israel, i.e., the sons of Jacob, are twelve in number, so does the world rest on twelve pillars. And some say: There are seven pillars, as it is stated: “She has hewn out her seven pillars” (Proverbs 9:1). Rabbi Elazar ben Shammua says: The earth rests on one pillar and a righteous person is its name, as it is stated: “But a righteous person is the foundation of the world”(Proverbs 10:25). 

This single pillar suggested by Rabbi Eleazar certainly seems to be metaphoric rather than literal, given the context of the surrounding verses of the Book of Proverbs from which it is taken. A metaphorical understanding, however, does not fit in with the rest of the discussion. For, having established what lies beneath the Earth, the Talmud then addresses the nature of the skies above it and records the precise order and number of layers of the heavens. This technical discussion is generally not understood as being merely a metaphor. For example, it is this passage that is used by Maimonides to establish his own cosmology.  In light of this, it is reasonable to assume that Rabbi Yose’s claim that the Earth rests on pillars that are supported by God is his description of reality.

The Rabbinic Flat Earth

Whether it stood on seven pillars or only one, the Earth was considered by the sages of the Talmud to be flat. As recorded in the Jerusalem Talmud, people lived on this flat Earth completely surrounded by water:

ירושלמי עבודה זרה3:1

אָמַר רִבִּי יוֹנָה. אַלֶכְּסַנְדְּרוֹס מַקֶּדוֹן כַּד בְּעָא מֵיסַק לְעֵיל. וַהֲיָה סְלַק וּסְלַק סְלַק עַד שֶׁרָאָה אֶת הָעוֹלָם כַּכַּדּוּר וְאֶת הְיָּם כִּקְעָרָה. בְּגִין כֵּן צַּייְרִין לֵהּ בְּכַדּוּרָה בְיָדֵהּ. וִיצוּרֶינָּה קְעָרָה בְיָדֵהּ. אֵינוּ שַׁלִּיט בַּיָּם. אֲבָל הַקָּדוֹשׁ בָּרוּךְ הוּא שַׁלִּיט בַּיָּם וּבַיַּבָּשָׁה. מַצִּיל בַּיָּם וּמַצִּיל בַּיַבָּשָׁה

Rebbi Yonah said, when Alexander the Macedonian wanted to ascend he rose, and rose, and rose, until he saw the Earth as a ball and the ocean like a plate

“The opinion of our sages of blessed memory in these matters is well known: They believed that the Earth and the Great Ocean were flat.”

— Midrash Rabbah Perush Maharzu 6:8.

Another talmudic sage, Rabbi Natan, noted that the stars do not seem to change in their positions overhead when walking far distances. The assumption underlying his explanation for this observation was that the Earth is flat. Covering this flat Earth was an opaque cap referred to as the rakia, which is most commonly translated as the sky or firmament. Rava, a fourth-century Babylonian sage who lived on the banks of the river Tigris, determined this cap to be 1,000 parsa in width, while Rabbi Yehudah thought that he had over- estimated this thickness. There were others who added to the picture of the sky; on today’s page of Talmud Resh Lakish announced that it actually was made up of seven distinct layers.

חגיגה יב, ב

רֵישׁ לָקִישׁ אָמַר: שִׁבְעָה, וְאֵלּוּ הֵן: וִילוֹן, רָקִיעַ, שְׁחָקִים, זְבוּל, מָעוֹן, מָכוֹן, עֲרָבוֹת. וִילוֹן — אֵינוֹ מְשַׁמֵּשׁ כְּלוּם, אֶלָּא נִכְנָס שַׁחֲרִית וְיוֹצֵא עַרְבִית, וּמְחַדֵּשׁ בְּכׇל יוֹם מַעֲשֵׂה בְרֵאשִׁית, שֶׁנֶּאֱמַר: ״הַנּוֹטֶה כַדּוֹק שָׁמַיִם וַיִּמְתָּחֵם כָּאֹהֶל לָשָׁבֶת״. רָקִיעַ — שֶׁבּוֹ חַמָּה וּלְבָנָה כּוֹכָבִים וּמַזָּלוֹת קְבוּעִין, שֶׁנֶּאֱמַר: ״וַיִּתֵּן אוֹתָם אֱלֹהִים בִּרְקִיעַ הַשָּׁמָיִם״. שְׁחָקִים — שֶׁבּוֹ רֵחַיִים עוֹמְדוֹת וְטוֹחֲנוֹת מָן לַצַּדִּיקִים, שֶׁנֶּאֱמַר: ״וַיְצַו שְׁחָקִים מִמָּעַל וְדַלְתֵי שָׁמַיִם פָּתָח. וַיַּמְטֵר עֲלֵיהֶם מָן לֶאֱכוֹל וְגוֹ׳״

Reish Lakish said:There are seven firmaments, and they are as follows: Vilon, Rakia, Shechakim, Zevul, Ma’on, Makhon, and Aravot.The Gemara proceeds to explain the role of each firmament: Vilon, curtain, is the firmament that does not contain anything, but enters at morning and departs in the evening, and renews the act of Creation daily, as it is stated: “Who stretches out the heavens as a curtain [Vilon], and spreads them out as a tent to dwell in” (Isaiah 40:22). Rakia, firmament, is the one in which the sun, moon, stars, and zodiac signs are fixed, as it is stated: “And God set them in the firmament [Rakia] of the heaven” (Genesis 1:17). Shechakim, heights, is the one in which mills stand and grind manna for the righteous, as it is stated: “And He commanded the heights [Shehakim] above, and opened the doors of heaven; and He caused manna to rain upon them for food, and gave them of the corn of heaven” (Psalms 78:23–24). 

Given this model, there would have to be a place where the opaque cap touched the Earth, and Rabba bar Bar Hanah in fact claimed to have touched this Earth-sky interface:

בבא בתרא עד, א

אָמַר לִי תָּא אַחְוֵי לָךְ הֵיכָא דְּנָשְׁקִי אַרְעָא וּרְקִיעָא אַהֲדָדֵי שְׁקַלְתָּא לְסִילְתַּאי אַתְנַחְתָּא בְּכַוְּותָא דִרְקִיעָא אַדִּמְצַלֵּינָא בְּעֵיתֵיהּ וְלָא אַשְׁכַּחְתֵּהּ אָמֵינָא לֵיהּ אִיכָּא גַּנָּבֵי הָכָא אֲמַר לִי הַאי גִּלְגְּלָא דִרְקִיעָא הֲוָה דְּהָדַר נְטַר עַד לִמְחַר הָכָא וּמַשְׁכַּחַתְּ לַהּ

A certain Arab also said to me: Come, I will show you the place where the earth and the heavens touch each other. I took my basket and placed it in a window of the heavens. After I finished praying, I searched for it but did not find it. I said to him: Are there thieves here? He said to me: This is the heavenly sphere that is turning around; wait here until tomorrow and you will find it.

The Flammarion Engraving, from here.

Turtles all the way down

In classic Jewish teaching, the Earth rests on twelve pillars. Or seven. Or just one. Other cultures have their own cosmology myths, of which perhaps the most well-known is a story in which the world is carried on the back of a turtle. Here is a version told by the Delaware “Indians” (or native Americans, as we would call them today):

First there was only water, then the Great Turtle gradually rose above water level, and the Creator placed mud on his shell. The mud dried and the Great Tree grew in the middle of the earth. As the Tree grew towards the sky a sprout became a man, then the great Tree bent down and in touching the earth caused a sprout to become a woman. From this man and woman all of humanity descended.

Susan Culver. Turtles All The Way Down, from here.

The belief that the Earth rests on the back of a Turtle is apparently also shared by the Iroquois, and when the turtle moves, there are earthquakes. In Hindu belief, Kurma is a turtle incarnation of the God Vishnu. This incarnation is also known as Akupara (Sanskrit: अकूपार), and it supports the world on its back. The earliest reference to the myth in Western literature is from the Jesuit Emanuel da Veiga (1549–1605), who described it in a letter written in 1599:

Others hold that the earth has nine corners by which the heavens are supported. Another disagreeing from these would have the earth supported by seven elephants, and the elephants do not sink down because their feet are fixed on a tortoise. When asked who would fix the body of the tortoise, so that it would not collapse, he said that he did not know.

In Chinese mythology, Ao is a turtle whose legs were chopped off by the goddess Nuwa and used them to support the sky. “It’s not quite carrying the world on its back,” wrote Eric Grundhauser on the site Atlas Obscura, “but it still puts a terrapin at the center of the universe, making sure that the very sky doesn’t fall down.”

The obvious question is, on what does the turtle that is supporting the world stand? And the answer is: another turtle, of course. It is “turtles, all the way down,” a phrase that has come to mean infinite regress. Here is how the late great physicist Steven Hawking told the story in his bestselling book A Brief History of Time:

A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the centre of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise." The scientist gave a superior smile before replying, "What is the tortoise standing on?" "You're very clever, young man, very clever," said the old lady. "But it's turtles all the way down!"

To avoid its own infinite regress, Rabbi Yose imagined that world rested on pillars, which rested on water, which rested on mountains, which rested on the wind, which rested on a storm, which rested on the arms of God. It wasn’t turtles all the way down, as it was for some other cultures. It had an end, and the end was God.

---

Want more on rabbinic cosmology? Try these posts:

• Where Heaven and Earth Touch

• The Sun's Orbit Around the Earth

• How High is the Sky? (And How to Measure It)

Happy Birthday Galileo

Galileo Galilei in a 1636 portrait by Justus Sustermans.

Today, February 15th, is a special day. It is the birthday of Galileo Galilei, who was born in Pisa on that day in 1564. Among his many achievements were his careful observations of the Earth’s moon, the identification of four of Jupiter’s moons, and the discovery that Venus, when observed through a telescope, has phases, just like that of our own moon. The only reasonable explanation of this was that Venus orbited the Sun, and not the Earth. And just like that, the geocentric model of the universe in which everything revolved around the Earth, came to a grinding halt.

Galileo’s Jewish Connection

Galileo taught astronomy to anyone who would listen, including Jews, and his most important Jewish student was Joseph Solomon Delmedigo who was born in Candia on the Island of Crete in 1591. At the age of fifteen Delmedigo left for Italy, where he enrolled in the University of Padua. For seven years there he studied astronomy, mathematics, natural science and medicine, and was taught by none other than Galileo Galilei, who was soon to become famous for both his observations of the planets and his clash with the Church.

When Delmedigo graduated he traveled to Lublin, Vilna, and Livona, where he spent much of his time working as a physician. He ultimately settled in Amsterdam where he published his Sefer Elim, a long book (it runs over four hundred pages) that deals with philosophy, science, mathematics, and astronomy.

“Galileo my Teacher” from Delmedigo, Sefer Elim, Amsterdam 1629. 148.

In this book Delmedigo outlined the reasons he accepted the Copernican model of the universe. In addition to explaining all of the theoretical support for the heliocentric model, he cited experimental evidence. If the planets revolved about the Sun and were illuminated by it, the amount of light that they reflect would depend on their location and distance from the Earth. And this is precisely what Delmedigo and his famous teacher had observed through the telescope. 

My teacher Galileo observed Mars when it lay close to the Earth. At this time its light was much brighter than that of Jupiter, even though Mars is much smaller. Indeed it appeared too bright to view through the telescope. I requested to look through the telescope, and Mars appeared to me to be elongated rather than round. (This is a result of its clarity and the movement of its rays of light.) In contrast, I found Jupiter to be round and Saturn to be egg-shaped.

This glorious passage reminds us that religiously observant Jews were sometimes at the very cutting edge of the new astronomy. How many could claim to have been instructed by the great Galileo himself?

But don’t get carried away

The historian Andre Neher (d. 1988) viewed Joseph Delmedigo as a fearless trailblazer whose goal was not only to influence his own community, but also the Catholic Church itself. In a paper published in 1977 he wrote:

When Delmedigo published Elim in 1629, he used the term “Rabbi” in speaking of his teacher Galileo. Rabbi Galileo! Was this not something of a challenge directed to the inquisitors in Rome who were then preoccupied with Galileo and who were not to let him go until his death in 1642? Free Galileo, Delmedigo seems to be saying, or release him to us; in the midst of our Jewish community, he will not be subjected to any trial, we shall not require him to make any retraction, we shall welcome him and honor him like a Rabbi in Israel!

Well, not quite. As I have written elsewhere, this account is linguistically, historically, and conjecturally incorrect. In the first place, although the term used by Delmedigo to describe Galileo was indeed the word rebbi, in this context, it means “my teacher,” and not “my rabbi.” By translating it in this way Neher was able to support his claim that the Jews were open, receptive, and respectful to new ideas emerging in astronomy; but the linguistic reality (and much else besides) does not bear this out.

Secondly, in the years prior to the publication of Sefer Elim in 1629, Galileo had not become the “preoccupation” of the Inquisition. The work that led to the trial by the Inquisition, Dialogue Concerning the Two Chief Systems of the World, was not published until 1632. And so Neher’s claim that Delmedigo was writing a message to release Galileo is chronologically incorrect. Finally, the notion that the Jewish community would not punish one of their own for expressing antinomian views is inaccurate. It was, after all, in Amsterdam itself, the city in which Delmedigo’s books were published, that the Jewish community excommunicated Spinoza in 1656 on account of “the horrible heresies which he practiced and taught.” Although Neher’s assessment of Delmedigo as challenging the Inquisition on behalf of Galileo was not accurate, it he was certainly correct in noting the important role that Galileo must surely have played in the education of the young Jew Joseph Delmedigo from Crete, who grew up and became the first Jewish Copernican.

A selection from the Talmudology Library Galileo Collection

Want more Galileo-related Talmudology posts? Try Jews and their Telescopes, available here.

[A repost, obviously, because it was also his birthday last year.]

Rosh Hashanah 25 ~ The Length of the Lunar Month

ראש השנה כה, א

תָּנוּ רַבָּנַן: פַּעַם אַחַת נִתְקַשְּׁרוּ שָׁמַיִם בְּעָבִים, וְנִרְאֵית דְּמוּת לְבָנָה בְּעֶשְׂרִים וְתִשְׁעָה לַחֹדֶשׁ. כִּסְבוּרִים הָעָם לוֹמַר רֹאשׁ חֹדֶשׁ, וּבִקְּשׁוּ בֵּית דִּין לְקַדְּשׁוֹ. אָמַר לָהֶם רַבָּן גַּמְלִיאֵל: כָּךְ מְקוּבְּלַנִי מִבֵּית אֲבִי אַבָּא — אֵין חִדּוּשָׁהּ שֶׁל לְבָנָה פְּחוּתָה מֵעֶשְׂרִים וְתִשְׁעָה יוֹם וּמֶחֱצָה וּשְׁנֵי שְׁלִישֵׁי שָׁעָה וְשִׁבְעִים וּשְׁלֹשָׁה חֲלָקִים

The Sages taught in a baraita: Once the sky was covered with clouds, and the form of the moon was visible on the twenty-ninth of the month. The people thought to say that the day was the New Moon, and the court sought to sanctify it. However, Rabban Gamliel said to them: This is the tradition that I received from the house of my father’s father: The monthly cycle of the renewal of the moon takes no less than twenty-nine and a half days, plus two-thirds of an hour, plus seventy-three of the 1,080 subsections of an hour.

According to Rabban Gamliel, a lunar month cannot be shorter than 29 days, 12 hours and 792 chalakim (where one chelek is 1/1080 parts of an hour). If witnesses claim to have seen a new moon before this time has elapsed after the previous new moon, they must be mistaken. According to the medieval commentator Menachem ben Solomon (1249–1315)known as the Meiri, this period is also the longest period for a lunar month.

How the Lunar Month varies

The average length of a lunar month, that is, the period between two new moons, is 29.53059 days, which is 29 days 12 hours and 44 minutes. But this is an average, and the actual length of the month varies. This is because the moon’s rotation around the earth is not uniform. When the moon is closest to the earth (called the lunar perigee) it speeds up, and when it is furthest from the earth (at the lunar apogee) it slows down, though only by a little in each case.

From here.

Here are the lengths of the lunar months for this calendar year. Note the longest month marked in red, and the shortest month, shown in green. They differ by six hours and twenty minutes!

Lengths of the lunar months in 2021
Successive new moons	Length of lunar month
Dec 14, 2020, to Jan 13, 2021	29 days 12 hours 44 min
Jan 13 to Feb 11	29 days 14 hours 06 min
Feb 11 to Mar 13	29 days 15 hours 15 min
Mar 13 to Apr 12	29 days 16 hours 10 min
Apr 12 to May 11	29 days 16 hours 29 min
May 11 to Jun 10	29 days 15 hours 53 min
Jun 10 to Jul 9	29 days 14 hours 24 min
Jul 9 to Aug 8	29 days 12 hours 34 min
Aug 8 to Sep 6	29 days 11 hours 02 min
Sep 6 to Oct 6	29 days 10 hours 14 min
Oct 6 to Nov 4	29 days 10 hours 09 min
Nov 4 to Dec 4	29 days 10 hours 28 min
Dec 4, 2021, to Jan 2, 2022	29 days 10 hours 50 min

The corrupted text in today’s Page of Talmud

In bis book Calendar and Community, the British scholar Sacha Stern pointed out that the period of the lunar moth, called a lunation, is exactly the same as in the present day rabbinic calendar. “However, the phrase אֵין חִדּוּשָׁהּ שֶׁל לְבָנָה פְּחוּתָה (‘not …less than’) which implies a minimal value, is inappropriate for what should represent a fixed value.” He continues:

Moreover, the mean lunation is totally out of context in this passage. The context of this passage is the Mishnaic, empirical calendar, which is based on the appearance of the new moon; calculation of the molad is therefore irrelevant. R. Gamliel was only establishing that the moon could not have been sighted before the 29th day of the previous month. All he could have stated, therefore, was the minimal number of days in an empirical lunar month.

Other scholars like David Gans (1743), Hayyim Slonimsky (1852) and Hayyim Yehiel Bornstein (1904) also recognized this problem. Stern therefore suggests that the text we have in our Talmud is a later addition.

Originally the text would have read: אֵין חִדּוּשָׁהּ שֶׁל לְבָנָה פְּחוּתָה מֵעֶשְׂרִים וְתִשְׁעָה יוֹם (‘not after less than 29 days’) - and no more. The interpolation שְׁנֵי שְׁלִישֵׁי שָׁעָה וְשִׁבְעִים וּשְׁלֹשָׁה חֲלָקִים (‘and a half, two-thirds of an hour and 73 parts’) would have been made by an editor who thought that the mean lunation - not the minimal number of days in the month - was meant in this passage. The absence of manuscript evidence does not undermine this argument; it only suggests that the interpolation must have been made relatively early, perhaps in the late Geonic period.

The origin of 29-12-793

If Professor Stern and his intellectual predecessors are correct, the origin of the 29-12-793 period for a lunation is not in fact in the Talmud. So where does it come from? In the twelfth century Rabbi Avraham bar Hiyya acknowledged that the calculation is identical to that found in the Almagest, a Greek language compendium on mathematics and astronomy which was composed by Ptolemy in the second century. In that book Ptolemy gives the lunation in the standard Babylonian sexagesimal system as 29d, 31i, 50ii and 20iv, (where one i=1/60 of the day, one ii is a sixtieth part of that and so on). It is exactly the same length as the rabbinic lunation. Rabbbi Avraham bar Hiyya claimed that Hipparchus (the second century B.C.E scholar who Ptolemy used has his source) had taken this value from the Jewish sages - the ancestors of Rabban Gamliel referred to on today’s page of Talmud. But, as Sacha Stern noted, “it seems far more plausible to assume on the contrary, that it was the rabbis who borrowed their lunation from Ptolemy.” This assumption led a number of Jewish scholars to conclude that the molad calculation of 29- 12-793 could not have been instituted before the ninth century.

This is because Ptolemy’s Almagest was not known to astronomers in the Near East before its translation into Arabic in the early ninth century…It is likely that Ptolemy’s calculation of the conjunction was only then transmitted to the Jews, who soon incorporated it into the fixed rabbinic calendar. Although somewhat conjectural, this theory remains completely plausible, particularly as evidence of the present day molad calculation only begins to emerge in the ninth century.

Stern also admits that it is also possible that rabbinic calendar makers took their lunation period of 29-12-793 directly from the Babylonians, without resorting to Ptolemy’s Almagest. If that happened, “the rabbinic lunation could have been adopted long before the ninth century.” Either way, we got it from the Babylonians.

“Whether the molad calculation was borrowed from Babylonian astronomers, or from an Arabic translation of Ptolemy’s Almagest that would have been made at the ninth century Abbasid capital of Baghdad, in the heartland of Babylonia, the geographical origins of this molad would have been the same. It was in Babylonia, indeed, that this molad would have become known to the Jews and incorporated into the present-day rabbinic calendar. ”

— Sacha Stern Calendar and Community. Oxford University Press 2001; 209-210.

Where does that 1/1080 measure come from?

In 1989, shortly before his death, Otto Neugebauer (d. 1990), who was described as “the most original and productive scholar of the history of the exact sciences, perhaps of the history of science, of our age” published a paper that reviewed the transmission of the standard Babylonian value for the lunation. In it, he noted that in the third century B.C.E (!) in Mesopotamia, there existed a small unit of measure called “barleycorn” which represented a fraction of 1/6 of a finger breadth. The finger breadth is in turn a faction of a palm, and the palm of the cubit, so that 1 cubit = 180 barleycorns. But, noted Neugebauer, “measures can lose their specific meaning and become terms for fractional parts in general….Similarly, the barleycorn, embedded in a sequence of sexagesimally arranged units, retains only its fractional significance as 18 units of 60ths, ie 1/1080.” And so the Babylonians used this measure, which we inherited as halakim (parts). representing 1/1080 of an hour.

The Babylonians also discovered the nineteen year cycle around 600 B.C.E. which today is known as the Metonic cycle. It is is the period after which the phases of the moon recur at the same time of the year. They kept careful records of the time for a number of lunar cycles, and used these to calculate the average lunation. These were later adopted by the Romans. And by us.

No, It’s not a miracle

Some organizations, keen to spread the word about Judaism, have looked to today’s page of Talmud as proof of the divine origins of the oral law. Here is an excerpt from the Aish Hatorah Discovery Book:

So just how long is a lunar month, according to the reckoning of the Talmudic sages? The Talmud in Rosh Hashanah 25a tells us: Rabban Gamliel said...I have it on the authority of my father’s father that the renewal of the moon takes place after not less than twenty-nine and a half days, two-thirds of an hour and seventy-three parts of an hour.

Okay, class, you do the math. Two-thirds of an hour remembering that an hour is divided into 1,080 parts equals 720 parts. Add to that another 73 parts and you have 793 parts. So that according to the ancient calculation of the Sages of the Talmud, a lunar month is 29 and days plus 793 out of 1,080 parts of an hour. 793 out of 1,080 equals 0.734259 hours, which equals 0,03059 days. Add to that 29.5 days, and the average length of the lunar month according to the Rabbis is 29.53059 days.

What is so incredibly amazing about all this is the fact that, in our own times, the scientists and researchers at NASA have spent years of research using satellites, hairline telescopes, laser beams and supercomputers and all this in order to determine the exact length of the synodic (lunar) month. And the calculation they came up is that the length of the lunar month is 29.530588 days. The difference between this figure and that used by the Sages is .0000006, or one sixth millionth of a day!!!

Incredible! How could the Sages of millennia ago have been able to calculate the exact length of the lunar month with such incredible precision, enabling them to accurately and successfully balance the solar and lunar cycles for so many thousands of years?! With absolutely no modern technological tools and equipment, how could the Rabbis of old have had access to such accurate information way ahead of their time?! [Can you say G-d?]

We actually have a tradition, based on an ancient Midrash, that when G-d commanded Moses regarding the establishment of the calendar and the Jewish holidays based on the sanctification of the New Moon, He also gave to Moses all the secrets and vital information necessary to accurately calculate and balance the solar and lunar cycles.

Maybe accepting the Torah as G-d’s truth doesn’t require such a leap of faith after all?

There may be lots of good reasons to follow traditional Jewish practice, but, contra Aish Hatorah, the knowledge of the length of the lunar month is not one of them. It was an inheritance we took from the Babylonians, and unless Aish is suggesting that God revealed the average length of the lunar month to them, knowing the history of the Jewish lunation reveals something else and just as impressive. It is the ingenuity of the human mind.