Halakha of the Day

Rabbi Abraham Eben Ezra (1089-1164): Torah and Mathematics

HIS LIFE

Rabbi Abraham Eben Ezra was born in Tudela, in Navarre, in northern Spain, in 1089. He was very close to Rabbi Yehuda HaLevi, who was about 14 years older. His son Isaac married Yehuda HaLevi’s daughter (according to others, it was Rabbi Abraham himself who married her).

As a young man he moved to Cordoba. He was always poor, and he refused to take money from anyone. He tried his hand at business but never succeeded. I once heard (though I could not find the source) that he said of himself that his luck in business was so bad that if he started selling shrouds, people would stop dying.

Rabbi Eben Ezra traveled the world for more than three decades. First North Africa: Morocco, Algeria, and Tunisia. Then Europe: Italy, France, and England. Then the Middle East: Egypt, Persia, and Baghdad. Everywhere he went he stayed with the local Jewish community, and once they recognized his knowledge of Torah, they received him with great respect. He wrote mostly while traveling, and more than once he dedicated his works to the communities that hosted him or to his patrons. It is said that in France he met Rabbenu Tam (1100-1171), and in Egypt, Maimonides (1135-1204). He died in 1164, and according to Rabbi Abraham Zacuto in his Sefer HaYuchasin, he was buried in the Land of Israel.

COMMENTARY ON THE TORAH

Rabbi Eben Ezra wrote more than 60 books on a wide range of subjects. His best-known work is his commentary on the Torah (the Pentateuch). Its method was new: searching for the “peshat,” the literal meaning of the text, through rigorous linguistic analysis of every word.

Unlike Rashi, Eben Ezra avoided citing the Midrashim at every turn. He saw no need to repeat what the reader could already find in the Midrash. He also criticized certain allegorical commentaries that, in his words, “circle around the point instead of getting to the point.” For Eben Ezra, the point was the literal and grammatical meaning of each word. And that meaning had to be examined carefully: not only by the root of the word, but also by its context, its place in the verse, and every other place the same word appears in the Bible.

This literal reading was something new. But to leave no room for doubt, he made clear that his method did not apply to verses of the Torah dealing with precepts or commandments. There, the only valid interpretation is the one we received through the Oral Torah, as recorded in the Talmud.

ASTRONOMY

Less well known is that Rabbi Eben Ezra also wrote dozens of books on scientific subjects. One example is “The Book of the Foundations of the Astronomical Tables,” which he originally wrote in Latin. That tells us he had a deep command of the language in which science was transmitted at the time. Rabbi Eben Ezra was a rabbi who was also part of the scientific community of his day.

NAVIGATION

He also wrote a treatise on the astrolabe, an instrument for finding one’s way by the position of the stars and essential for navigation. The astrolabe was to the Middle Ages what GPS is today. The illustration accompanying this article shows Rabbi Eben Ezra (in the middle) holding an astrolabe. The book’s Hebrew title was Keli HaNechoshet, “the copper instrument,” after the metal astrolabes were made of.

MATHEMATICS

Rabbi Eben Ezra wrote several books on mathematics. The most important is Sefer HaMispar, “The Book of Number,” which he wrote in Italy around 1146. It is a manual of practical arithmetic in seven chapters: multiplication, division, addition, subtraction, fractions, proportions, and square roots.

The big novelty of the book was the positional decimal system, the same one we use today: nine digits and a zero, where the value of each digit depends on its position. In Christian Europe at the time, people still calculated with Roman numerals, which are clumsy for arithmetic. Eben Ezra explained the method using Hebrew letters: alef for 1, bet for 2, and so on up to tet for 9. For the empty place he drew a circle, which he called “galgal” (circle or wheel). He was one of the first in Europe to present and explain the number zero.

He did this more than fifty years before the famous Italian mathematician Fibonacci (1170-1240), whose Liber Abaci, from 1202, is considered the book that introduced the decimal system to Europe. Thanks to his many travels, Rabbi Eben Ezra was one of the main transmitters of this system to Jewish communities and to the Western world.

He also wrote Sefer HaEchad, “The Book of One,” on the properties of the numbers 1 through 9, and Sefer HaIbbur, on the calculations of the Jewish calendar. He also translated into Hebrew a commentary on the astronomical tables of al-Khwarizmi, the Persian mathematician whose name gave us the word “algorithm.”

A curious fact: in one of his books on the heavenly bodies, he calculated how many different ways the seven planets known in his time (which included the sun and the moon) could come together in the sky, two at a time, three at a time, and so on. He arrived at the correct answer: 120 combinations. It is one of the earliest known calculations in combinatorics, a branch of mathematics that would develop centuries later.

TORAH AND SCIENCE

For Eben Ezra, Torah and scientific knowledge do not contradict each other. On the contrary, they complement each other and need each other in order to observe and appreciate the wisdom of the Creator. The fact that the universe can be understood and explained through mathematical formulas and predictable, unchanging laws reveals the existence of an intelligent Creator. Maimonides developed this idea in depth in Hilkhot Yesode HaTorah, chapter 2. For anyone who wants to go deeper, I recommend “Just Six Numbers” by Martin Rees, one of the world’s most prominent astrophysicists.

POETRY

Finally, Rabbi Eben Ezra was also a great poet. Some of the poems he wrote more than 800 years ago are still sung today. For example: AGADELKHA ELOQE KOL NESHAMA, KI ESHMERA SHABBAT, and the deeply moving poem with which we open the Yom Kippur prayers: LEKHA ELI TESHUKATI.

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