The Convergence of Judaism and Islam. Religious, Scientific, and Cultural Dimensions

Al-Khwarizmi’s Mathematical Doctrines in Ibn-Ezra’s Biblical Commentary r 187

It was found written in the book of deeds of the sage Rabbi Abraham

Ibn-Ezra that once he traveled by sea with fifteen of his students.

And there were also fifteen hollow men (Reikim) with him there.

Then one day God cast a storm into the sea and the boat was about

to break down and sink. The captain then ordered that half the men

on board be thrown into the sea to ease the load. The sage Ibn-

Ezra saw this and said to the captain: “What you tell us to do is

right because it is better that half of us die and not all of us. So let us

cast lots to decide who will be the ones to be thrown into the sea.

And this is what we shall do. All thirty men will stand in one row

and we shall start counting from the first one to the ninth and

this ninth one will be thrown overboard. This way we shall go on

until every man captured as number 9 is thrown away into the sea.”

And the men agreed to do so and they said to the sage Ibn-Ezra:

“Rise, for this is your duty. You will align us as you like.” And he got

up and aligned them in such a way that always in the ninth place

was caught one of the hollow men until they were all thrown from

the boat and the students came out clear. And this is how he aligned

them: First he stood four students, then five hollowed, and two stu-

dents, and one hollowed, and three students, and one hollowed, and

one student, and two hollowed, and two students, and three hol-

lowed, and one student, and two hollowed, and two students, and

one hollowed.

In this story the bad guys are called Reikim (hollow or empty), meaning
that they were void of good deeds and learning. This reminds us of the
empty Small Wheel denoting zero, and accordingly we shall now use 0 to
indicate an evil man. And to comply with binary language we shall use 1 to
indicate a righteous man (a student in this story). So this is how the above
lineup would look (and it is easy to check that every ninth symbol is 0).

1 1 1 1 0 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0

To celebrate the “victory” of Ibn-Ezra and the men of virtue in this
story, there is a short poem attributed to Ibn-Ezra in some editions of the
book mentioned above. I bring here the Hebrew original, followed by my
poor English translation.