186 r Michael Katz
- Ibn-Ezra’s manipulations concerning specific numbers may look like
nothing much more than games. They may be amusing, but at least some
of them are also trivial. - With enough patience and imagination, any number can be shown
to have quite a few unique mathematical properties. As an example, we
note that more than a millennium before Ibn-Ezra, Philo of Alexandria,
in his book Al Beriat ha-Olam (On the Creation of the World), provided
lists of properties of the numbers 4 and 7. - The specific properties Ibn-Ezra lists stem from the fact that we work
within the decimal system. In his eloquent treatment of the decimal sys-
tem, Ibn-Ezra seems to ignore the fact that this system is not God-given
(even though He gave us ten fingers). Ibn-Ezra can hardly be blamed for
this, since throughout history the decimal system (perhaps because of
the ten fingers) was universally the most popular one. However, as is well
known, there were always other systems, like the duodecimal system and
most notably nowadays the binary system. And needless to say, in any
nondecimal system, the properties Ibn-Ezra singles out with regard to,
say, the number 9, as exhibited in the “clock” above, would relate to an-
other number. Ibn-Ezra himself noted this in his mathematics books.
It is easy to agree with these arguments. Still, no one can deny the ele-
gance with which Ibn-Ezra integrates mathematics into his biblical exege-
sis. And no one can take away from him his account of the basic tenets of
arithmetic in the paragraph we are studying here. I would also venture to
say that in the dichotomous division mentioned above (five against five),
together with the continued reliance on the number 1 (and the awareness
of the notion of zero), we may perhaps see hints of the binary system
(alongside the decimal system, epitomized by the number 9).
It is on this combination (Ibn-Ezra’s liking of dichotomies on the one
hand, and of the number 9, on the other) that the following story rests. It
is borrowed from a small book entitled Mahalach Shevilei ha-Daath (The
Course of Wisdom’s Paths), where it is called Tahbulla (stratagem). The
book was written by Rabbi Moshe Kimhi in the twelfth century and has
since been published with commentaries in several editions. The story
appeared as an appendix in some of these editions, making its way to the
entry “Ibn-Ezra” in the Hebrew Encyclopedia. It shows the respect, mixed
with humor, with which Ibn-Ezra was held in spite of the criticism leveled
against him. So here it is, translated from Hebrew almost word by word: