182 r Michael Katz
commonplace nowadays, seemingly obvious and natural. We take it for
granted, hardly ever noticing the ingenuity behind it, assuming perhaps
that it was like this always and everywhere. But it wasn’t. For instance,
roman numerals, based on the decimal system without the position prin-
ciple, require different symbols in different positions, and so the number
above would be:
MMMCCCXXXIIIWithout the compactness enabled by the position principle, arithme-
tic would not have reached the advanced stage where it is today. It was
from Hindu mathematicians that this principle was borrowed and im-
planted into medieval Arab mathematics. And it was from the writings of
al-Khwarizmi, translated into Latin, among others, that the principle was
imported to Europe and incorporated into western mathematics.
And this is also where the notion of zero, as a number or an empty
place, comes into the picture. It is instrumental in discerning, for exam-
ple, the number three thousand and thirty-three from the number three
hundred and thirty-three. In our present-day writing, the first of these
two numbers is:
3033In Ibn-Ezra’s writing, in line with his work discussed here, it would be:
גג ג
And with the Small Wheel, it would become:
גג0ג
Note that even though Ibn-Ezra used Hebrew letters, for example, the
third letter Gimmel -whose gematric value is 3, and hence he wrote from
right to left as is common in Hebrew, the number as a whole would be
ordered just as we always see it ordered. For counting in Hebrew used to
start from units (3 and 30 rather than 33).
The Number 9
From the discussion above, another number, 9, emerges as deserving our
respect. It doesn’t designate a specific letter of the Holy Name, but it is,