Cardinal numbers are quintessential numbers. Bertrand Russell would say, in defining “number”, that number is the class of all classes which have the same number of members. That is, the number 5 is that which is characteristic of all 5-member sets. A number, a cardinal number, then describes the size of a collection, an unordered collection. If talking about time, we might say One Day, Two Days, Three Days.

* * * * * * ...

Ordinal numbers, on the other hand, are points on a line. They are imbued with order: the second number follows the first, the third number follows the second, and so on. The successor of a number is always a larger number, never a smaller number. Thus we might say First Day, Second Day, Third Day.

---+---+---+---+---+-->

Does this sound familiar, at this time of year? It should – it’s the big counting that every Jew does, the Omer. And the counting is indisputably cardinal, we say “Today is, e.g., eleven days, which are one week and four days [in/to] the Omer.” Why do we count cardinal days rather than ordinal days? I would think ordinal would be more intuitive, as we’re counting days and weeks towards a goal of the Feast of Weeks. Other periods of time are counted ordinally, e.g. the days of the week and the Biblical month numbers (the modern names were adopted from the Babylonians). But days of the month tend to be cardinal: chaf-vav Nisan, etc., unlike our English usage where we talk about the twenty-sixth of the month.

Some (e.g. R’ Soloveitchik) seem to think that the preposition we choose, in or to, suffices to distinguish between counting as cardinal or ordinal numbers. Not so. The count itself is cardinal or ordinal, and we use a cardinal count: one day, two days, etc. Russell Hendel notes in Rashi Yomi that the prepositions (in or to) often switch meaning dependent on context, so the choice of preposition is not dispositive.

Meanwhile, the Lubavitcher Rebbe recognizes the same problem I do, but leaves the reasoning implicit and unexplained: “the lessons should be obvious.” No, they’re not.

Shemaryahu Talmon, in an article on a calendar from the Qumran 4 cave, (4Q325) notes that days of the week for ritual purposes, such as the period of a family’s priestly service, are cardinal. (*Solving riddles and untying knots*, Jonas C. Greenfield et al)

Perhaps there’s a secular/religious division there? Ritual numbers are cardinal, calendrical numbers are ordinal?

R’ Benzion Milecki, citing the Zohar on human achievement, suggests that each day’s work is cumulative, so that what one achieves on day two depends on what he did on day one, etc. That seems a bit far-fetched, inasmuch as the “work” one does during the Omer, self-work on the kabbalistic “lower seven attributes”, was invented by the siddur printers after it became known that the Ari meditated on the seven attributes during the Omer (see *U’Sfartem Lachem haShalem*, by R’ Daniel Frisch, the Matok Mid’vash). The style of counting long predates the Ari.

R’ Micha Berger, building on R’ Elozor Reich, suggests that since the Torah asks us to count *complete* days, perfect days, we count them as wholes, as integers. Thus we can count them at the beginning of the day, as Tosfos requires – once a moment of the new day has passed, we are into the wholeness of the day, and can count the whole day. Otherwise, we would have to wait for the whole day to pass before counting it, recognizing that another whole day has passed. That sounds vaguely plausible.

But I tend to think of these kinds of subtleties as arising from some kind of halachic or conceptual requirement, and only later, acquiring homiletic or mystical meanings, much as the covering of the Challah arises out of “poreis mappah umekadeish”, spreading the tablecloth and making Kiddush; only later did we get the homiletic reason of “the bread is embarrassed to be blessed after the wine” or “the dew covered the manna above and below on the Shabbat”).

Russell Hendel has another thought attributed to R’ Soloveitchik that intrigues, which leads me to speculate: perhaps it’s a consequence of being cardinal numbers that if one forgets to count for a whole day, he loses the ability to say the bracha. Why? Because if one forgot to count the day, the day is gone, and can’t be retrieved. So from then on, the count is qualitatively different, as it is missing something, and is thus not a perfect count. If we counted ordinally, and lost a day, well, the number line continues, and even if we missed day 14, by the next day the number line is still 15 days long. That gives me an idea – perhaps it is because of the requirement of *temimus*, perfection, in the count, that we count cardinally. Only then can the count be qualitatively perfect or not perfect, while with an ordinal count, the count goes on whether or not one missed a day.

Does anyone have any better ideas, arising out of older considerations, as to why cardinal rather than ordinal?

## 5 comments:

Beris is on Yom haShemini, an ordinal 8th day. In contradiction to your suggestion that "Ritual numbers are cardinal".

Another difference between cardinals and ordinals is the fencepost problem. The 8th day is after 7 days. (The first day is when the baby is zero days old. The second day is when he's 1 day old. Etc...)

I don't know what to make of that, but it seems to be fertile ground for finding the difference in usage in ritual. In this case, a possible connection to excluding the first day of Pesach.

-micha

No, that's not ritual, we don't have a count of the days, do we? When your sons were born, did you have to count "day one, day two, ..., day eight"?

That's only timing, which is duration. The bris happens on the 8th day, if the boy is healthy etc., no matter what. But if you miss a day counting the Omer, you lose the bracha. If a woman doesn't count the seven days, some say she can't go to mikva. Does she say "one two" or "first second"? Is there a prescribed formula?

The Kohen counts sprinklings cardinally; viz. the Avodah on Yom Kippur: Achat, achat v'achat, achat v'shtaim, etc.

Ah... I didn't understand. I was referring to the verse reading "bayom hashemini" as opposed to "acharei shiv'a yamim". After all, calendar dates aren't counted by the practitioner either, and in the same sentence you said those were ordinal. So I thought specification of the number was also part of it.

AFAIK, there is no formula to how to count shiv'ah neqi'im.

-micha

Cardinals and ordinals are essentially the same for finite numbers, although they disagree for transfinite numbers. At least in the set theoretic sense. As far as English goes, we generally count with cardinals, thus Sefirah is cardinals.

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