It’s commonly said that given two Jews, you will have three opinions. But can this statement be generalized for numbers greater than two? In this post, I will examine three different approaches to the problem, and determine whether a universal mathematical law describing this phenomenon can be described.

(Throughout, n will represent the number of Jews participating in a given discussion, and m, the number of opinions actively being held by said Jews.)

The Inductive Approach

In the base case where n = 1, it is assumed that m is also equal to 1. (This holds only for the ideal case of a spherical Jew in a vacuum- in other cases, one Jew may hold multiple opinions simultaneously.) Given this base case, if the number of additional opinions generated by the entry of another Jew to the room can be determined, we can then generalize for all values of n.

However, observation of this inductive step is difficult- as new opinions are generated and collide with each other, they produce a shower of anti-opinions, kvetches, and gamma radiation. Further research is required.

The Textual Approach

In the Talmud, it becomes clear that the sages had different views on the matter. Shammai held that the number of opinions varied linearly with the number of Jews present, e.g. m = n + 1.

Beit Shammai say: We are commanded with regard to the mitzvah to be fruitful and multiply. It is in accordance with the Divine Will for the number of opinions to multiply.

However, Hillel advocated for a quadratic approach, perhaps where m = (n^2 + n) / 2, creating the series [1, 3, 6, 10…]

Beit Hillel say: Of the breastplate of decision, the verse states: “It shall be square and doubled, a span in length and a span in width.” Who wishes to arrive at a decision, he must consider the square of those present.

If the great minds of the past could not resolve this dispute textually, is there another way?