In preparation for entering the Land of Israel a census is taken of Am Yisrael. The Torah lists the final number as [Bemidbar 26:51] 601,730 people. This number is eerily reminiscent of the number of people in a census taken by Moshe in Parashat Bemidbar. In that particular census the total number was [Bemidbar 1:46] 603,550 people. The difference between the two censuses is less than two thousand people – a third of one percent. While the two censuses are separated by only a few parshiot, they are separated chronologically by about thirty-nine years. How coincidental is it that the population of Am Yisrael remained essentially constant over two generations? It turns out that the closer we look at the two censuses, the more surprising the coincidence becomes.
A few months after the census in Parashat Bemidbar, Am Yisrael are sentenced to wander in the desert for forty years. Every person above the age of twenty is doomed to die there in the Sinai. As both censuses include only those above the age of twenty, this means that there is no overlap at all between the people counted in the two censuses. This is precisely what the Torah tells us [Bemidbar 26:64-65]: “Among [those in the second census] there was no man who had been [included] in the census of Moshe and Aharon when they counted the Children of Israel in the Sinai Desert. For Hashem told them, ‘They shall surely die in the desert,’ and no one was left of them but Calev the son of Yefuneh and Yehoshua the son of Nun.” What are the chances that two completely different sets of people would have nearly the same number of members?
Not only were the people that were counted in the two censuses different, the types of people who were counted were also different. In the census in Parashat Bemidbar Moshe counts [Bemidbar 1:2] “every male… all those who serve in the Army.” This makes perfect sense as this census was taken in preparation for conquering the land and only men would participate in battle. Conversely, in Parashat Pinchas Moshe counts [Bemidbar 26:2] “the heads of the houses of the Children of Israel”. The “heads of the houses” are not necessarily male. In cases where the father died and left only daughters, then they took their father’s place in the census. The verse in Bemidbar [26:33] clearly shows that the daughters of Tzlofchad, a man who died in the wilderness, were included in the census. This makes perfect sense as this census was taken in preparation of divvying up the land, and each and every household received an inheritance. Now we stir the pot once again: Between the first and second census the misbehaviour of Am Yisrael led to multiple plagues in which thousands of people died. For instance 14,700 people die in the plague that occurs after Korach’s aborted revolt. Another 24,000 are killed in the plague that occurs at the end of Parashat Balak after Am Yisrael are seduced by the Midianite women. And yet we still end up with essentially the same number of people: six hundred thousand and change. Just like the first time. How lucky is that?
Rav Elchanan Samet addresses these questions and more, but I’d like to propose an answer of my own. When Hashem speaks to Avraham Avinu at the Brit Bein HaBetarim (“Covenant of the Pieces”), He tells Avraham that one day he will be the father of a great nation [Bereishit 15:5]: “Look heavenward and count the stars, if you are able to count them… So will be your descendants.” How many stars are there in the universe? The most accepted doctrine posits that there are about 100 octillion (100 x 1027) stars in the universe. Avraham couldn’t see them all: Some of the stars are so far away that their light hasn’t yet reached the earth. Maybe Hashem was referring to the number of stars that can be seen with the naked eye. On a clear night without any light pollution a person can see no more than two thousand stars. So how many descendants did Hashem promise to Avraham? An octillion? Two thousand? Or perhaps six hundred thousand and change?
In order to continue, we must learn about the “Hilbert Hotel”, first discussed in 1924 by the great mathematician David Hilbert. The “Hilbert Hotel” is often used to demonstrate a number of paradoxes pertaining to the concept of “infinity”. The Hilbert Hotel is a hotel with an infinite number of rooms, manned by a mathematically inclined bellman. One day the Hilbert Hotel is completely full. The front door opens and a person walks in. Weary from travel, he asks for a room. This being the Hilbert Hotel, the bellman says “No problem!” He knocks on all the doors, and tells each guest to move to the next room over. This leaves the first room available, and our weary traveller can set down his bags and go to sleep. The paradox here is that “infinity-plus-one” still equals infinity. Back to the Hilbert Hotel. A bus pulls up and an infinite number of people get off the bus. Is there room for all of them? Our bellman thinks for a second and then he tells all the guests to look at their room number and to move to the room whose number is twice their room number. The person in Room 1 goes to Room 2, the person in Room 2 goes to Room 4, the person in Room 3 goes to Room 6, and so on. As a result, all of the odd-numbered rooms become available, and everybody on the bus has a place to rest his weary bones. The paradox here is that “infinity-times-two” still equals infinity.
Let’s move from the “Hilbert Hotel” to “Hashem’s Desert Inn”. Before Hashem commands Moshe to count Am Yisrael, He blesses Aharon’s grandson, Pinchas. Pinchas has just committed a violent act of religious passion, and as a result of Pinchas’s actions a plague that had killed 24,000 Jews is stopped in its tracks. Hashem blesses Pinchas with [Bemidbar 25:12] “a covenant of peace”. Hashem continues the blessing [Bemidbar 25:13]: “It shall be for him and for his descendants after him [as] an eternal covenant of Priesthood”. Most of the commentators comment on why Hashem had to give Pinchas the position of Kohen (Priest) even though he was descended from Aharon. I’m much more interested in the use of the word “eternal”. Hashem does more than bless Pinchas with Priesthood – He blesses Pinchas with infinity. This blessing is a case of quid pro quo. Pinchas cleaved to Hashem. Hashem is infinite. Ergo Pinchas attained some measure of Hashem’s vastness. But how? Immediately after Hashem blesses Pinchas, He commands that the second census be taken. The close proximity of the blessing and the census inextricably links the two episodes. The point of the census is not to show how many people had a share in the Land of Israel. The Talmud in Tractate Zevachim [118b] teaches that it took a full seven years to defeat the Canaanites before the land could be allocated. This would render data from the census in Parashat Pinchas outdated. I suggest that the entire point of the census is to show that Am Yisrael, by virtue of Pinchas, had attained the infinite. They had attained the blessing that Hashem bestowed upon Avraham. To paraphrase Hilbert, “601,730 times infinity” is equal to “603,550 times infinity”. While “12 times infinity” or “231 times infinity” is also equal to “603,550 times infinity”, had the two censuses not been so close the message of infinity would have been lost.
Rav Soloveichik, writing in “On Repentance”, explains the verse in Psalms [147:5] “His understanding cannot be calculated (ein mispar)” as “To His understanding numbers are irrelevant”. Hashem is infinite, and so no number is greater or more meaningful than any other number. It is for this reason that Hashem can exact punishment in this world for a sin, even though by sinning a person contaminates an infinite number of worlds. And it is for this reason that Am Yisrael can be called [Devarim 7:7] “the smallest of the nations”. Quantitatively, perhaps. But qualitatively – not even close.
Ari Sacher, Moreshet, 5775
Please daven for a Refu’a Shelema for Moshe Dov ben Malka
 This idea is introduced in “Parashat Derachim” by R’ Yitzchak Maitles.
 We’re not even going to mention an even earlier census in Parashat Pekudei in which the result is precisely the same as in the census in Parashat Bemidbar.
 In his first (yellow) set of sefarim in his shiur on Parashat Bemidbar.
 A countably infinite number of rooms, Ben.
 See, for instance, Rashi ad loc.
 This is not 100% true. First Hashem commands Moshe to destroy the Midianites, but  the command is connected with the previous episode, and  it is not carried out until Parashat Mattot.