Rabbi Bernie Fox



The Strange Correspondence between the BeMidbar Census and the Population Reported in Sefer Shemot

And their entire number was six hundred three thousand five hundred fifty.  (BeMidbar 1:46)

Sefer BeMidbar opens with Hashem commanding Moshe to conduct a census of the male population of Bnai Yisrael.  The census included all males of age twenty or older.  It covered all of the Shevatim – the tribes – with the exception of Shevet Leyve.  Moshe performed Hashem’s command.  Our pasuk relates Moshe’s finding.  The number of individuals in the census was 603,550.  This is the second census of Bnai Yisrael explicitly discussed in the Torah.  The first is found in Sefer Shemot.  There, Hashem commanded Moshe to collect a coin from every male of age twenty and above.[1]  These coins were subsequently melted down and used in the construction of the Mishcan –the Tabernacle.  The Torah reports that the coins collected numbered 603,550.[2]  This is the same number reported in our parasha.  Rashi points out that it is impossible for these two accounts to refer to a single census.  The account in Sefer Shemot refers to a census taken prior to the building of the Mishcan.  In fact, the coins collected were used in the Mishcan’s fabrication.  The account in our parasha takes place after the assembly of the Mishcan.  This prompts an obvious question.  How could these two censuses result in the same number?  Both indicated a population of 603,550.

Rashi offers a somewhat complicated answer.  In order to be counted in the census, one was required to be of age twenty or older.  According to Rashi, this did not mean that one had actually reached his twentieth birthday.  Instead, it was required that the person would be age twenty or older that year.  The first census was taken in Tishre.  Tishre is the first month of the year.  Many men did not reach age twenty until later in the year.  Nonetheless, these men were included in this census.  The second census was taken in Iyar of the same year.  By this point, additional men had reached their twentieth birthday.  However, these individuals did not affect the outcome of the census.  They had been counted in the original census in Tishre.[3]

Nachmanides rejects Rashi’s explanation.  He raises two objections.  First, he does not accept Rashi’s basic premise.  Rashi posits that the first of the two censuses included all individuals who would become age twenty or older in the twelve months beginning from Tishre.  Nachmanides rejects this assumption.  He insists that each census included only those who had actually reached their twentieth birthday.  Second, it seems that according to Rashi no one died between Tishre and Iyar.  If deaths had occurred, the second census would have resulted in a lower number.  Nachmanides insists that it is unreasonable to assume that, in a nation of over 600,000, no one died.

Nachmanides offers a completely different explanation for the identical outcomes of the two censuses.  He explains that the outcomes were not at all identical!  The two censuses did not count the same group.  In the census in our parasha, Moshe was commanded to exclude Shevet Leyve.[4]   Hashem’s directions to Moshe in Sefer Shemot do not mention the exclusion of Shevet Leyve.  Rashi assumes that, although their exclusion is not mentioned, Shevet Leyve did not participate in the contribution of coins described in Sefer Shemot.   Nachmanides disagrees and asserts that Shevet Leyve was included in the first census.  In other words, the first census resulted in a count of 603,550 including Shevet Leyve.  The second census produced the same number.  But it did not include Shevet Leyve.[5]  

Gershonides raises an obvious objection against Nachmanides’ answer. What has Nachmanides gained?  His original objective was to explain the strange stability in population.  It is only reasonable for some change to have occurred in the nation’s population during the course of the year.  Nachmanides explains that the nation did grow.  However, this growth was not directly reflected in the censuses.  This is because the first census was more inclusive.  However, Nachmanides’ answer creates a different problem.  It results in a bizarre coincidence.  The two censuses measured different groups.  They were separated by an interval of seven months.  Yet, they produced the same outcome!

Based on these considerations, Gershonides suggests an alternative explanation.  First, he agrees with Rashi that Shevet Leyve was excluded from both censuses.  Second, he accepts Nachmanides’ assertion that only those who had actually reached their twentieth birthday were counted in either census.  Once these premises are accepted, an entirely different approach is required to explain the agreement between the censuses.  The Torah is telling us that the population of the nation remained completely stable between these two censuses.  The Torah is revealing a miracle.  Of course this raises a question.  Every miracle has a purpose.  What was the purpose of this miracle?  Why did Hashem exercise His providence to maintain this remarkable stable population of Bnai Yisrael over a seven month period?

Gershonides answers this question.  He observes that in each census the Torah indicates a minimum age of those included.  Only those of age twenty or older were counted.  He explains that there was also a maximum age for these censuses.  Those over sixty were not counted.  Nachmanides also agrees with this assertion.[6]   Gershonides then makes a simple observation.  What would be the normal pattern of population growth for this age group? 

In order to answer this question, we must conduct a simple, two-step, analysis.  First, we would expect the number of younger members to be greater than the number of older members.  The subset of those between twenty and thirty years of age should be far larger than the subset of those between fifty and sixty.  This is because the more senior age group will have a higher mortality rate.  Second, the relative mortality rates of these two subsets will affect the growth pattern of the entire group.  The population of the nation should grow.  This is because the number of people entering the group at age twenty should be far greater than the number leaving the group after age sixty.

We are now ready for Gershonides’ answer.  The Torah states that the population of Bnai Yisrael between the ages of twenty and sixty was stable.  Based on the analysis above, we know that this should not occur.  Normally, this population should grow.  How could stability occur?  Stability could only occur if the number of men leaving the group after age sixty was equal to the number entering at age twenty.  This would require a remarkably low mortality rate for all men under sixty!  The persistently low mortality note would inflate the number of people graduating out of the census group between the first and second census.  This is the miracle the Torah is revealing.  Hashem protected Bnai Yisrael.  He granted them long-life.  This blessing is reflected in the two censuses.[7]





The Encampment in the Wilderness as a Representation of the Sinai Revelation

And you should appoint the Leveyim over the Mishcan of Testimony and over its utensils and all associated with it.  They will carry the Mishcan and its utensils and will minister to its needs.  And around the Mishcan they will camp.  (BeMidbar 1:50)

The Mishcan was located in the center of the camp of Bnai Yisrael.  The Mishcan was surrounded by the camp of the Leveyim.  The other tribes were assigned positions around the perimeter of the Leveyim’s camp.

Nachmanides explains that this pattern reflected the encampment around Mount Sinai.  The majority of the nation was not permitted to approach the mountain.  The elders could ascend with Moshe to the lower levels of the mountain.   Only Moshe could climb to the top of the mountain.  The Mishcan represented Sinai.  The people could not approach the mountain.  Neither could the nation camp directly around the Mishcan.  This area was reserved for the Leveyim.

The Leveyim were charged with the duty of dedicating themselves to the study and teaching of the Torah.  Through committing themselves to this mission, they earned the right to serve in the Mishcan.  They attained the status of the elders at Sinai.  They could not enter the inner sanctuary of the Mishcan, but they were permitted to camp directly around the structure.[8]

This pattern represents the Torah’s outlook upon our relationship with Hashem.  Moshe ascended to the top of the mountain.  This was because of Moshe’s wisdom and righteousness.  These qualities enabled Moshe to come as close to Hashem as humanly possible.  The elders did not achieve Moshe’s level of human perfection.  However, they possessed sufficient wisdom to climb the lower slopes of the mountain and draw closer to the presence of Hashem.  Those lacking the wisdom and righteousness of Moshe and the elders were required to distance themselves from the mountain.

Maimonides explains that love of and closeness to the Creator are not derived from religious fervor or asceticism.  They develop through a profound understanding of the Torah and Hashem’s infinite wisdom.  It is only through the Torah and the revelations of His wisdom that we can know Hashem.  True love of Hashem corresponds with our knowledge and understanding of Hashem and His Torah.[9]

The encampment symbolized this concept.  The various groups were placed around the Mishcan in a specific pattern.  Each was assigned a position appropriate to the Torah knowledge associated with the group.  This served as a constant reminder of the method by which each of us can draw closer to Hashem.


[1]   Sefer Shemot 30:12-13.

[2]   Sefer Shemot 38:26.


[3]   Rabbaynu Shemuel ben Meir (Rashbam) Commentary on Sefer Shemot 30:16.

[4]   Sefer BeMidbar 1:49.

[5]   Rabbaynu Moshe ben Nachman (Ramban/Nachmanides), Commentary on Sefer Shemot 30:12.


[6]   Rabbaynu Moshe ben Nachman (Ramban/Nachmanides), Commentary on Sefer BeMidbar 26:64.

[7]   Rabbaynu Levi ben Gershon (Ralbag/Gershonides), Commentary on Sefer BeMidbar, (Mosad HaRav Kook, 1998), p 1.

[8]   Rabbaynu Moshe ben Nachman (Ramban/Nachmanides), Commentary on Sefer BeMidbar Introduction.

[9]   Rabbaynu Moshe ben Maimon (Rambam/Maimonides) Mishne Torah, Hilchot Teshuva 10:6.