Double Parshiyos and the Leap Year

Question #1: When is it a good idea to have doubles? Question #2: Disproportionate readings Why are the last four parshiyos of the Torah so short? Would it not make sense that the weekly readings be more evenly divided? Question #3: Why does is take them so long to catch up? Sometimes the weekly reading […]

Holding the Torah Upright

According to some rishonim, the mitzvah to raise the Torah (hagbahah) is mentioned in parshas Ki Savo. Question #1: Holy Roller “I was in a shul, and when they took out the sefer Torah, they opened it and carried it all around the shul, showing everyone with a yad where the beginning of the keri’ah […]

You Can’t Take It with You — Moving and Removing Mezuzos

YOU CAN’T TAKE IT WITH YOU! Question #1: “We are moving residences, and I understand that I must leave the mezuzos in my old home. However, they are beautiful, mehudar mezuzos that I would like to use in my new dwelling. Is there any way that I can take these mezuzos with me?” Question #2: […]

What Happens When We Do Something Wrong?

Since the Aseres Hadibros which include the laws of Shabbos are in Parshas Va’eschanan, we have an opportunity to discuss what happens when we do something wrong on Shabbos. Question #1: Cholent caper Shimon looks rather sheepish when he asks this shaylah on Shabbos morning: During the night, he tasted the cholent and decided it […]

My Vows I Shall Fulfill

It is rather obvious why we are studying this topic this week – since the laws pertaining to vows are the first subject mentioned in Parshas Matos. Question #1: Quiz question Can performing a mitzvah become a liability? Question #2: Is this a “klutz question?” What does it mean that I am doing something “bli […]

Bill’s Saga or The Power of a Single Word

Since parshas Pinchas discusses many of the relationships of Hashem and His people, I’ll share with you the following true story: Bill’s Saga or The Power of a Single Word There was a knock on the door to my shul office. I knew Bill, an active member of one of the large Conservative temples in […]

The Right Type of Help

Since one of the sources for the prohibition of bishul akum is in Parshas Chukas, this presents an ideal time to review these laws. Household Help Shirley* asks me: “We hired a very nice Polish lady to help around the house, keep an eye on the kids and do light housekeeping. Can we have her […]

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The Numbers Game

Because this article explains some basics of how Torah is taught by Chazal, I think it is appropriate to the week of Shavuos.

Question #1: Pie r squared

Yanki is supposed to be watching his weight and therefore needs to figure out how many calories are in the pie he beholds. To figure out how big the pie is, he measures the diameter of the pie, and divides it in half to get the length of its radius. He then multiplies the length of the radius by itself to get “r squared,” and multiplies the result by three so that he knows the area of the pie’s surface. Is there anything wrong with his calculation?

Question #2: Puzzled by the pasuk

“How can the pesukim tell us that the relationship between the circumference of a circle to its diameter is three-to-one, when simply taking a string and measuring around it demonstrates that it is noticeably longer?”

Question #3: Performing mitzvos accurately

“How accurate a calculation must I make when determining the size of an item to be used for a mitzvah?”


In numerous places, both Tanach and Chazal approximate certain mathematical values, such as evaluating the ratio of the circumference of a circle to its diameter as three to one. The problem is that we can demonstrate mathematically that the ratio is greater than three and is almost 3 1/7. This leads to the following questions:

(1) Why would Chazal calculate using inaccurate approximations?

(2) When making halachic calculations, may we rely on these estimates, or do we need to be mathematically more accurate?

(3) A corollary question is: when providing an estimate, one must allow for a margin of error. Does halachah require a margin of error, and, if so, how much?

The Slide Rule versus the Calculator

Let me begin our discussion with a modern analogy, if something I remember can still be considered “modern.” When I first studied sophisticated mathematical estimates, I learned to use a slide rule, which today is as valuable to an engineer as an abacus. Relative to the calculator, a slide rule does not provide accurate measurements, and someone using a slide rule must allow a fairly significant margin of error in one direction or the other, depending on the situation.

Today, complex computations are made with calculators, which provide far more accurate results that can be rounded off, as necessary, to the nearest tenth, millionth, quadrillionth or smaller. Of course, using a calculator still requires one to round upward or downward, but because it is much more precise, the margin of error is greatly reduced.

How Irrational Are You?

Numerous halachic questions require mathematical calculations, involving what we call “irrational numbers.” An irrational number means one that cannot be expressed in fractional notation. Another way of explaining an irrational number is that its value can never be calculated totally accurately, but can only be estimated.

The two most common examples of irrational numbers that show up in Chazal are:

(1) Pi

The ratio of the circumference of a circle to its diameter, which we are used to calling by the Greek letter ∏ (pronounced like the word “pie,” and spelled in English “pi”). Since the 19th century, the letter pi has been used to represent this number, because the Greek word for peripheryis peripherion, which begins with the letter ∏. Hundreds of years earlier, the Rambam (Commentary to the Mishnah, Eruvin 1:5) noted that the ratio of the circumference of a circle to its diameter is an irrational number that can only be approximated, and that the scientists of his era used an estimate of 3 and 1/7, which is actually slightly greater than the value of ∏. The Rambam explains that since there is no accurate ratio, Chazal used a round number, three, for this calculation.

(2) The diagonal of a square

The length of a diagonal of a square, which is equal to the side of the square multiplied by the square root of two (√2). Chazal calculated the length of a diagonal of a square to be 1 and 2/5 times its side, which is slightly smaller than the value of √2. (Another way of expressing this idea is that the ratio between the diagonal and the side is 7:5.) The fact that Chazal’s figuring is somewhat smaller than the mathematical reality is already proved by Tosafos (Sukkah 8a s.v. kol).

Since both pi and the square root of two are irrational numbers, they can only be estimated, but can never be calculated with absolute accuracy.

Based on the above-quoted statement of the Rambam, we can already address one of our earlier questions: “Why would Chazal calculate using inaccurate approximations?” The answer is that any computation of the correlation of the circumference of a circle to its diameter will be an estimate. The only question is how accurate must this estimate be for the purpose at hand.

Chazal or Tanach?

Although the Rambam attributes the rounding of pi to Chazal, in actuality, there are sources in Tanach that calculate the ratio of the circumference of a circle to its diameter as three-to-one. Both in Melachim (I 7:23) and again in Divrei Hayamim (II 4:2), Tanach teaches that the Yam shel Shlomoh, the large, round pool or mikveh that was built in the first Beis Hamikdash, was thirty amos in circumference and ten amos in diameter, which provides a ratio of circumference to diameter of three-to-one. Thus, we can ask a question of the Rambam: Why does he attribute this ratio to Chazal, rather than the source for Chazal’s calculation, the pesukim?

In fact, the early commentaries to these verses already ask how the verse can make a calculation that we know is not accurate. The Ralbag suggests two options: either that the numbers used are intended to be a very broad estimate, or, alternatively, that the diameter is measured from the external dimensions of the mikveh, whereas the circumference is measured from its inside, which makes the estimate closer to mathematical reality.

According to the second approach of the Ralbag, no Biblical source uses an estimate of three-to-one as a substitute for pi. This will explain why the Rambam attributed the estimation of pi as three to Chazal, rather than to the Tanach. The Rambam was fully aware that one could interpret the verses according to the second approach of the Ralbag, in which case, there is no proof from the verse. He, therefore, attributed this estimate to Chazal.

Gemara Eruvin

The Ralbag’s approach reflects an earlier passage of Gemara. The Mishnah in Eruvin (13b) states that if the circumference of a pole is three tefachim, its diameter is one tefach, which means that the Mishnah assumes a ratio of three-to-one. The Gemara questions how the Mishnah knows that the ratio is three-to-one, and then draws proof from the above-quoted verse that the Yam shel Shlomoh was thirty amos around and ten amos across. The Gemara then debates whether the calculations of the Yam shel Shlomoh indeed result in a ratio of three-to-one, because one must also include the thickness of the poolitself, which offsets the computation. The Gemara eventually concludes that the verse was calculating from the inside of the pool, not its outside, and therefore the thickness of the pool’s containing wall is not included in the calculation (Eruvin 14a).

Nevertheless, this Gemara’s discussion leaves the mathematician dissatisfied, a question already noted by Tosafos. If the internal diameter of the Yam shel Shlomoh was ten amos, its circumference must have been greater than thirty amos, and if its circumference was thirty amos, then its internal diameter must have been less than ten amos.

A Different Question

The Rosh, in his responsa, is bothered by a different question, based on Talmudic logic rather than on mathematical calculation. He finds the Gemara’s question requesting proof for the ratio between a circle’s circumference and its diameter to be odd. The ratio between a circle’s circumference and its diameter is a value that one should calculate. By its nature, this is not a question that requires a Biblical proof or source.

In the literature that we have received from the Rosh, he asks this question in two different places. In his responsa (Shu’t HaRosh 2:19), we find a letter that he wrote to the Rashba, in which he asked the Rashba a series of questions that the Rosh notes bother him tremendously, and to whom he has no one else to turn for an answer. One of the questions the Rosh asks is: “Why does the Gemara ask for a Biblical source for a mathematical calculation?”

It is curious to note that a later commentary mentions that, in all the considerable literature that we have received from the Rashba, we have no recorded answer of the Rashba to this question of the Rosh (Cheishek Shlomoh to Eruvin 14a).

Another Comment of the Rosh

The Tosafos HaRosh commentary to Eruvin, which was published for the first time relatively recently, is the second place where the Rosh asks why the Gemara wanted a Biblical source for a mathematical calculation.  There, the Rosh provides an answer to this question:  Since the calculation of three-to-one is not accurate, the Gemara wanted a biblical source as proof that we are permitted to rely on this estimate.

(The Cheishek Shlomoh, whom I quoted above, provides the same answer to this question as does the Rosh in his Tosafos. The Cheishek Shlomoh never saw the Tosafos HaRosh, which had not yet been printed in his day.)

Curiosity about the Tosafos HaRosh

There is an interesting historical point that can presumably be derived from the fact that, in the Tosafos HaRosh, the Rosh answers the question that he raised and accredits this answer to himself. This should be able to prove which work the Rosh had written earlier, and also whether he ever received an answer to his question from the Rashba. This analysis is based on the following question: Why did the Rosh cite an answer in his Tosafos¸but not in his responsum, which was addressed as a question to the Rashba. There are three obvious possibilities:

(1) Although the Rosh wrote this answer in his Tosafos, he was dissatisfied with it, and therefore wrote a question to the Rashba. I would reject this answer because, if it is true, then, in his correspondence to the Rashba, the Rosh would have mentioned this answer and his reason for rejecting it.

(2) The Rosh indeed received an answer, either this one or a different answer, from the Rashba. I reject this approach also, because, were it true, the Rosh would have quoted the Rashba’s answer in his Tosafos and, if need be, discussed it.

(3) Therefore, I conclude that the Rosh, indeed, never received an answer to the question he asked of the Rashba and subsequently reached his own conclusion as to how to answer the question, which he then recorded in the Tosafos HaRosh. This would lead us to conclude that the Tosafos HaRosh was written later in his life than his responsa, or, at least, this responsum.

Mathematical Accuracy

At this point, we can address one of earlier questions.When making halachic calculations, may we rely on these estimates, or do we need to be mathematically more accurate? We might be able to prove this point by noting something in the Mishnah in Eruvin quoted above. The Mishnah there ruled that, under certain circumstances, an area that is fully enclosed on three of its sides and has a beam a tefach wide above the fourth side is considered halachically fully enclosed, and one may carry inside it. The Mishnah then proceeds to explain that if the beam is round and has a circumference of three tefachim, one may carry inside the area because, based on the calculation that the relationship of its circumference to its diameter is three-to-one, the beam is considered to be a tefach-wide. However, as the Rambam notes, a beam that has a circumference of three tefachim is actually less than a tefach in diameter, and therefore one should not be permitted to carry in this area!

The Aruch HaShulchan (Orach Chayim 363:22; Yoreh Deah 30:13) notes this problem and concludes that one may carry in this area. He contends that this is exactly what the Gemara was asking when it requested Scriptural proof for a mathematical calculation. “Upon what halachic basis may we be lenient in using this estimate of three-to-one, when this will permit carrying in an area in which the beam is less than a tefach wide? The answer is that this is a halachah that we derive from the verse.”

To clarify this concept, the Chazon Ish notes that the purpose of mitzvos is to draw us nearer to Hashem, to accept His reign, and to be meticulously careful in observing His laws. However, none of this is conflicted when the Torah teaches that we may use certain calculations, even if they are not completely mathematically accurate. In this instance, relying on these estimates is exactly what the Torah requires (Chazon Ish, Orach Chayim 138:4). As expressed by a different author, the Gemara (Eruvin 4a; Sukkah 5b) teaches that the measurements, the shiurim, required to fulfill mitzvos are all halachah lemoshe misinai, laws that Moshe Rabbeinu received as a mesorah on Har Sinai. Similarly, these estimates of irrational numbers mentioned above are all halachah lemoshe misinai that one may rely upon to fulfill mitzvos, whether or not they are mathematically accurate. The same Torah takes these calculations into consideration when instructing us which dimensions are required in order to fulfill specific mitzvos (Shu’t Tashbeitz 1:165).

In the context of a different halachah in the laws of Eruvin, the Mishnah Berurah makes a similar statement, contending that we can rely on Chazal’s estimates, even when the result is lenient. However, the Mishnah Berurah there vacillates a bit in his conclusion, ruling that one can certainly rely on this when the issue is a rabbinic concern (Shaar Hatziyun 372:18). In a responsum, Rav Moshe Feinstein questions why the Mishnah Berurah limits relying on this approach, and Rav Moshe rules unequivocally that one may rely on these estimates even when it involves leniency in de’oraysa laws (Shu’t Igros Moshe, Yoreh Deah Volume3 #120:5).

How Straight Are My Tefillin?

Personally, I find the context of Rav Moshe’s teshuvah very interesting. There is a halacha lemoshe misinai that requires that the boxes of the tefillin, the batim, must be perfectly square. Rav Moshe was asked whether there is a halachic preference to use scientific measuring equipment to determine that one’s tefillin are perfectly square. Rav Moshe rules that there is neither a reason nor a hiddur in measuring the tefillin squareness this accurately. Since Chazal have used the calculation of 1.4 or a ratio of 7:5, which we know is an estimate, to determine the correct diagonal of a square, there is no requirement to make one’s tefillin squarer than this, and it is perfectly fine simply to measure the length of each of the sides of one’s tefillin and its two diagonals to ascertain that the ratio between the diagonal and the side is 7:5.

In the above-cited responsum, Rav Moshe notes that he had heard that the Brisker Rav, Rav Yitzchak Zeev Soloveichek, had ruled that it was preferable to check one’s tefillin in the most scientific method available. Rav Moshe writes that he finds this suggestion very strange and disputes its being halachically correct (Shu’t Igros Moshe, Yoreh Deah Volume3 #120:5).

When making halachic calculations, may we rely on these estimates, or do we need to be mathematically more accurate?” The answer is that, indeed, the purpose of Chazal’s making these estimates was that observing halachah does not require that these calculations be mathematically precise, provided they meet the criteria that the halachah established.

An Alternate Approach

Although the majority of late authorities conclude that the calculations of Chazal are, indeed, part of the halachos of shiurim, this is not a universally-held position. The Tashbeitz, a rishon, wrote a lengthy responsum on the topic, in which he presents two ways to explain why Chazal used estimates that are not precisely accurate. His first approach reaches the same conclusion as we have already found in the later poskim, that these measurements are included within the halachos of shiurim that are part of the halachah lemoshe misinai.

The second approach of the Tashbeitz, however, differs with the above-mentioned halachic conclusion. In his second approach, he contends that all the above estimates were meant for pedagogic, but not halachic purposes. The rounding of pi to three and the diagonal of a square to 1.4 were provided to make the material easily comprehensible to all students, since every individual is required to know the entire Torah. Thus, when Chazal used these estimates in calculating the laws, their intent was to enable the average student to comprehend the halachic material, not to provide the most accurate interpretation. When an actual halachic calculation is made, it must be totally accurate. Any halachic authority involved would realize that he must use a highly accurate mathematical computation and then round either upward or downward as necessary for the specific application. (A similar position is held by Chiddushim Uviurim, Ohalos 5:6.)


Certainly, the majority of late halachic opinions conclude that the estimates of Chazal are meant to be halachically definitive and not simply pedagogic in nature. However, I leave it to the individual reader to ask his or her posek what to do when a practical question presents itself.


May I Participate in the Census?

In honor of this week’s Haftarah, I present the following halachic discussion:

Question #1: Counting sheep

Why would someone count sheep when he is trying to stay awake?

Question #2: Counting from a list

Is it permitted to count people from names on a list?

Question #3: Ki Sissa or Hoshea?

The Gemara bases the prohibition to count the Jewish people from the opening words of this week’s Haftarah: And the number of the children of Israel shall be like the sand of the sea that cannot be measured and cannot be counted (Hoshea 2:1). Why does the Gemara attribute the prohibition to this source in Hoshea, when the prohibition is mentioned in the Torah in the beginning of Parshas Ki Sissa?

Answer: Analyzing the Sources in Chazal

The Mishnah teaches that to determine which kohen would be awarded the mitzvah of removing ashes from the mizbei’ach, a lottery procedure was used, whereby the kohanim interested in performing the mitzvah extended their fingers, which were then counted. The person in charge picked a number much greater than the assembled kohanim, and then counted fingers until they reached that number. The kohen on whom the number landed performed the mitzvah (Rashi ad loc.).

The Gemara asks why they didn’t simply count the kohanim themselves, and answers that it is prohibited to count Jews (Yoma 22b) — counting fingers is permitted, counting people is not (Rambam, Hilchos Temidim Umusafim 4:4). We are aware of one common application of this mitzvah: when counting people for a minyan, one counts words of a ten-word pasuk, rather than counting the people directly (Sefer HaItim #174; Kitzur Shulchan Aruch 15:3).

Here is another application: to determine how many places one needs to set at a table, one should not count heads, but one may count sets of legs (Shu’t Torah Lishmah #386).

The Gemara cites three Biblical sources for this prohibition:

1. When the nation of Ammon threatened the Jewish community of Yaveish-Gilad, Shaul gathered a large Jewish army (Shmuel I 11:8). According to one opinion in the Gemara, Shaul counted the members of his army by having each soldier throw a piece of broken pottery into a pile. Thus, even to fulfill a mitzvah, one may count Jews only in an indirect manner.

2. Before attacking Amalek, Shaul gathered the Jewish people and had each person take a sheep from Shaul’s herds. By counting the sheep, he knew how many soldiers he had (Shmuel I 15:4, see Rashi). Again, we see that he used an indirect method to count them.

3. And the number of the children of Israel shall be like the sand of the sea that cannot be measured and cannot be counted (Hoshea 2:1). Taking the verse not only as a blessing, but as a commandment, the Gemara derives a prohibition against counting the Jewish people.

Isn’t the Torah a Clearer Source?

The obvious question is, why does the Gemara not quote the pasuk in the Torah as a source for the prohibition?

When you will take the headcount of the children of Israel to determine their numbers, each man should give atonement for his life to Hashem when being counted. Thereby, no plague will result from the counting. This is what whoever is counted should give: a half shekel (Shemos 30:12 -13).

This pasuk implies that the only permitted way to count Jews is indirectly, by having each one donate a half-shekel and then counting the coins. This seems to be the source of Shaul’s knowing to count the Jews indirectly. It is indeed odd that the Gemara quotes Shaul’s practice as the source for the prohibition, rather than Shaul’s own source, the Torah itself!

Before answering this question, I want to analyze a different point that we see in the pasuk. The Torah says: each man should give atonement for his life to Hashem when being counted. Thereby, no plague will result from the counting. In the discussion of no other mitzvah does the Torah say, “fulfill this commandment so that no plague results.” Why, suddenly, does the Torah apply such an expression in this case?

Rabbeinu Bachya (ad loc.) explains that when we count an individual separately, it causes the heavenly tribunal to note all his deeds, and this may result in his being punished for his sins, which otherwise would not be punished now.

Others explain the concern in terms of ayin hora. Abarbanel, for example, explains that counting people by head causes ill to enter through their eyes and mouth into their body, whereas counting fingers does not cause the ayin hora to enter them. I leave to the reader to decide whether he is referring to physical or metaphysical harm.

Why the Prophets?

So, indeed, if we see from the Torah, itself, that counting Jews is prohibited and potentially very harmful, why did the Gemara base its comments on the deeds and words of the Prophets?

The commentaries present several approaches to answer this question. Here is a sample of some answers:

(1) The Gemara is proving that one may not count Jews, even for the purpose of performing a mitzvah, something that the Torah did not expressly say (Sfas Emes to Yoma ad loc.). The practices of Shaul and the verse in Hoshea make clear that one may not count Jews directly, even for the sake of a mitzvah.

(2) The Gemara needs to prove that we may not count even a small group of Jews, whereas the pasuk in Ki Sissa may be prohibiting only counting the entire people (Mizrachi; Sfas Emes).

(3) The verse in Ki Sissa could mean that one may count the Jews in a normal census, but that, afterwards, they all provide a half-shekel as an atonement to make sure that no one suffers (Makom Shmuel, quoted by Shu’t Tzitz Eliezer 7:3). This last approach suggests that the verse When you will take the headcount of the children of Israel according to their numbers be explained in the following manner: When you take a regular census of the children of Israel, each man should give atonement for his life to Hashem when counting them – after you conduct your census, each person should give a half-shekel, to make sure no harm results. Indeed, the census could cause harm, but that does not necessarily mean that the Torah prohibited it. However, the stories of Shaul and the verse in Hoshea prove that the Torah prohibited counting Jews directly, since Shaul counted the people by counting sheep, rather than conducting a census and then having them all donate a half-shekel as atonement.

(4) One can interpret the verse in Ki Sissa to mean that the generation of the Desert, who had worshipped the eigel hazahav, the Golden Calf, was at risk, and that counting them might cause a plague (Maharsha to Yoma ad loc.; see also Ohr Hachayim to Shemos 30:2). However, one cannot prove from Ki Sissa that there is an inherent prohibition or risk in counting Jews when they have not violated such a grievous sin. However, the stories of Shaul or the verse in Hoshea prove that one may not count Jews, even when they have not violated serious prohibitions.

Thus, we see several possible ways to interpret why the Gemara did not consider the Torah source as adequate proof to prohibit counting the kohanim in the Beis Hamikdash, but instead rallied proof from later sources. As we will see shortly, there are actual distinctions in practical halacha that result from these diverse explanations. But first, a different question:

Counting from a List

For the purposes of fulfilling a mitzvah, may one count Jews by listing their names and then counting their names? Is this considered counting people indirectly, since one is counting names and not people, or is this considered counting the people themselves?

Advertising Campaigns to Help the Needy

Creative advertising campaigns aimed at generating tzedakah funds did not originate with modern organizations, such as Oorah or Kupat Ha’ir. About 200 years ago, Rav Yisrael of Shklov, a major disciple of the Vilna Gaon and an author of several scholarly Torah works (including Taklin Chadtin on Shekalim and Pe’as Hashulchan on the agricultural mitzvos), was organizing a fundraising campaign for the Yishuv in Eretz Yisrael in which he wanted to link donors to individual beneficiaries by listing the needy of Eretz Yisrael by name. Rav Yisrael held that this fundraising approach =did not violate the prohibition of counting Jews[MSOffice1] , since counting names on a list is an indirect way of counting people, and, furthermore, it was for the sake of fulfilling a mitzvah. He held that this is similar to Shaul’s method of counting his soldiers.

However, the Chasam Sofer disagreed, contending that counting names on a list is considered counting people directly. Even though one is not looking at their faces, counting from a list is considered counting the person and is therefore halachically different from counting fingers, legs, half-shekels, lambs or pottery shards (see Koveitz Teshuvos Chasam Sofer #8; Shu’t Kesav Sofer, Yoreh Deah #106). We will see shortly that this dispute exists to this day.

The Census

Is the State of Israel permitted to conduct a census of its population? Does an individual violate the mitzvah by working as a census taker or by providing the census takers with information?

This question was hotly debated by halachic authorities, even when the pre-state Zionist organizations began counting the Jewish population, and continued with the censuses of the State of Israel. Those who permitted the census provided a variety of reasons to justify it, the primary one was that servicing the medical, educational, economic, and safety needs of a large population requires knowing how many people there are. These authorities accepted that this qualifies as a dvar mitzvah, and that counting by list, or via computer and machine calculation is considered indirect counting (Shu’t Mishpatei Uziel 4:2; Noam XV=).

On the other hand, several prominent poskim prohibited taking the census or participating in it (Shu’t Tzitz Eliezer 7:3). On the 27th of Iyar, 5732 (May 11, ’72), the Steipler Gaon released a letter stating the following:

In the coming days, census takers will be counting the Jewish people. One should be careful not to answer them at all, to inform them that it is forbidden to take a census, and that it is possible that this is a Torah violation, as explained in the Gemara Yoma 22, the Rambam in the fourth chapter of Temidim and Musafim, and the Ramban in Parshas Bamidbar. Furthermore, the Tosafos Rid in Yoma writes that it is prohibited to do so even indirectly, unless one is accomplishing a mitzvah. It is explained in Kesav Sofer… that it is prohibited to do so even through writing. Furthermore, taking a census involves the possibility of danger.

At the same time, the Beis Din of the Eidah Hachareidis also issued a letter prohibiting participating in the census or answering any questions from the census takers, and reiterated that they had banned this ten years before at the previous census.

Subsequent to his publishing a responsum in which he prohibited participating in the census, the Tzitz Eliezer (7:3) was asked whether someone wishing to determine the numbers of people who made aliyah may count how many people there are. He answered that for the purposes of a mitzvah, one may count indirectly. However, we should note that such figures are often counted simply for curiosity or publicity, which the Tzitz Eliezer prohibits (22:13).

In a more recent responsum dated Elul 24, 5755 (September 19, ’95), Rav Vozner (Shu’t Shevet Halevi 9:35) writes that the heter of taking a census because of divrei mitzvah applies only when the statistics are used solely for divrei mitzvah. However, he permits the census for a different reason — because the census counts the entire population of Israel and not specifically Jews. Furthermore, even though the census in Israel includes a breakdown into religious groups, since thousands of those who are listed by the government as Jewish are not, Rav Vozner does not consider this as counting Jews. He adds that since no one is counted by name or family and the data does not correlate at all to the number of Jews, he does have any halachic objection to participating in the census.

On the basis of Rav Vozner’s responsum, there certainly should be no difficulty in participating in the United States census, since this also counts people and not Jews.


As Rav Hirsch points out, the census conducted in this week’s parsha is performed in the desert, demonstrating that its purpose was not for economic or political reasons. Rather, just as last week’s parsha closed with the counting of the flocks by their shepherds, so too, this week’s parsha begins with counting G-d’s flock by its Shepherd. Every individual is counted as an independent member of that flock to demonstrate the importance of his individual commitment and contribution.

What Is a Temurah?

Question: Two Temurahs

“Why does the Torah mention the mitzvah of temurah twice at the end of this week’s parshah, Bechukosay, once at the beginning of Chapter 27 and again at its end?”


The concept of offering korbanos is foreign to us, since, unfortunately, our Beis Hamikdash still remains in ruin and we are neither required nor permitted to offer korbanos anywhere else. Precisely because this topic is so unfamiliar, we should utilize every opportunity to familiarize ourselves with these laws. There are numerous reasons that underscore the importance of this topic, including:

(1) When our Beis Hamikdash is rebuilt — may it be speedily in our days — we will have to know all the laws about offering korbanos.

(2) It is part of the Torah we are required to know, and will also help us better understand this week’s Torah reading.

(3) The concept of uneshalmah parim sefaseinu (Hoshea 14:3), that when we are unable to offer korbanos, our reading and studying these Torah sections fulfills our requirement to offer the korbanos.

(4) There are some very important and little known laws that affect us today. We will soon study them.

What Is Temurah?

Towards the end of this week’s parshah, the Torah mentions a very unusual concept called temurah. Someone who had consecrated an animal to be his korban subsequently changes his mind and decides to substitute a different animal for the korban. By doing so, he violates the Torah’s prohibitions of lo yachalifenu velo yamir oso, “do not exchange it and do not substitute in its stead.” The Torah teaches that as a result of his declaration, both animals now have the sanctity of that korban (Vayikra 27:10). This means that the declaration succeeded in creating sanctity on the new animal, but failed to remove the sanctity from the original animal. Now, use of either animal for personal benefit is prohibited min hatorah. The animal that attained sanctity because of the second declaration is itself called a temurah (pl., temuros), so the word temurah refers both to the prohibited act and to the animal that is now affected by that act.

What Happens to the Animal?

What ultimately happens to an animal that has just become a temurah?

Each of the several types of korbanos has specific details as to how it is offered. Consequently, although every temurah animal has sanctity, its status will be determined by the specific korban for which it was dedicated.


One of the most common types of consecrated korbanos is the shelamim, whose name comes from the word shalom, peace. Rashi (Vayikra 3:1) explains two approaches for its name:

(1) The purpose of a shelamim is to bring peace to the world.

(2) The meat of a korban shelamim is divided: most of it is eaten by the owner in Yerushalayim. He may share it with any tahor person he chooses. A portion of the shelamim, the breast meats and the right thigh, is given to the kohen to eat in Yerushalayim and share with whomever he desires. The mizbei’ach (the altar) receives much of the fat of the animal, the kidneys, its diaphragm meat (which butchers often call the “skirt steak”), and a small part of the liver. Thus, “everyone” is made happy by this korban, and it brings peace to the world.

No Gender Discrimination

Shelamim is unique among the commonly consecrated korbanos in that one may offer an animal of either gender of any of the three types of kosher beheimah (domesticated animal — bovines, sheep or goats) and that there is no age restriction once the animal is seven days old. Of the other three main types of common consecrated korbanos, chatas must be female, whereas both olah and asham must be male. Both chatas and asham have other requirements as far as species, and asham has specific age requirements.

Temuras Shelamim

Now that we understand some of the basics of shelamim, our question is what happens to a temuras shelamim. This is the subject of a dispute in the Mishnah (Temurah 17b, 18a), but the halachic conclusion is that a temuras shelamim is treated just as a shelamim. It is offered as a korban and its meat is then divided: part eaten by the kohen and his family, a small part burnt on the mizbei’ach and the majority eaten by its owner.

Temuras Olah

The other very common type of consecrated korban is the olah, which is completely burnt on the mizbei’ach. In the case of olah, both the original korban and its temurah are offered in the Beis Hamikdash with all the details of the appropriate halachos observed. In this way, a temuras olah is treated similarly to temuras shelamim.

There is, however, one case when this cannot be done, which is when the temuras olah is a female animal. Since an olah must be male, the female temurah cannot be offered. This creates a very interesting predicament, since the female now has the sanctity of an olah, yet it cannot be offered as such because of its gender.

To resolve this difficulty, the temurah is sent out to pasture temporarily. The plan is that, left to her own devices, she will eventually develop a blemish that invalidates her as a korban. This requires a bit of explanation:

The Torah requires that all animals offered in the Beis Hamikdash be unblemished. There is an extensive list of physical shortcomings that invalidate an animal from being offered as a korban. For example, an animal whose legs are of uneven length is invalid as a korban, even though the animal is otherwise perfectly healthy. Also, an animal that shows evidence of damage, such as a split lip, is invalid as a korban. A blemish is called a moom and an animal bearing such a blemish is called a baal moom.

In the case of most korbanos, a consecrated animal that has become blemished is redeemed with the redemption money used to purchase a replacement korban. After the baal moom korban is redeemed, it may be slaughtered and eaten, but one may not work it.

This is what happens to a female temuras olah. She is sent out to pasture with the hope that she will eventually develop a moom that will invalidate her as a korban. When that happens, she will be redeemed, the redemption money being used to purchase a new korban olah.

It is prohibited min hatorah to blemish a korban intentionally (Rambam, Hilchos Issurei Mizbei’ach 1:7); however, one may release the animal to the pasture in the hope that it becomes blemished.

Temuras Chatas

There are other instances when one cannot offer the temurah animal in the Beis Hamikdash. For example, both chatas and asham korbanos are offered to atone for specific sins. If someone creates a temurah of either a chatas or an asham, the temurah has sanctity that will preclude its being used any more by the owner, although it will be invalid for offering in the Beis Hamikdash. Exactly what one does with these animals is discussed by the Gemara and the rishonim but includes too many details to discuss in this article.


The temurah of another korban, bechor, has yet a third status. A bechor is a firstborn male animal of a kosher species whose mother is fully owned by a Jew or Jews. An unblemished firstborn male was given to a kohen who brought it as an offering in the Beis Hamikdash. Its meat was eaten by the kohen and his family anywhere in Yerushalayim when they were tahor, and the kohen was able to share it with any tahor person, similar to the laws of a shelamim.

If the bechor is blemished, the halachah is unlike other korbanos, where the blemished animal is redeemed with redemption money that is used to purchase a replacement korban. The owner of a blemished bechor gives the animal to a kohen, who now owns it as his personal property, although he is still forbidden to work the animal and may use it only to slaughter for meat. It is one of the matanos kehunah, the gifts provided to the kohen, so that he can devote himself to his responsibilities as a teacher of the Jewish People. Should the kohen choose to, he may sell it to someone else. There are some other specific laws regarding where it may be slaughtered and how it may be sold, but it may be eaten by anyone, even a person who is tamei.

Temurah of Bechor

We have now seen that the korban of bechor is unusual, in that a blemished bechor loses some of its sanctity as a korban and as a result is slaughtered and eaten. The temurah of a bechor, therefore, also has halachic status different from other temuros. The owner gives the temuras bechor to a kohen, who sends the animal to pasture until it develops a blemish, at which point he may slaughter it and consume it (Mishnah Temurah 21a).

Temuras Maaser

When the Beis Hamikdash stood, every farmer was required to gather all his newborn kosher animals three times a year and send them though the opening of a pen, one at a time. The farmer counted each animal aloud, and marked each tenth animal exiting the pen with a red mark (Mishnah Bechoros, Chapter 9). This tenth animal has the halachic status of maaser, which is a type of korban. One could not work this animal. Instead, the owner was required to bring it to the Beis Hamikdash, where it was offered as a korban. The owner received most of the meat of this korban, which he was required to eat in Yerushalayim.

This korban shares many halachos with the bechor mentioned above. For example, just as a blemished bechor is not redeemed but is slaughtered and eaten, so too, a blemished maaser is slaughtered and eaten.

There is a difference between the bechor and the maaser, in that the owner is required to give the bechor to a kohen, whereas the maaser he keeps for himself.

There is a similarity between the temurah of bechor and that of maaser in that the temurah is not offered, although it, also, may not be worked, but one waits until it develops a blemish, at which point it can be slaughtered and eaten. In the case of maaser, the owner keeps the animal which he now may eat.

With this information, we can now answer the question asked above:

“Why does the Torah mention the mitzvah of temurah twice at the end of this week’s parshah, once at the beginning of Chapter 27 and again at its end?”

Checking the two pesukim, one will see clearly that the first verse (Vayikra 27:10) is addressing temurah of most korbanos, whereas the second verse (Vayikra 27:33) is addressing the temurah of a maaser animal. As Rashi explains on the latter verse, the halachah of temurah for maaser is different from that of other korbanos, which are usually either offered as a korban or redeemed. Whereas it has the sanctity of a korban, the temurah of a maaser prohibits only working the animal. One awaits its developing a blemish, and then slaughters it for its meat.

Who Can Make Temurah?

A person cannot create a temurah unless he is the owner of a korban. This means that if Jerry walks down the street one day and decides that he wants to substitute a different animal for Yosef’s korban, no temurah has happened. Yosef has to make the temurah for his own korban, or, alternatively, authorize someone to make temurah on his korban.

Who Is the “Owner” of a Korban?

Technically, the person who creates the temurah does not have to be the person who originally declared the animal to be a korban, although temurah can be declared only with the authority of the “owner” of the korban, meaning the person who is to benefit from its offering. If one person declared an animal to be a korban for the benefit of another, it is the beneficiary of the korban who is considered its “owner,” not the donor. Therefore, if the beneficiary of the korban subsequently decided to substitute a different animal, he will violate temurah and both animals will become sanctified, whereas if the donor did so, he did not violate temurah, and only the original animal has the sanctity of the korban. In the latter case, the replacement animal has no sanctity at all and can be worked with or used as one chooses.

Temurah on Birds?

The laws of temurah apply only to animal korbanos and not to korbanos of birds or of flour (Mishnah Temurah 13a). Therefore, if someone who has turtledoves set aside for his offerings decided to substitute something, whether a bird, an animal or anything else for the turtledoves, he has not violated the prohibition of creating temurah. Since the declaration was totally ineffective, the original turtledoves will be offered and the substitute animal or bird has no sanctity whatsoever.

Unusual Temurah Laws

There are several curious aspects to the laws of temurah and sanctifying offerings. One can create a temurah only when the original offering is owned by an individual, but not when it is a communal offering (korban tzibur) or even when it is a korban owned by two or more partners (Mishnah Temurah 13a). Notwithstanding the fact that one cannot make such a temurah, the Rambam (Hilchos Temurah 1:1) rules that one who attempts to substitute an animal for a communal korban violates the Torah’s prohibition and incurs the punishment of malkus. Nevertheless, since the temurah is completely ineffective, the new animal has no sanctity whatsoever. (The original animal is also, of course, not affected, and it is offered as the korban for which it was intended.)

Multiple Temurah

Someone can even create several temurah animals at the same time. For example, if the owner tried to remove the sanctity of the original animal by substituting two or more animals in its place, all the new animals become consecrated as korbanos, and the original animal still retains its korban status (Mishnah Temurah 9a).

Negligent Temurah

One of the interesting laws of temurah is that someone can create temurah even though he did not intentionally violate the Torah’s prohibition (Temurah 17a; Rambam, Hilchos Temurah 1:2; Tosafos, Temurah 2a s.v. Ha). For example, someone who did not realize that temurah is prohibited will still have created two animals that are holy.

Minor Temurah

Here is another unusual aspect to the laws of Temurah. The Gemara teaches that, under certain circumstances, an eleven-year-old girl or a twelve-year-old boy can declare an animal to have the sanctity of a korban, provided that he or she is the owner of the animal (Temurah 2b). This is true even though they are halachically minors and not obligated to observe mitzvos.

The Gemara (2b) discusses whether a minor who can consecrate a korban can also create a temurah. This is highly surprising; a minor cannot violate the prohibition of creating temurah, one would think that he cannot create a temurah either. Evidently, the creation of a temurah is not dependent on violating the prohibition of temurah.


Do we live with a burning desire to see the Beis Hamikdash rebuilt speedily in our days? Studying the halachos of the korbanos should help us develop our sensitivity and desire to see the Beis Hamikdash again in all its glory. May we soon merit seeing the kohanim offering all the korbanos in the Beis Hamikdash in purity and sanctity and Klal Yisrael in our rightful place in Eretz Yisrael as a light unto the nations!

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This Torah Article is Dedicated

Leilui Nishmas
Devorah bas Yaakov ע”ה
Olga Simons
By Her Granddaughter

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