Ari Sacher

“Approximate Precision” Parashat Emor 5778

Parashat Emor introduces us to the holidays in the Jewish calendar. The Torah prefaces its introduction with an “introduction-to-the-introduction” [Vayikra 23:2]: “Hashem’s appointed [holidays] that you shall proclaim as holy occasions. These are My appointed holidays”. Surprisingly, the first holiday introduced is not a holiday, per se, but, rather, Shabbat [Shemot 23:3]: “[For] six days work may be performed but on the seventh day it is a complete rest day, a holy occasion; you shall not perform any work. It is Shabbat to Hashem in all your dwelling places”. After getting Shabbat out of the way the Torah can now introduce the holidays and so it repeats its introductory sentence nearly verbatim [Vayikra 23:4]: “These are Hashem’s appointed holidays, holy occasions, which you shall proclaim in their appointed time:” With the introductions now finally completed, the Torah dives into the laws of the holidays, beginning with Pesach.

One could be pardoned for thinking that this parasha was accidentally released before it had been completely edited. Why would the Torah first prepare us to learn about the holidays and then suddenly segue to a discussion on the Shabbat, a topic that has already been discussed numerous times in the Torah? And if the Torah really wants to talk about Shabbat, then why not hold off on the introductory verse for the holidays until after Shabbat has been discussed? And if the Torah so badly wanted the introductory sentence for the holidays to come before the discussion of Shabbat, then why repeat it again only two verses later? Why not just go directly to the topic at hand?

The commentators address some of these issues in a piecemeal fashion. For instance, Rashi, addresses our first question. Quoting the Midrash, he writes “Why does the Shabbat [designated by Hashem] appear here amidst the holidays [designated by Am Yisrael]? To teach you that whoever desecrates the holidays is considered [to have transgressed as severely] as if he had desecrated the Shabbat and whoever who keeps the holidays is considered as if he has kept the Shabbat [and his reward is just as great].” In this shiur we will present a more holistic approach that endeavours to answer all of the questions posed above.

The Jerusalem Talmud in Tractate Rosh Hashanah [1:3] is troubled by the verse “These are Hashem’s appointed holidays… which you shall proclaim…” Whose holidays are they – Hashem’s or ours? The Talmud answers “In the past they were ‘Hashem’s holidays’ but from then on ‘you shall proclaim them’”. Rav Chaim Kanievski explains that before the Torah was given at Sinai, the holidays “belonged” to Hashem. After the Torah was given, Am Yisrael took ownership. Rav David Frankel, writing in the “Korban HaEdah”, explains that before the Torah was given, Hashem, in some Divine way, would keep the holidays. There are varied ways of understanding this esoteric idea. One could posit that the Talmud is teaching that each holiday embodies a concept that, like Hashem, is eternal and infinite. For Pesach, that concept could be freedom and for Yom Kippur it might be repentance. A more Hassidic explanation would assert that as the Torah is the Word of Hashem, man mimicking Hashem (by keeping the Torah after it was given to man) and Hashem mimicking man (by keeping the Torah before it was given to man) are really two sides of the same coin.

With all due respect, we’re going to try to keep things prosaic here. Let’s turn our attention to the blessing we make in Kiddush on Shabbat and compare it with the one we make on Yom Tov. On Shabbat we bless Hashem “Who has sanctified the Shabbat” and on Yom Tov we bless Hashem “Who has sanctified Israel and the holidays”. Why don’t we bless Hashem “Who has sanctified Israel and the Shabbat”? The answer pertains to a seminal difference between Shabbat and a holiday. Our Sages refer to Shabbat’s holiness as “keviya v’kayma” – “eternally fixed”. Man needs to do nothing to bring on the Shabbat. As soon as the sun dips below the horizon on Friday evening it is Shabbat. There is nothing man can do to move it by even a fraction of a second. Shabbat is sanctified by Hashem, alone. Holidays are different. A holiday is determined by its Hebrew date, which is, in turn, determined by Am Yisrael. When two witnesses come to the Sanhedrin (High court) and testify that they have seen the new moon, the Sanhedrin declares that a new month (Rosh Chodesh) has begun. But it goes far beyond that: When the Torah says that “you shall proclaim” the holidays, it is giving the Sanhedrin a certain amount of leeway. The Talmud in Tractate Rosh Hashanah [25a] teaches that the Sanhedrin may choose to ignore the testimony of the witnesses in order to push off the new month by one day[1]. The celestial phenomenon of the new moon is only a trigger – it defines a period of time that can be Rosh Chodesh. But it is Am Yisrael who determine when the new month actually begins. Hashem sanctifies Am Yisrael so that we, in turn, can sanctify the holidays.

The problem is that when you take something from Hashem and give it over to man, it’s going to get messy. Man lacks Hashem’s infinite precision. It’s part and parcel of being mortal. And that is precisely the point. Hashem gave Torah to man so that he could refine himself, wholly cognizant that man is finite, imprecise, and prone to error.

An example of the Torah accounting for human imprecision is the number pi (π), the ratio between the diameter of a circle and its circumference. The value of pi is approximately 3.1415. Pi is an “irrational number”, meaning that it cannot be expressed as a fraction of any two integers and, more importantly, pi goes on forever after the decimal point. This is problematic, as the value of pi is critical for the determination of certain halachot. For instance, the minimum size for a sukkah is 49 square tefachim (handbreadths)[2]. What is the minimum radius for a circular sukkah? Mathematically, the precise answer is , or approximately 3.95 tefachim. What is the precise numerical value? The answer is that it is impossible to calculate, even on the most powerful computer. So what is the normative Halacha? The Rambam writes in his Commentary on the Mishnah [Eiruvin 1:5] “The ratio of the diameter to the circumference of a circle is not known and will never be known precisely.  This is not due to something lacking on our part (as some fools think), but this number [pi] cannot be known because of its nature and it is not in our ability to ever know it precisely.  But it may be approximated… to three and one-seventh… But because this ratio is not precise and is only an approximation, [the rabbis of the Mishnah and Talmud] used a more general value and said that any circle with a circumference of three has a diameter of one and they used this value in all their Torah calculations”. Our Sages knew that in a perfect world the value of pi is closer to 3.14159265358979323, but as far as its implementation in an imperfect word, it would be sufficient to say that pi equals three. And so if a person sits in a round sukkah with a radius of greater than  ≈ 4.04 tefachim[3] then he gets credit on the Divine ledger for sitting in a sukkah[4]. He has performed the mitzvah as well as mortally possible.

Let’s return to the Torah’s discussion of the holidays. The Torah introduces us to the holidays by first telling us that certain times are more holy than others. It then tells us that there is one day each week that is imbued with ultimate holiness, a holiness untouched by human hands, and that is Shabbat: Hashem’s appointed holiday. The Torah then tells us about another kind of holiday, a day imbued with a human, messy, imprecise kind of holiness. These are the days that Am Yisrael shall proclaim as holy. By keeping these holidays – and the rest of the Torah – to the best of our human abilities, we perfect ourselves in preparation for “Yom she’kulo Shabbat” – “A day that is completely Shabbat”, speedily in our days.

Shabbat Shalom,

Ari Sacher, Moreshet, 5778

Please daven for a Refu’a Shelema for Yechiel ben Shprintza, and Tzvi ben Freida.

[1] They might do this if accepting the testimony means that Yom Kippur will fall on Friday or Sunday.

[2] 1 [tefach] = 48 [cm]

[3] Yes, I know that the square root of 3 is also irrational, but let’s leave that for now.

[4] It is unclear if a person is considered as having performed the mitzvah if he sits in a sukkah with a radius between 3.95 and 4.05 tefachim. According to the true value of pi he seems to have performed the mitzvah, while according to the value of pi accepted by our Sages he has not.

About the Author
Ari Sacher is a Rocket Scientist, and has worked in the design and development of missiles for over thirty years. He has briefed hundreds of US Congressmen on Israeli Missile Defense, including three briefings on Capitol Hill at the invitation of House Majority Leader. Ari is a highly requested speaker, enabling even the layman to understand the "rocket science". Ari has also been a scholar in residence in numerous synagogues in the USA, Canada, UK, South Africa, and Australia. He is a riveting speaker, using his experience in the defense industry to explain the Torah in a way that is simultaneously enlightening and entertaining. Ari came on aliya from the USA in 1982. He studied at Yeshivat Kerem B’Yavneh, and then spent seven years studying at the Technion. Since 2000 he has published a weekly parasha shiur that is read around the world. Ari lives in Moreshet in the Western Galil along with his wife and eight children.
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