Parashat Pekudei - The Centrality of One-Third

שליש המידה ומרכזיותו

The Centrality of One-Third

A Third of the Measure

We open with the following intriguing Medrash, which compares the Torah's commandments to the angels on high:

1. Eliezer ben Yaakov says: Whoever has tefillin on his head and arm, a mezuzah on his doorpost, and tzitzit on his clothing, is likely not to sin, as is written, "The triple strand will not quickly unravel;" it is also written, "The angel of G-d camps around those who fear Him and saves them." (Yalkut Shimoni, Parashat Sh'lach, 750)

The three mitzvot that are called here "angel of G-d" are tefillin, mezuzah, and tzitzit. They have something most interesting in common: The one-third point. How so?

1) Arm-tefillin are placed on the biceps, the uppermost of the three parts of the arm.

2) The ideal way of making tzitzit is by tying together one-third of the length of each of four folded strings, and leaving the remainder – two-thirds – to hang down as individual strings.

3) The mezuzah must be placed at the bottom of the top third of the doorpost.

We have found a common denominator; now we must find its significance. Let us therefore consider the most central vessel in the Mishkan (Tabernacle): The Ark of the Covenant, Aron HaBrit, with the two angel-like cherubim upon it:

וַיִּהְיוּ הַכְּרֻבִים פֹּרְשֵׂי כְנָפַיִם לְמַעְלָה סֹכְכִים בְּכַנְפֵיהֶם עַל הַכַּפֹּרֶת

The cherubim's wings were spread upwards,
shielding the Ark cover with their wings. (Shmot 37,9)

The height of the Ark was ten tefachim (handbreadths) high, including one tefach for its cover. The Torah does not tell us how high the cherubim's wings reached above the Ark, but our Sages taught us in the Oral Torah: "The cherubim stood to one-third the height of the sanctuary" (Sukkah 5b). Since we know that the Mishkan was 60 tefachim high (ten amot, approximately five meters), we can easily calculate that cherubim reached 20 tefachim above the Mishkan floor: ten tefachim for the Ark itself, and another ten for the cherubim and their wings.

How did the Sages derive the cherubim's height? They learned it from the special set of large cherubim that King Solomon made for the Holy Temple (in addition to the smaller set atop the Ark). The Temple stood 30 amot high, and King Shlomo built the cherubim ten amot tall – having learned this one-third ratio from the Mishkan. We thus see that the

1/3 ratio must be maintained, in both the Mishkan and the Mikdash.

But why one-third? What is its significance? Let us proceed further and consider the following puzzling Rabbinic teaching. Regarding Yaakov Avinu’s dream of the ladder on which the angels of G-d ascended and descended, the Medrash says:

"The angel is a third of the world, as is written (Daniel 10,6), Its body was like tarshish." (Medrash B'reshit Rabba 68,12)

Using the notrikun system, an orthographic method of interpretation, the word tarshish can be understood as tre-shesh, or "two out of six" – one-third.

Are the Sages actually telling us that the size of non-physical angels can be measured?! And even if so, of what world are they one-third? Are they a third of the entire universe, which itself cannot be measured?

Not at all. It is obvious that we must understand this in the context of the measurements of the cherubim, as we learned above. The cherubim represent angels, who are said to be “one-third of the world” – and therefore the cherubim must be structured to symbolize this same measurement: a third of the Holy Temple sanctuary.

And yet again we ask: What is the significance of one-third?

The Center of Gravity

The Jerusalem Talmud (Sukkah 5,2) teaches us a very interesting engineering rule: If we wish to place an object on the floor in a stable manner, its base must be at least a third of its height. This principle is based on the fact that the average height of a person is three amot (up to the shoulders), and he requires a base of one-by-one amah in order to stand comfortably with his feet spread apart. The "one-third" point thus indicates the "center of gravity."

In this context, the same Gemara mentions the row of menorahs that were placed at the Holy Temple entrance during the Simchat Beit HaShoevah (Water Drawing) celebrations on Sukkot. Each candelabrum was 100 amot (some 50 meters) high, and the Gemara notes that each therefore required a base at least 33 amot wide. Given that there was no room for so many bases of that size, the Gemara concludes that the menorahs stood "by miracle."

Another important Halakhic rule is presented elsewhere in the Yerushalmi (Maasrot 1,2):

1. Ze'ira said: The Torah states, "Tithe all the seed crop that the field gives forth, year by year" (Dvarim 14,22). This means that we must tithe that which can be planted and grown – excluding whatever has not yet grown to a third of its full development, for it cannot be planted as productive seed.

When wheat or oat grain reaches a third of its total growth, it has attained a critical stage in its development. It is at this point that the grains are sufficiently advanced to be planted in the earth and bring forth a new generation. Thus, with the discovery of this botanic principle, we learn an important parallel rule: The turning point in the development of life is when continuity for future generations is enabled.

This point is the “one-third mark” - the "determining stage" for tithing a crop, when it reaches a third of its growth. If this stage is reached in the first, second, fourth or fifth year of the seven-year Shemitah cycle, then its additional tithe follows the laws of those years and must accordingly be eaten in Jerusalem; but if it is reached in the third or sixth year, then its law is that must be given to the poor.

The definition of the "one-third" point, then, is this: It is the center of gravity, both physically – in terms of solid, stable positioning on the ground – and in terms of the ultimate goals of life, namely, the continuity of life for future generations.

The Center of Life: One's Mission

Let us return to that with which we began: The cherubim stand to one-third of the height of the Beit HaMikdash and Mishkan. The message here is strong and clear: The cherubim are angels, and angels are holy emissaries of the Creator.

They are not alone, however, for every creature in the world has a task, and is sent to the world as a Divine emissary to fulfill it. When wheat, for instance, reaches a third of its growth, it is ready to fulfill its mission of continuation, by being planted. Even a Bar Mitzvah boy, as we will see below, reaches a third of his full independent development as he matures physically and becomes a man ready to bring forth a new generation – whether it be children, or students, or recipients of kindness who will then pass it on to others. He thus fulfills the primary aspect – the center of gravity – of his mission in the world.

Let us sharpen this point. When the cherubim – angels, Divine emissaries – reach a third of the Sanctuary's height, they are ready to carry out their mission. So too, animals and plants are ready at the one-third point to fulfill their mission of creating their next generations. This is what the Sages taught: "The angel is a third of the world."

By the same token, the Torah's mitzvot remind us that we, too, are emissaries – sent by G-d to fulfill our missions. His One Name is engraved on the "one-third" point: in the Tefillin (on our bodies), the Tzitzit (our clothes), and the Mezuzah (our homes). One-third is the "center of gravity."

Stability

Let us mention some other examples in which the one-third point denotes the point of stability. Our Sages of the Medrash (B'reshit Rabba 85,10) learned from the Torah that a fetus can be recognized as such at the age of three months – one-third of the full pregnancy period:

Sumchus said in the name of R. Meir: From where do we know that a fetus in its mother's womb is not recognizable before three months? As is stated: ויהי כמשלוש חדשים, Three months after [Yehuda's encounter with Tamar], he was told that… she was pregnant." (B'reshit 38,24)

The embryo becomes "stabilized" during the first three months of pregnancy, after which there is no chance that the mother will become pregnant again (a phenomenon known as superfetation) and endanger it. We learn this from the Gemara (Brachot 60a), which lists several milestones in pregnancy, and states that the time to pray that a second pregnancy not evolve is only within the first three months.

Another example of one-third as a stabilizing point is found elsewhere in the Gemara (Shabbat 92a). The Sages teach that the weight of an object carried by two people on a pole is distributed as follows: one third above the pole, and two-thirds below it. That is to say, the pole must be attached to the item's 1/3 mark from the top, thus guaranteeing maximal stability and ensuring that the object will not overturn. Regarding the altar carried by the Levites, for example, one-third of its height was above the poles, and the rest was suspended below them.

Yet another interesting example appears in the same Tractate (Shabbat 35a):

Abaye said: The amount that will not spill from the top is a third [i.e., a barrel of seeds and the like can bear another half of its height without spilling].

In addition, in Bava Kama (9b) we learn:

1. Ze'ira says: When one wishes to beautify a mitzvah, he should not spend more than a third.

For example, if one buys an etrog for Sukkot for 100 shekels, and later finds another one more beautiful, he should buy the second one only if it costs up to 150 shekels, for he is permitted to pay only up to a third more (of the total price). Both of these examples show that the original can hold its own if its increase is no more than a third of the total.

Preserving the Whole

What is the smallest percentage of an entity needed to preserve its quality?

The Sages of the Sanhedrin (Great Court) give us the answer: one-third. We know that the Sanhedrin judges may leave the Holy Temple grounds only for certain specific reasons – but under no circumstances may there ever be fewer than 23 of them in the Holy Temple at any given time. That is, one-third of the total of 70 must always be there. Thus, the large Sanhedrin is 70 members, and a small Sanhedrin numbers 23 – one-third.

Yet another example: In the Mussaf prayer of Rosh HaShanah, we mention ten verses each of Malchuyot (G-d's Kingship), Zikhronot (G-d's remembrance and knowledge of each us), and Shofarot (regarding shofar blasts and their significance). Yet, R. Yochanan ben Nuri teaches in the Mishna (Rosh HaShanah, chapter 4) that if only three of each are recited – a third of the required number – this is sufficient.

Bar Mitzvah

Let us now turn our attention to the age of Bar Mitzvah, i.e., when one takes upon himself the yoke of the Torah's commandments. This age, of course, is 13 years and one day. How long is an average lifetime?

יְמֵי שְׁנוֹתֵינוּ בָהֶם שִׁבְעִים שָׁנָה וְאִם בִּגְבוּרֹת שְׁמוֹנִים שָׁנָה
Our lives… are seventy years; if with great strengths - eighty years. (Psalms 90,10)

The 80 years in which we live can be divided into two parts: Up to age 40, and the remainder. Shmuel, one of the greatest Talmudic sages and a doctor as well, instructed his student Rav Yehuda that up until age 40, his nourishment must come mostly from solid foods, and that from then on, he should drink more than he eats, (Shabbat 152a)

This shows us that the main period of growth is until age 40, when one must supply his body with abundant food. From then on, his body grows weaker, and he must drink relatively large amounts in order to impede the desiccation process.

The spiritual significance of this process is very clear: Until age 40, a person works and produces for himself, while after that, he gives of himself to others, like a candle: the oil is consumed, but the light that it gives off grows stronger. This also explains why the Talmud (Sotah 22b) sets the age 40 as the best age for teaching Jewish Law: Until then, one is not yet “ripe” or ready to take upon himself the responsibility needed to teach laws to the public.

This also explains yet another statement in the Gemara (Avodah Zarah 5b):

One cannot clearly understand his teacher's actions until 40 years of age, as is written: "G-d did not give you a heart to understand, eyes to see, and ears to hear – until today" (Dvarim 29,3).

The source for this teaching is that which Moshe Rabbeinu says at the close of the 40 years of desert wandering. The Nation of Israel is about to enter into Eretz Yisrael and begin living in accordance with natural law. Bnei Yisrael are about to take responsibility for themselves, no longer to be governed by open miracles. Looking back at the events of the preceding four decades, they realize that their physical and mental preparation for the conquest and settlement of the Land, in accordance with G-d's command, is now complete. All this – after precisely 40 years in the desert.

By the same token, a student cannot grasp the meaning of his teacher's actions until he reaches the point at which he can take his teacher's place, namely, age 40. "Do not judge another until you reach his situation," we are taught in Pirkei Avot (2,4). This is why only at age 40, when the student can teach others, can he truly understand his teacher's behavior.

Thus, 40 years is the half-way mark in our lives. It is the point that marks the transition from developing our own identity, to the period in which we give to others, show concern for the public and are able to guide the community.

Everything now falls into place. If we divide the 40 years of self-development into thirds, we get 13 years and some. This is precisely the age of Bar Mitzvah: 13 years and one day (the extra day represents the "remainder"). This is the point at which the child takes responsibility for his actions.

This is also the age at which a child becomes physically able to procreate (Sanhedrin 68b) and build the next generation – children for whom he will become responsible. Hashem arranged man's development such that as he becomes able to make achievements in various areas, he can also accept responsibility for the results of those actions. Just as wheat grain cannot be productive if it has not reached a third of its development, as we saw above, so too, the age of Bar Mitzvah is the "one-third" point that guarantees the continuity and stability of the coming generations.

And still more: Bar Mitzvah age is also the age at which a boy becomes liable for punishment by a human court. He is now obligated in tefillin, for he can be responsible for personal hygiene and cleanliness, as well as purity of thought. In short, he is now obligated in everything the Torah commands a Jew, and will receive punishment and reward in accordance with his deeds.

Let us conclude with the following remarkable Midrashic teaching about the Tablets of the Law and their links with both our world and the upper worlds:

1. Berechya said: The Tablets at Mount Sinai were six tefachim long. Allegorically, two tefachim were in G-d's hand, two tefachim were in Moshe's hand, and two tefachim separated between them. (Shmot Rabba 28,1)

What are our Sages trying to tell us? Moshe, representing mankind, has a grasp on one-third of the Tablets – and since this is the minimum that represents the whole, the Torah is entirely ours! Similarly, G-d has a grasp on the same amount, meaning that the Torah is entirely His as well! The Torah is both of This World and the Upper Spiritual Worlds.

This is the wonder of the Torah's revelation in so many different ways and facets. To us it appears as if it is all ours – while the deep truth of the matter is that it is entirely spiritual and Divine wisdom.

The most important lesson we can learn from these ideas is that we exist in order to fulfill our G-d-given mission in this world; whatever we fail to complete, will be passed on to the next generation – our children, our students, and anyone who can continue the acts of kindness that we have begun. Passing this torch of fulfilling G-d's exalted will to the next generations is the "center of gravity," the ultimate purpose: the one-third mark of our mission in this world.