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The Hebrew ט"ו connotes 15:as in gematria, where each letter is assigned a numeric value, the letter ט connotes 9, the letter ו connotes 6. Hence ט"ו בִּשְׁבַט, Tu B'Shvat, connotes “the 15th of Shvat”.

The original source for celebrating Tu B,Shvat as New Year fםr Trees is in the Mishnah:

“There are four New Years:… On the first of Sh’vat is New Year for Trees, according to the Academy of Shammai; the Academy of Hillel says, on the fifteenth thereof” (Rosh Hashanah 1:1).

The practical application of New Year for Trees is for Trumot and Ma’asrot, the tithes which a Jew is obligated to give the Kohanim [Priests]: fruits and vegetables must be tithed, one-tenth donated to the Holy Temple and the Kohanim who administer therein.

These tithes must be calibrated year-by-year:

“We may not donate from the fruits of this year for the fruits of last year, nor from the fruits of last year for the fruits of this year, and if someone were to donate such, it is not a tithe, as the Torah says ‘Tithe all produce…year-by-year’ (Deuteronomy 14:22)… If someone picked [for example] an etrog on the eve of Tu bi-Sh’vat before sunset, and then picked another etrog after sunset, then the one cannot be offered as a tithe for the other…because Tu bi-Sh’vat is the New Year for Trees” (Rambam, Laws of T’rumot 5:11).

Why is Tu BShvat the cut-off date for tithing fruit of trees?

– The Talmud cites the explanation offered by Rabbi Elazar, who cited his mentor Rabbi Osha’yah: “Because by then the majority of the year’s rain has fallen, and the majority of the solar cycle is yet to come” (Rosh Hashanah 14a).

The “solar cycle” which the Talmud refers to here is the period from the Winter Solstice (approximately December 22) to the Spring Equinox (approximately March 20), the time when the majority of fruits blossom in Israel.

So the 15th of Sh’vat is a good time to mark New Year for [fruit] Trees.

What is the principle behind Hillel and Shammai’s disagreement as to whether the New Year for Trees fall on the 1st of Sh’vat (Shammai) or the 15th (Hillel)?

– I suggest that Hillel and Shammai represent two different ways of viewing the world. Hillel represents the actual, Shammai represents the potential.

A simple example is the Hillel-Shammai dispute concerning Chanukah (Shabbat 21b): Beit Shammai ruled that one lights eight candles on the first night of Chanukah, seven candles on the second night, six candles on the third night, and so on down to one candle on the eighth and final night.

Beit Hillel ruled the opposite: one candle on the first night, two candles on the second night, and so on up to eight candles on the eighth and final night.

Rabbi Yosé bar Avin, one of the last of the Amora’im of the Land of Israel, explains the reason for this difference: “According to Beit Shammai, it corresponds to the days still to come; according to Beit Hillel, it corresponds to the days that have gone” (ibid.).

That is to say, according to Shammai the candles indicate how many days are still left in the future (the potential); according to Hillel, the candles represent which night of Chanukah this is (the actual).

Another example is the difference in their approaches to Shabbat:

“They said of Shammai the Elder: all his life he ate in honour of Shabbat. If he would find a goodly animal, he would say: This will be for Shabbat. If he would then find a second animal better than that, he would reserve the second [for Shabbat] and eat the first [during the week].

“But Hillel the Elder had a different trait, for all that he did was for the sake of Heaven, as it is said, Blessed be Hashem day by day (Psalms 68:20). Similarly, it was taught: Beit Shammai say: מֵחַד שַׁבָּיךְ לְשַׁבְּתָיךְ (“From the first day of the week [prepare] for Shabbat”). But Beit Hillel say: Blessed be Hashem day by day” (Beitza 16a).

The Ramban (Commentary to Exodus 20:8) cites the Mekhilta de-Rabbi Shimon bar Yohay, suggesting that Shammai based his custom on the command זָכוֹר אֶת יוֹם הַשַּׁבָּת לְקַדְּשׁוֹ – “Remember the day of Shabbat to sanctify it” (Exodus 20:8). The inference of the Ramban’s words is that Hillel based his custom on the parallel verse שָׁמוֹר אֶת יוֹם הַשַּׁבָּת לְקַדְּשׁוֹ, “Safeguard the day of Shabbat to sanctify it” (Deuteronomy 5:12).

So this, too, exemplifies the classic difference between Hillel and Shammai:

The command to “זָכוֹר, remember the day of Shabbat to sanctify it” applies before Shabbat – זָכוֹר, remember the Shabbat before it comes, such as by calling the days of the week “the first day of Shabbat”, “the second day of Shabbat”, and so on. That is to say, “Remember the day of Shabbat to sanctify it” is the potential, Shammai’s perspective.

By contrast, “שָׁמוֹר, Safeguard the day of Shabbat to sanctify it” applies specifically on Shabbat itself (see Bereishit Rabbah 16:4) – the actual, which is Hillel’s perspective.

It is at this time of the year that the fruit on the trees begins to ripen. So Shammai marks the 1st of Sh’vat as New Year for Trees, when the fruits are just beginning to bloom: this is the time when the fruits are still potential.

By contrast, Hillel marks the 15th of Sh’vat as New Year for Trees, when the fruits are already [almost] ripe: this is the time when the fruits are no longer potential, they already exist in actuality.

Another way to view this Hillel-Shammai dispute is by the moon: Rosh Chodesh Sh’vat, the 1st of the month, is of course New Moon; the 15th of the month is Full Moon.

Now the moon represents Israel: “An eclipse of the sun is a bad omen for the idolaters, an eclipse of the moon is a bad omen for Israel, because Israel calibrates [its calendar] by the moon, and the idolaters by the sun” (Sukkah 29a).

The moon represents Israel: it waxes and wanes, sometimes disappearing entirely – but it always bounces back, as bright as ever. Just like Israel, which alone of all the nations in history has never been eradicated.

Other nations come and go. Ancient Egypt no longer exists: modern Egypt is an Arab nation, occupying the same place as ancient Egypt, but with a different language (Arabic), a different religion (Islam), a different culture, a different ethnicity from the original Egyptians.

Whether the ancient nations like Babylon, Persia, Rome, and Edom, or more recent nations such as Yugoslavia, Abyssinia, Bengal, and Champa – other nations disappear with time.

Only Israel remains eternally – even though frequently persecuted, even eclipsed to near-invisibility.

Like the Moon, however dim Israel appears, it always returns to its former brightness.

And so Shammai looks to the 1st of Sh’vat, the New Moon, the time of renewal, the time when our brightness is eclipsed, and only future potential.

Hillel, by contrast, looks to the 15th of Sh’vat, the Full Moon, the time of actual maximum brightness.

In this, as with almost all Hillel-Shammai disputes, we follow Hillel’s opinion. And so today, ט"ו בִּשְׁבַט, Tu bi-Sh’vat, the 15th of Sh’vat, we celebrate the New Year for Trees.