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There are three reasons given why the Torah begins with a beit, the second letter of the Hebrew alphabet, as opposed to an aleph, which is the first letter:

1) The Talmud Yerushalmi (Hagiga 2:1) states that since the word arrur, meaning “curse” begins with an aleph, it was preferable to begin the Torah with a beit, which is the first letter of the word baruch, meaning “blessed.” The problem with this explanation is, as the ibn Ezra states, that there are many words beginning with a beit which do not carry a positive denotation. As well, there are many words beginning with an aleph that do carry a positive meaning.

2) The Midrash (Hane’elam on Shir hashirim) states that just as the shape of the letter beit is closed from three sides and open from the fourth, so G-d created the world complete on three sides, leaving the fourth direction – north – open. This was done so that just in case someone deluded might come along and declare that he is G-d, we would be able to respond, “Okay, please go and close up the fourth side of the world that was left open.” The problem with this explanation is that the world was created for the Torah, not the other way around. When G-d decided to create the universe, he “looked into the Torah and created the world.” Therefore, it makes little sense to say that the Torah was written in a way to conform to the world. Quite the opposite; since according to the Torah, the first letter of the alphabet is “aleph,” it should have been the first letter of the Torah, as well.

3) According to kabala (see book of discourses of the previous Lubavitcher Rebbe, 1940, p. 68), the Torah that we learn here in the physical world comes down to us from the higher spiritual world of Atzilut. As it exists in Atzilut, the Torah begins with an aleph. And in order to allude to the fact that as it exists in our world it relates to a lower level, the Torah begins with a beit. Here, though the problem is that the Torah was given “to us,” as we say in the blessing over the Torah, “that He gave us.” That is, the same Torah that exists in Atzilut and even higher, is the Torah that He gave to the Jewish people. So, if so, why shouldn’t the Torah down here begin with an aleph as well?

In addition to the above difficulties, there is a story from the Talmud (Megila 9A) relating how a group of scribes translated the Torah into Greek for Ptolemy, the king. G-d rendered a miracle, and all seventy scribes translated the Torah in the exact same fashion. Among the “changes” they made in order to fit Ptolemy’s needs (as a non-Jew), they all translated the beginning of the Torah with the words, Elokim barah breishit – “G-d created in the beginning.” Since the first word of their translation is Elokim, the translations all began with an aleph. Hence, it is clear that there is a very sound basis for beginning the Torah with an aleph, rather than a beit. So, why did all the reasons for beginning the Torah with a beit not apply to Ptolemy the king? Why was it appropriate to begin his translation with an aleph?

The explanation is the following. There are two elements in the relationship of the Jew to the Torah. First, there is the relationship of the Jew to the Giver of the Torah – G-d. And second, there is the relationship to the Torah itself, which we are commanded to learn and grasp intellectually. The latter of course is an intellectual activity, obligating us to study and internalize the Torah. The first element, though, transcends intellect, since the connection with G-d goes beyond what we are capable of understanding and feeling. But without the first element – connection with the Giver of the Torah - we learn the Torah with a different attitude altogether. The Torah becomes a subject, separate from us as people, unless we develop a connection with the One above. Once we develop that connection, we are able to learn the Torah in a much more intimate fashion, feeling at all times the importance and vitality that the Torah imparts to us. The letter aleph represents that connection – it is the relationship of the Jew to the Giver of the Torah. On the other hand, the beit symbolizes the second element in the relationship of the Jew to the intellect of the Torah – the obligation of the Jew to learn Torah in this world. First of all, we need the connection. But that connection, symbolized by the aleph, is beyond intellect and therefore beyond the letters of the Torah. But once the connection is there, we have to learn the Torah, and that is our main occupation in this world, which is why the Torah begins with the letter beit.

All explanations of a particular word of the Torah are interconnected. Here, all three explanations stem from one general point; the aleph of the Torah alludes to clinging and ascending spiritually, beyond intellect. And the beit alludes to learning and understanding the Torah. The three explanations above express this concept in three different ways; within the Torah itself, the effect of the Torah upon man, and the effect of the Torah upon the world.
1) The relationship of the Torah to itself corresponds to the explanation from kabala - When we learn the Torah without any consciousness of the Giver of the Torah, then the Torah becomes (in our minds) like a separate entity, just as the lower worlds seem to be separate from G-d. This is alluded to by the beit, symbolizing the lower worlds. However, when we learn it with full recognition of the Giver of the Torah, then the Torah reveals its true cleaving to the higher world of Atzilut, symbolized by the aleph.

2) The relationship of the Torah to the one who learns it connects to the explanation from the Talmud Yerushalmi – When we learn Torah without awareness of the Giver of the Torah, we remain separate from G-d. We may come to know His Torah, but we may not follow its precepts, or we may follow them but only coldly and robotically, without any excitement and attention to detail. This is alluded to by the aleph of arrur (“cursed”). But if we learn with full awareness of the Giver of the Torah, then we draw down a blessing (baruch) into the world.

3) The relationship of the Torah to the world corresponds to the explanation from the Midrash – When we learn Torah with full awareness of the Creator, we are like the beit that is surrounded by three sides, and our learning is what draws down and completes the fourth side of the beit. However, learning Torah without awareness of the Creator results in a world that remains in need of rectification – there is noone there to fix and fill in the fourth side.

Now, we may also understand the significance of the translation of the Torah into Greek, during which all seventy scribes began their translations with the letter aleph. Ptolemy the king was a non-Jew, and as such his obligation to learn the Torah was not equivalent to the Jewish obligation. While a Jew must learn the entire Torah, aware and cleaving to the One above, a non-Jew must only learn those sections that apply to his obligation to observe the seven Noahide commandments. And he is certainly not obligated to “involve” himself in the Torah in order to cleave to G-d and become imbued with awareness of the Giver of the Torah. Therefore, the non-Jewish relationship to Torah lacks the first element that is present in the Jewish relationship – awareness and clinging to the One above. The only obligation of the non-Jew is the intellectual awareness of what he has to observe. This, for the non-Jew, is the aleph – the highest spiritual level that he may attain in relationship to the Torah. While for the Jew, the aleph is associated with cleaving to G-d, for the non-Jew the aleph is associated with the knowledge that he must attain of the seven Noahide commandments – and that is why it was appropriate for the scribes to begin Ptolemy’s translation with an aleph.

From Likutei Sichot of the Lubavitcher Rebbe, ztz’l, vol. 15, pp. 1-6 Rabbi David Sterne, Jerusalem Connection in the old city of Jerusalem