The fulfillment of the mitzvah of the Four Species involves moving the bundle of all four species to the six directions - left, right, front, above, below, and back - three times each. In addition, there is a dimension that applies only to the lulav, the palm branch, but not to the other three species - namely that only the lulav is shaken. This dimension is further underscored by the custom of the Chabad Rebbes who would shake the lulav both after moving the species in each of the six directions and then again upon returning it to their chest. Indeed, Torah law requires a lulav to be at least one handbreadth taller than the other species. Why? So that it can be shaken.

By descending to this physical plane…a soul attains the potential to progress….

Souls in the spiritual realms are described as "standing", for they are rooted to a single level. Although they ascend, they are considered as being on one plane because these ascents are measured. By descending to the plane of the physical and devoting itself to the observance of the Torah and its mitzvot, a soul attains the potential for progress, and indeed, in an unlimited manner. This potential is demonstrated in a Jew's shaking back and forth during prayer and Torah study.

In fact, the Zohar states that a Jew shakes during prayer because "the soul of man is the candle of G‑d". Just as a candle flickers back and forth because it is drawn to its source, so too the soul shakes during Torah study, for Torah study inspires a soul and connects it to its spiritual source.

On the surface, this shaking runs contrary to the intellectual thrust necessary for Torah study. This is because the Torah must be comprehended thoroughly, and its study involves making fine distinctions, and this necessitates a state of contemplative reserve. Nevertheless, it is necessary to shake while studying Torah, for this indicates that even as the Torah is enclothed in an intellectual framework, it remains G‑d's wisdom. And when a person is involved in the comprehension of the Torah, it must be evident that the inner dimension of his activity is a clinging to G‑d.

This binding to G‑d generates the potential for unbounded progress, for G‑d is the essence of infinity. Since the ultimate connection with G‑d is achieved through Torah study, it is Torah study that generates the potential for unbounded progress. For this reason, the lulav, which is identified with the study of the Torah, is shaken.

Of course, the potential for progress generated by the Torah also has an effect on a person's observance of the mitzvot. And thus when the lulav is shaken, the other species are also moved. [Likkutei Sichot, vol. 10, p. 151] It is only after seeing an idea from all six sides, that one can truly grasp it….

Not only does Torah study produce the potential for unlimited progress, this potential is also reflected within Torah study itself. There are two manifestations of this concept:

First, a person must study Torah in a manner that leads to an increase every day. Every day, a person must gain new knowledge. This is the difference between the study of Torah and prayer. With regard to prayer, one repeats the same prayers every day. With regard to Torah study, by contrast, each day must bring an increase.

Secondly, our sages state, "A person will never comprehend the words of Torah unless he stumbles in them." One of the interpretations of this statement is that Torah study requires an intellectual give and take, a process of question and answer. At first, a person has one understanding of an idea. Later, his thinking shifts, and he sees it from a different vantage point. And then he adopts a third perspective. Thus he "moves" back and forth. It is only after seeing an idea from all six sides, that one can truly grasp it. [Likkutei Sichot vol. 5, pp. 151-2]