Leap-Month of Adar
Last week we explained, based on Rav Natan of Breslav, the deeper significance of the "leap years" which add an extra month in order that a year made up of lunar months can be synchronized with the seasons. The sun, which is the origin of light, represents the absolute source of truth. But this truth is reflected and expressed to a greater or lesser degree in our imperfect world. This is often symbolized in Chasidic thought by the fact that the moon merely reflects the light of the sun, and does so erratically: at the time of the new moon the night sky is dark, at the full moon the moon reflects far more light.
According to this symbolism, our job on earth is to align our actions as much as possible towards G^d's light as revealed in the Torah. This will ultimately result in restoring the "deficiency" of the moon and bringing about a state where this material, sublunary world perfectly expresses God's will.
Rav Natan adds two insights to this widespread understanding. First of all, he explains that the "real" truth according to our circumstances is not the supernal truth represented by the sun, nor the circumscribed this-worldly truth represented by the moon, but precisely the unity or reconciliation of the two. (This is significantly different from a Platonic perspective where the worldly expression of truth is considered a mere illusion or distortion.) The other insight is that the lack of harmony between sun and moon is represented not only by the amount of light but also by the lack of synchronization. The moon is not only an imperfect mirror, it is also an imperfect timekeeper. Thus intercalation is also a way of bringing together the sun and the moon and making this world a more perfect expression of holiness. This is done by a Beit Din, who represent the ability to exercise judgment in accordance with Torah.
Based on this, Rav Natan explains why the leap month is specifically Adar. Adar is the month that especially exemplifies this aspect of truth. The nature of Amalek is that they completely deny Godliness in the world, and believe that all is according to chance or nature. (While Rav Natan does not say so, we can point out that Haman chose the time to carry out his plan by chance, the PUR or die, and that the holiday is named Purim precisely for this scheme. Note also that the die were cast for which month, hinting perhaps at the identification of Amalek solely with the barren "lunar" aspect of reality. See Esther 3:7.)
That is why Hashem states that His name will not be complete until Amalek is wiped out (Shemot 17:16 and Rashi's commentary). The two aspects or parts of the four-letter name correspond in our mystical symbolism precisely to the sun and moon aspects of holiness. Since Amalek stubbornly deny any connection between the two, they constitute an obstacle to their complete unity and synchronization. Only when the darkness of denial is completely overcome can Hashem's radiance be completely realized in this world.
Another halakha related to Adar is that this is an auspicious month for judgments with non-Jews (Mishna B'rura 686:8). We can relate this also to the insight of Rav Natan.
Some of the nations which are our sometime rivals have a calendar based solely on the lunar month; the calendar years are not at all related to the cycle of the seasons. This reminds us of an excessive tendency to realism, to conducting our affairs according the circumscribed reality of the "real world" without being enlightened and inspired by higher ideals.
Other nations have a calendar based solely on the solar year; the months are not at all related to the cycle of the moon. This reminds us of an excessive tendency to idealism, to act according to higher ideals even when these are completely inappropriate to the actual circumstances we face.
The Jewish calendar, adding an extra lunar month to remain synchronized with the solar year, overcomes both of these tendencies. Thus it gives us a "victory" in attaining true and balanced judgment in the "court" of our relations with other nations.
Based on Likutei Halakhot Dayanim III:11,12,19