Shofar and Torah arouse Divine mercy

עיקר השופר לעורר רחמים בזכות התורה דאיתא עלה במחשבה לברוא במדה"ד וראה שאין העולם מתקיים ושיתף עמה מדה"ר.

The essence of the shofar is to arouse rachamim (mercy) in the merit of the Torah, for it is brought that it arose in the [Divine] thought to create the world with the attribute of strict justice (middas hadin), and He saw that the world could not endure, so He joined to it the attribute of mercy (middas harachamim).

The shofar's purpose is to awaken Divine mercy. The Sefas Emes recalls the Midrash: the world could not stand on strict justice alone, so Hashem partnered justice with rachamim — and that partnership, he will show, is the Torah.

זה התורה דאיתא מי שאין בו דעת אסור לרחם עליו.

This is the Torah, for it is brought: "One who has no da'as (understanding) — it is forbidden to have mercy on him."

Chazal teach that mercy properly rests upon one who possesses da'as. The capacity that makes a person a fit recipient of rachamim is da'as — the knowledge that comes from Torah.

והקב"ה בחסדו נתן לנו התורה שנזכה לדעת ועי"ז מרחם עלינו.

And the Holy One, blessed be He, in His chesed gave us the Torah so that we would merit da'as, and through this He has mercy upon us.

By granting us the Torah, Hashem gave us the very da'as that makes us worthy of His mercy — so the Torah is the channel through which rachamim becomes possible.

לכן נק' התורה רחמנא בגמ' שכל הרחמים בא בכח התורה.

Therefore the Torah is called "Rachmana" (the Merciful One) in the Gemara, for all mercy comes through the power of the Torah.

The Gemara's name for the Torah, "Rachmana," reveals its essence: it is the source through which all Divine mercy flows into the world.

וע"ז נאמר אתה הראת לדעת שחונן לנו הקב"ה דעת התורה.

And concerning this it is said: "You have been shown, that you may know" (Devarim 4:35) — that the Holy One, blessed be He, graces us with the da'as of the Torah.

The verse "Atah hareisa lada'as" alludes to Hashem granting us the knowledge of the Torah — the da'as that draws His mercy upon us.

וזהו יודעי תרועה בדעת.

And this is "those who know the teruah" — with da'as.

"Yodei teruah" — the verse praising those who know the sound of the shofar — really means those who possess the da'as of Torah, which is what awakens mercy through the teruah.

וכן כתיב מדי דברי בו כו' רחם ארחמנו.

And so it is written: "As often as I speak of him… I will surely have mercy upon him" (Yirmiyahu 31:19).

The very act of "speaking of him" — words of Torah and connection — draws down a doubled measure of rachamim, "rachem arachamenu."

ולכן על ידי השופר עומד מכסא דין ויושב על כסא רחמים:

Therefore, through the shofar, He rises from the throne of judgment and sits upon the throne of mercy.

Because the shofar arouses the merit of the Torah — the source of all rachamim — it moves Hashem, so to speak, from the throne of din to the throne of rachamim on the Day of Judgment.

Summary: The shofar's purpose is to arouse Divine mercy through the merit of the Torah. Since the world could not stand on strict justice alone, Hashem joined rachamim to it — and that mercy comes through the Torah, which grants us da'as, the very quality that makes a person a fit recipient of mercy. This is why the Torah is called "Rachmana," and why blowing the shofar on Rosh Hashanah lifts Hashem from the throne of judgment to the throne of mercy.