Eternal Imprint of Holiness
בפסוק אבד תאבדון כו' ל"ת כן לה' כו'
On the verse "You shall surely destroy [all the places where the nations served their gods]" (Devarim 12:2), the Torah continues, "You shall not do so for Hashem your God" (Devarim 12:4).
The verse commands the total destruction of every site of idol worship, while warning that one must never treat the service of Hashem in that same manner.
ויש לפרש דקאי עמ"ש מקודם ואבדתם כו' שמם מן המקום ההוא
And one may explain that this refers back to what was stated earlier, "And you shall destroy their name from that place" (Devarim 12:3) — that the very name of the idol is to be obliterated from the place where it stood.
The Sfas Emes ties this back to the earlier command to wipe out even the name of the idol from its place — idolatry leaves no lasting trace once destroyed.
אבל סטרא דקדושה נודע כי בכל מקום שיש השראת קדושה נשאר לעולם רשימה
But on the side of kedushah it is known that in every place where there has been a resting of holiness, an imprint remains there forever.
He contrasts this with kedushah: wherever holiness has once rested, a permanent residue of that holiness is left behind that never disappears.
לכן אף שבהמ"ק חרב מ"מ לשכנו תדרשו כמ"ש ציון היא דורש כו' מכלל דבעיא דרישה
Therefore, even though the Beis HaMikdash lies in ruins, nevertheless "to His dwelling place shall you seek" (Devarim 12:5), as it is written, "Tziyon — there is none who seeks her" (Yirmiyahu 30:17), from which it is inferred that she requires seeking.
Because of this enduring imprint, even though the Beis HaMikdash is destroyed, the Torah still bids us to seek out His dwelling place; the verse in Yirmiyahu teaches that Tziyon is precisely the thing that demands our seeking.
עי"ז ובאת שמה
And through this — "and there you shall come" (Devarim 12:5).
It is specifically through that seeking that the promise "and there you shall come" is fulfilled.
כי ע"י הזכירה שמבקשין בנ"י תמיד בפה ובלב בכל יום תמיד בנין בהמ"ק
For through the remembrance that Bnei Yisrael are always requesting, with the mouth and with the heart, every single day continually — the rebuilding of the Beis HaMikdash —
The constant longing of Bnei Yisrael, expressed both verbally and in the heart, for the rebuilding of the Beis HaMikdash, is itself the avodah of seeking.
עי"ז יתעורר כח הרשימה הנשאר קיים לעולם ויהי' הגאולה עי"ז במהרה בימינו אמן:
through this the power of the imprint that remains in existence forever is awakened, and through this the geulah will come speedily in our days, amen.
This yearning arouses the everlasting imprint of holiness that remains in the place, and through it the geulah will arrive speedily.
Summary: The Sfas Emes draws a sharp contrast between the side of impurity and the side of kedushah. Idolatry must be utterly destroyed, its very name erased, leaving no trace in the place where it stood; but wherever holiness has rested, an imprint remains forever. For this reason, even though the Beis HaMikdash lies in ruins, the Torah commands "to His dwelling place shall you seek," and Yirmiyahu's words "Tziyon — there is none who seeks her" teach that Tziyon specifically requires our seeking. The daily longing of Bnei Yisrael, voiced with both mouth and heart, for the rebuilding of the Beis HaMikdash is that very act of seeking. This yearning awakens the everlasting imprint of holiness left in the place, and through it the geulah will come speedily in our days.