Inner Root Of Yisrael
ובמדרש כי מראש צורים אראנו כו' משל לפקח שבא לשורש כו' ומצאן קשה כו'
In the Midrash on the verse "For from the top of the rocks I see him" (Bamidbar 23:9): a parable to a clever man who came to the root, and found it hard.
The Sfas Emes opens with a Midrash comparing Bilam to a clever man who reached the root of a tree but found it too hard to uproot.
פי' כי בלעם התפאר עצמו בזה שהשיג שורש בנ"י
The explanation is that Bilam prided himself in this, that he had grasped the root of Bnei Yisrael.
Bilam boasted that he had penetrated to the very source of Bnei Yisrael.
ובאמת הבורא ית' עשה הכל לטובת בנ"י שעל ידי שהשיג השורש נשתתק
But in truth, the Creator, may He be blessed, did all this for the good of Bnei Yisrael, for through grasping the root he was struck dumb.
In reality Hashem arranged this for the benefit of Bnei Yisrael, because once Bilam reached their root he was rendered powerless to curse.
ובלק הי' רואה במדריגה קטנה שיש לבנ"י תוך כל האומות לכן עלה בדעתו ללחום עמהם
Balak saw only the lower level that Bnei Yisrael possess while they are among all the nations, and therefore it entered his mind to wage war against them.
Balak perceived only the diminished level of Bnei Yisrael as they appear mixed among the nations, which gave him the false confidence to attack.
אבל בלעם ע"י שהראהו כח השורש של בנ"י ושם לא יש שום מגע נכרי ושום כח שר וסט"א אינו נוגע שם
But Bilam, since Hashem showed him the power of the root of Bnei Yisrael, and there no foreign contact has any hold, and no power of an angelic minister nor of the Sitra Achra can touch that place.
Bilam, by contrast, was shown the inner root of Bnei Yisrael, a place that no foreign influence, no angelic minister, and no Sitra Achra can ever reach.
וז"ש וירא כו' ישראל שוכן לשבטיו הוא יעקב אע"ה ישראל סבא וז"ש לשבטיו
This is the meaning of "And he saw... Yisrael dwelling according to its tribes" (Bamidbar 24:2) — this refers to Yaakov Avinu, peace be upon him, Yisrael Saba, and that is the meaning of "according to its tribes."
The verse "Yisrael dwelling according to its tribes" hints at Yaakov Avinu, called Yisrael Saba, the unifying root from which the tribes branch out.
וז"ש מה טובו אהליך יעקב משכנותיך ישראל
And this is the meaning of "How goodly are your tents, Yaakov, your dwelling places, Yisrael" (Bamidbar 24:5).
The blessing "How goodly are your tents, Yaakov, your dwelling places, Yisrael" expresses this same idea through its two names.
הם ב' הבחי'
These are the two aspects.
The two names Yaakov and Yisrael correspond to two distinct aspects of Bnei Yisrael.
יעקב הוא העבודה בעוה"ז בין האומות
Yaakov is the avodah in this world among the nations.
The name Yaakov represents the avodah carried out in this lowly world while surrounded by the nations.
וישראל הוא שורש בנ"י למעלה ושם מקום המנוחה בחי' מנוחת שבת דכתיב ביני ובין בנ"י אות הוא ואין שם מגע נכרי ושם שוכן ישראל במנוחה וזהו משכנותיך ישראל
And Yisrael is the root of Bnei Yisrael Above, and there is the place of rest, the aspect of the rest of Shabbos, of which it is written "Between Me and Bnei Yisrael it is a sign" (Shemos 31:17); and there no foreign contact has any hold, and there Yisrael dwells in rest, and this is "your dwelling places, Yisrael."
The name Yisrael represents the elevated root of Bnei Yisrael Above, the place of Shabbos-like rest sealed off as a private sign between Hashem and Bnei Yisrael, untouchable by any foreign hold.
ולמטה צריכין מכסה והגנה וז"ש אוהליך יעקב
And below, one needs a covering and a protection, and this is the meaning of "your tents, Yaakov."
Down in this world, by contrast, one requires a covering and shield against outside influences, which is why the verse calls it the "tents" of Yaakov.
ומ"מ ב' הבחי' תלוין זה בזה
And nevertheless the two aspects are dependent one upon the other.
Even so, these two aspects are bound together and each depends upon the other.
וכן הוא בפרטות כל איש ישראל שעל ידי שצנוע במעשיו ושומר עצמו בחיצוניות המדות בפשיטות זוכה אח"כ לבוא אל השורש והפנימיות:
And so it is in the particular case of every individual of Yisrael, that through being modest in his deeds and guarding himself in the outer character traits with simplicity, he afterward merits to come to the root and the inner dimension.
On the personal level, when a person conducts himself with modesty and guards his outward middos simply and sincerely, he eventually merits to reach his own inner root and pnimiyus.
Summary: The Sfas Emes explains that Bilam prided himself on having grasped the very root of Bnei Yisrael, yet Hashem orchestrated this for their good, since reaching that root left him powerless to curse. Balak saw only the lowered level of Bnei Yisrael as they appear among the nations and thought he could fight them, but Bilam was shown the inner root that no foreign force, angelic minister, or Sitra Achra can touch. This is the meaning of the two names in his blessing: Yaakov is the avodah in this world amid the nations, requiring a covering and protection like "tents," while Yisrael is the root Above, the place of Shabbos rest that serves as a private sign between Hashem and Bnei Yisrael. The two aspects are bound together and depend on one another. So too in each individual: through modesty and simply guarding his outer middos, a person merits to arrive at his inner root and pnimiyus.