After being warned not to go with Balak’s emissaries, Balaam acted against G-d’s command and proceeded to travel on his donkey to curse the Jewish People. Balaam’s donkey too disobeyed its master and first veered off the path, then scraped Balaam’s foot (regel) against a wall, and finally crouched underneath Balaam, refusing to continue. Following each act of disobedience, Balaam hit his donkey. Finally, the donkey miraculously opened its mouth and said, “What did I do to you that you hit me these three times (shalosh regalim)?” It soon became clear that the donkey was following the directives of an invisible angel, which suddenly Balaam was now able to see. The angel also told Balaam off for hitting the donkey three times (shalosh regalim). Another way to say “three times” in Hebrew is shalosh peamim, as each instance is called a paam. The word regel usually means “foot”, so why here does it mean “instance”? Moreover, what is the thematic connection between paam and regel?

The Malbim explains that the word paam means “corner”. (It is similar to the word peah.) For this reason the four corners on the bottom of the Ark (Ex. 25:12) are called arbah paamotav (“its four corners”). That being said, one’s feet are also called a paam because they are at the bottom corner of his person. In this way, the word paam appears to be synonymous with the word regel (foot). This explains the meaning of the doublet raglei ani, paamei dalim (“the feet of the poor, the feet of the destitute”) found in Isaiah 26:6.

Rabbi Shlomo Pappenheim of Breslau (1740-1814) writes that the word paam is derived from the bilateral root PEH-AYIN. Words derived from this root refer to consistent movement and/or sound. An example of this is the word efeh,which refers to the cries of a woman in childbirth (Isa. 42:14), and to the consistent noise of the rattlesnake. Similarly, the verb po’em refers to the consistent beat of the heart (Gen. 41:8) and a paamon (“bell”) is characterized by the sound of the clapper, or uvula, hitting a hollow shell. The word paam can also refer to the act of taking a step, or even a foot, because of the foot’s metronomous way of moving when one walks. Each time one’s foot touches the ground, he has taken another step, so, in essence, a paam is defined as each time one’s foot touches the ground. As an outgrowth of this meaning, the word paam came to mean "each instance” of anything that happens in the greater context of the world. Parallel to that, the word regel also refers to “an instance”. Because of this phenomenon, the phrases shalosh peamim and shalosh regalim can both mean “three times” and “three feet”.

The truth is that the word regel in the sense of “instance” appears in the Bible in only one other context: concerning the three festivals. Pesach, Shavuot, and Succot are described collectively in Exodus 23:14 as the shalosh regalim (“the three times”). On those three festivals there is a special commandment that requires all able-bodied Jewish men to present themselves before G-d in the Temple. Those “pilgrims” travelled to Jerusalem on foot, which further cements the association between the two meanings of the word regel. In this spirit, tradition applies a passage in Song of Songs to the thrice-yearly pilgrimages: “How beautiful are your footsteps (paam) in your shoes, daughter of nobles” (Songs of Songs 7:2).

As we already noted, the word paam also appears as a component of the Holy Ark, as Exodus 25:12 refers to its bottom corners as arbah paamotav (“its four corners”). Both Targum Onkelos and Rashi explain that the four paamim of the Ark refer to its four corners. Ibn Ezra, however, disagrees, and explains that it refers to four “feet” which were attached to the bottom of the Ark (see also Ramban there).

Rabbi Shmuel Dovid Walkin (d. 1979) offers a fascinating insight into why the Ark needed "feet" on its bottom. He notes that while the word paam might sometimes mean "foot", that is really a borrowed usage. The primary meaning of paam is "step". Accordingly, Rabbi Walkin explains that the Ark required "feet" to teach us an important lesson: man must always be on his feet—ready to move forward. Even the Ark — which was the pinnacle of holiness, as it housed the Tablets given to Moshe at Mount Sinai — needs feet, because it is not to remain stationary.

The "feet" on the Ark teach us that just as the Ark should not expect to remain stationary, so should any Jew never stagnate in his Torah studies. Rather, he should have “feet” with which he must continuously strive to reach greater and greater levels. This is alluded to in the word paam,which, unlike the word regel,denotes movement, not just the simple notion of a foot. Angels have a single regel (see Ezek. 1:7) because they are not destined to move from the way they were created. Angels have no free-choice, and, therefore, no opportunity for growth by making the correct decisions. Man, on other hand, is a mobile creature. Man has “feet” in the sense that man must constantly contend with changing situations that challenge him to make the right choices. Balaam, of course, failed do so, and so he is undeserving of the word paam in any sense of the word.

• L'iluy Nishmat my mother Bracha bat R' Dovid and my grandmother Shprintza bat R' Meir

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