And Abraham again took a wife, and her name was Keturah
Keturah is Hagar. Why is she called Keturah? For her deeds were [now] as pleasing as the ketoret [incense].
Midrash Rabbah on verse
Hagar was the Egyptian maidservant of Abraham’s first wife, Sarah. When Sarah had failed to conceive a child after many years of marriage, she implored Abraham to have a child with Hagar. Hagar did give Abraham a child, Ishmael, who turned out to be “a wild man, whose hand is against everyone and everyone’s hand is against him.’’ Sarah ultimately demanded of Abraham that he banish Hagar and Ishmael from their home. When Abraham hesitated, G-d instructed him, “Whatever Sarah tells you to do, harken to her voice.” Hagar drifted back to the paganism of her homeland and found an Egyptian wife for Ishmael.
Years later, however, we find Ishmael back in the Abrahamic fold, accompanying Abraham and Isaac to the Akeidah. And then, three years after Sarah’s death, Abraham remarries Hagar. The reconciliation is now complete—indeed it is Sarah’s son, Isaac, who brings Hagar back for her marriage with his father.
“Everything that happened to the Patriarchs,” say our sages, “is a signpost for their children. This is why the Torah elaborates on…the events of their lives…for they all come to instruct the future.” The same is true regarding the shifts in Abraham’s relationship with his “barbarous” wife and son: his expulsion of Hagar and Ishmael and their subsequent readmission into his family represent the different stages in our history of dealing with the “Hagars” and “Ishmaels” in our lives—the raw and unruly elements in our nature, society and environment.
The Spiritualist, the Miner, and the Future
There are three basic ways of dealing with the mundane in one’s life: disavowal, refinement or sublimation.
The first approach is that of the ascetic, whose reaction to mundanity is to escape it. Repelled by the corporeality of physical life, he reduces his involvement in the material to the bare minimum and devotes his life to spiritual pursuits.
Then there is the “refiner,” who approaches the untamed wilderness of materiality as a prospector panning for gold. He knows that much of what passes through his hands is profitless sludge, but he is searching for the nuggets of sublimity embedded within. So he doesn’t disavow the material, but neither does he embrace it unequivocally. His life is an exercise in selectivity: to extract the sparks of potential while rejecting the irredeemable dross.
The third approach is that of the “sublimator,” who refuses to regard any element of G-d’s creation as “irredeemable.” He insists that every creature, every force, every experience, no matter how lowly, can be transformed into something positive and holy. There is nothing that is intrinsically negative in G-d’s world, he argues; evil and corruption are never more than skin deep. Everything can, and should, be transformed into a force for good.
These three approaches are actually three stages in the history of human potential. On the second day of creation, G-d divided His creation into two domains, decreeing that “The lower realms shall not ascend to the higher realms, and the higher realms shall not descend to the lower realms.”  The breach between the spiritual and the physical was absolute: the spiritual could not be actualized, nor could the physical be sanctified. Man had a choice—he could either succumb to the mundanity of the material, or he could transcend it. “Refining” or “sublimating” the material was beyond the capacity of a world in which an inviolable boundary separated the holy from the profane.
This state of affairs prevailed for the twenty-six generations from Adam to Moses. Then G-d rescinded His decree. On the sixth of Sivan in the year 2448 from creation (1313 BCE), “G-d descended upon Mount Sinai,” setting the precedent that the supernal may permeate the earthly, “and to Moses He said: ‘Ascend to G-d,’ ” empowering the earthly to be elevated.
The era of “refinement” (birur) commenced. At Sinai, we were enfranchised to extract kernels of holiness from the husk of materiality. We were given a guidebook, the Torah, to teach us how to distinguish between that which can be positively utilized and that which must be rejected. The Torah spells out which foodstuffs are elevated when they energize our positive deeds, and which coarsen our minds and hearts and deaden our spiritual sensitivities; which relationships can bring love, joy and sanctity to our marital lives, and which are exploitative and debasing. The same applies to every area of life: the Torah instructs us which elements of physical life we are to embrace and develop, and which we are to reject and disavow. To attempt to go beyond this guide–to seek to sublimate that which the Torah decrees to be irredeemable–is futile and counterproductive. Just as pre-Sinai man was incapable of bridging the divinely imposed barrier between matter and spirit, so, too, are we capable of sanctifying only that which the Creator of life has empowered us to sanctify. 
Finally, G-d promises that there will come a time when “I shall remove the spirit of impurity from the earth.” A time when all evil and negativity shall cease from the earth and the positive essence of every creature and phenomenon in G-d’s world shall come to light. No longer will we face the daily challenge of winnowing the holy from the profane; no longer will we know the pain of being compelled to relinquish potent areas of our lives because of our inability to properly and constructively channel them. Instead, we will inhabit a world in which everything will naturally lend itself to a good and G-dly end.
Abraham lived in the pre-Sinai era. This means that, ultimately, his achievements were confined to the spiritual realm. He forged the Jewish soul, developing his own life into a paradigm of lovingkindness and commitment to G-d, and bequeathing these qualities to his descendants. He battled the near-universal paganism of his time, prevailing upon many of his generation to renounce their idols and recognize the one G-d. But the physical substance of creation was largely unaffected; the divine demarcation between the spiritual and the material was still in force, precluding any human endeavor to sanctify the mundane.
Nevertheless, as “father” and archetype of the Jewish nation, Abraham embodied the entire history of our mission in life. So Abraham’s life also included a transcendent “pre-Sinai” period, a “refinement” period, as well as the futuristic “sublimation” era. These three phases in the life of Abraham are delineated by the three sidrot (Torah sections) which the Torah devotes to Abraham’s life: Lech Lecha (Genesis 12-17), Vayeira (18-22) and Chayei Sarah (23-25).
The exclusively spiritual period in Abraham’s life lasted until his circumcision. The divine instruction to circumcise himself was Abraham’s “Sinai”—the first (and only) occasion on which G-d commanded a mitzvah (Torah commandment) to him. For the first time in his life, Abraham could perform a mitzvah—an act that carries a divine empowerment to transform a physical entity (in this case, his own body) into a vehicle of spirituality and G-dliness, through its utilization as an agent of divine will.
[This explains a curious detail of Abraham’s behavior related by the Torah. When Abraham wanted his servant, Eliezer, to take an oath, he told him to “place your hand under my thigh.” An oath is taken while holding a sacred object such as a Torah scroll or tefillin; here Abraham is telling Eliezer to swear on the part of his own body sanctified by the mitzvah of circumcision. Yet our sages tell us that “Abraham observed the entire Torah” though it was yet to be given [at Sinai] —so Abraham studied Torah, put on tefillin, affixed a mezuzah on his doorpost, etc. It would therefore seem that he had no shortage of “sacred objects” available to him. Why, then, did he have Eliezer place his hand “under his thigh,” contrary to all common standards of modesty and propriety?  But as explained above, the import of Abraham’s pre-Sinai mitzvot were of a wholly spiritual nature. Since G-d had not commanded him to do them, they remained human deeds, subject to the natural law that separated the spiritual from the material; while they had a profound effect on his own soul, the souls of his descendants, and the spiritual essence of creation, they had no impact on the material substance of the universe. The single exception was the mitzvah of circumcision, whose commandment by G-d constituted an empowerment to sanctify the physical. Thus, this was indeed the only sacred object available to Abraham.]
The significance of this watershed event in Abraham’s life is emphasized by the fact that, upon commanding him to circumcise himself, G-d changed Abraham’s name. Originally, the first Jew’s name was Abram; G-d added the Hebrew letter hei to make it Abraham. “Abram” is an acronym for the Hebrew words av ram—“exalted father”; “Abraham” stands for av hamon goyim—“father of a multitude of nations.” Before he was granted the commandment of circumcision, Abram was an exalted father—a progenitor of spiritual achievements and a bequeathor of a spiritual legacy; his deeds, however, remained “exalted,” beyond the realm of the material. Upon his circumcision, Abraham assumed a role of influence upon “a multitude of nations”—a role that involved his refinement and elevation of the pedestrian and the mundane (to the extent that this was possible before Sinai).
The Refining Female
“Male and female He created them,” is how the Torah describes G-d’s creation of human life. Indeed, this duality extends to all forms of life, and to all elements of creation—heaven and earth, sun and moon, energy and matter, and the numerous other physical models of the masculine and feminine. The same is true of the spiritual essence of life—our relationship with G-d comprises both a “male” initiating and achieving aspect, and a “female” receptive and nurturing element.
Thus we find that many mitzvot are commanded solely to the man, while others are the domain of the woman: a husband and wife, our sages explain, embody the two halves of a single soul; the deeds of each contribute to their common soul’s fulfillment of both the “masculine” and “feminine” elements of its mission in life. More specifically, each mitzvah is both a “male” and “female” act: it is an act of conquest, of aggressive appropriation of resources from an alien domain for holy purposes, as well as an act of nurture—of refining, purifying and developing the appropriated resource into a vessel of holiness. In the words of the Talmud, “Man brings home grain; but does he chew grain?”  Man wrests nutritive potential from the earth, but it is the woman who winnows the chaff from the cereal, sifts the fine flour from the coarse, and kneads, forms and bakes it to edible perfection.
Thus it was Sarah, the female half of Abraham’s soul, who effected the expulsion of Hagar and Ishmael. When Abraham hesitated, loath to relinquish the potent potentials implicit in his pagan mate and wild son, G-d said to him: “Whatever Sarah tells you to do, harken to her voice.” True, you are now Abraham, father of multitudes and elevator of the mundane, but in every refinement process there is the extractable ore and the unprofitable rubble. Hagar and Ishmael represent elements of My creation too crude, too volatile, to be redeemed by your efforts. Sarah, your feminine sense of differentiation, has rejected them—do as she says. 
However, Abraham’s life includes a post-Sarah era as well—an era in which the most savage of Ishmaels and the most foreign of Hagars have a place in Abraham’s family.  An era that is the forerunner and prototype for the age of sublimation, when “no longer will your Master be cloaked; your eyes shall see your Master” —when the divine essence of creation will no longer be shrouded in a mantle of corporeality and the positive utility of every creature will be manifest and accessible.
Based on the Rebbe’s talks and works, including an address delivered on Shabbat Chayei Sarah, 5737 (November 20, 1976) 
 The incense offered in the Holy Temple.
 Genesis 16:1-3.
 Ibid. 16:12; see Rashi on ibid. 21:9.
 Ibid. 21:12.
 Ibid. 21:21; Midrash Rabbah on ibid. 21:14.
 Midrash Rabbah on ibid. 22:3 (the Akeidah is the “Binding of Isaac,” related in Genesis 22). See also Rashi on ibid. 15:15 and 25:9.
 Born fourteen years after Ishmael.
 Midrash Rabbah on Genesis 24:62.
 Nachmanides on Genesis 12:6
 “And G-d said: ‘Let there be a firmament in the midst of the waters, and let it divide water from water.’ And G-d made the firmament, and divided the waters beneath the firmament from the waters above the firmament; and it was so. And G-d called the firmament ‘heaven.’ ’’
 Midrash Tanchuma, Va’eira 15—see following note.
 Midrash Tanchuma, ibid.: “Once there was a king who decreed: ‘The people of Rome are forbidden to journey to Syria, and the people of Syria are forbidden to journey to Rome.’ Likewise, when G-d created the world, He decreed: ‘The heavens are G-d’s, and the earth is given to man’ (Psalms 115:16). But when He wished to give the Torah to Israel, He rescinded His original decree, and declared: ‘The lower realms may ascend to the higher realms, and the higher realms may descend to the lower realms. And I, Myself, will begin’-as it is written, ‘And G-d descended on Mount Sinai’ (Exodus 19:20), and then it says, ‘And to Moses He said: Go up to G-d’ (Exodus 24:19).”
 While no “reason” can explain the divine will, Chassidic teaching offers many insights into the function of our dual mission in life, which consists of both a positive, developmental element and a negative, receptive one. For one example, see Yes and No, WIR vol. XI, no. 8.
 Nevertheless, we enjoy a weekly “taste” of the future on Shabbat, when mundane activities such as eating and sleeping are transformed intowholly sacred activities (as opposed to our weekday physical activities, in which the G-dly utility most be “extracted” from its material husk—see A Private World, WIR, vol. V, nos. 25 and 28). Another example is teshuvah, through which “sins are transformed into virtues,” transcending the Torah’s division of reality into redeemable and irredeemable elements (see Sin In Four Dimensions, WIR, vol. VII, no. 3, and Knowledge and Naught, WIR, vol. VI, no. 29).
 Zechariah 13:2.
 Thus our sages have said: “Why is the swine called chazir? Because in the future, G-d will give it back (l’hachaziro) to Israel.” (See sources cited in Likkutei Sichot, vol. XII, p. 75.)
 The Torah is divided into 53 sidrot, or weekly Torah readings.
 Genesis 24:2; cf. Jacob’s similar administration of an oath to Joseph (Genesis 47:29).
 Talmud, Yoma 28b.
 See Talmud, Niddah 13a; Tur and Shulchan Aruch, Orach Chaim 3:14.
 Genesis, 17:5; Torah Ohr, Lech Lecha 11a.
 Genesis 1:27.
 Zohar, part I, 91b; The Ari’s Likkutei Torah, Bereishit 15a. See Pre-Marital Marriage, WIR vol.VI, no.41.
 Talmud, Yevamot 63a.
 Thus Rabbi Menachem Mendel of Lubavitch explains the enigmatic passage in the Talmud (Bava Batra 58a) in which Sarah is described as holding Abraham’s head in her arms and picking lice out of his hair (Ohr Hatorah, Chayei Sarah 119b-125a).
 Thus Hagar is here called “Keturah,” connoting the fact that “her deeds were as pleasing as the ketoret.” For the ketoret, too, represents the transformation of the “irredeemable” elements of creation into a vessel of holiness (see Torah Ohr, Toldot 20b-c).
 Isaiah 30:20.
 Paradoxically, the Torah section that deals with the post-Sarah years of Abraham’s life is named Chayei Sarah— “the Life of Sarah”! In truth, however, this is no paradox, as these events represent the realization of the ultimate purpose of Sarah’s earthly life (see Likkutei Sichot, vol. XV, pp. 145-154).
 Likkutei Sichot, vol. XV, pp. 174-178; Reshimot #2, pp. 3-6.