At the end of "The Life of Sarah" is a story of Avraham taking another wife, Ketura. The Torah tells us that "Avraham gave all that he had to Yitzchak; but to the concubine-children...Avraham gave gifts." Interesting how Avraham can give everything to Yitzchak and somehow have leftovers to be given as gifts to these children of Ketura. Furthermore, what exactly are these gifts, and why didn't Yitzchak get any gifts? Are they better than what Yitzchak received? So, there are commentaries who say that these gifts are shmos hatumah (the names of unholiness); this interpretation derives from the missing Vav in the word "matanos" (gifts) which Chazal understood as indicating tumah (unholiness). This needs understanding, how these gifts are impure and why specifically because there is a missing Vav.
One of the students of the Arizal, the "Sifsei Kohen" says that the tachlis (purpose) in Avraham bringing more children into the world through Keturah is that there shouldn't be any psoles (waste, unrefined midot) given to Yitzchak. This is similar to Avaraham having Yishmael, which is even more of a refining act. This also needs explanation, for what is the idea behind this purifying? The idea is that, since the eating from the tree of knowledge, our entire existence and reality is infused with a mixture of good and bad. On the level of the tree of knowledge, our every good thought, speech, and action has in it measures of bad intention, and vice versa. In order to rectify this mixture, the Avos (Fathers) produced their different and contrasting children: through Avraham came Yitzchak and Yishmael, through Yitzchak came Yaakov and Eisav. In this way, they were mtaken (rectified) the eating from the tree, through separating the extreme aspects of their midot away from their main progenic continuation. Through the extreme and negative aspect of chesed, expressed in Yishmael's complete lack of gvul (boundaries), was Avraham's chesed refined; through having a separate manifestation of uncontrolled chesed can chesed be purified. But if so, then why was Avraham still in need of further refining his chesed through having the children of Ketura?
Shlomo Ha-Melech writes in Mishlei, "He who hates gifts will live". What is bad about receiving gifts? The guy gave with a full heart, what's the problem? The MaHaRaL says that there are two paths of acquiring in the world. One is bshoresh (from the root) and the other is bchiluk (separated from the root). For example, fruit that grows on a tree and fruit that is pasted onto a tree: the fruit that grows from the tree is an expression of the tree's chiyut (life force), it is an outcome and manifestation of the roots and essence of the tree; as opposed to fruit pasted onto a tree, that fruit will wilt because it is external and not from within. With a person who works for something, the fruit of his labor is expressing the soul that he put into it; a man who makes a table, so the table is him, he created it and it is him. "When you eat from the labor of your hands, Ashreicha V'Tov lach (Fortunate are you and good is it for you)" says David Ha-Melech. The MaHaRaL says that chiyut requires staying away from things labeled matana, from things that come from outside of me. The Mtziyus (reality) of this world is that to the extent that one labors and invests in something, to that extent, is it his, is it him; and to the extent that one receives something without having invested in it, to that extent, is it "pasted" on, it is not truly a manifestation and expression of his soul-essence and root.
ChaZaL learn out from the pasuq that Ketura is Hagar who did tshuva, who tied herself to Hashem. (Ketrua and Kesher (tie) are interchangeable.) But tying is not Dibuk; tying is an external connecting, while dibuk is deep union. The pasuq says, "Vdabak bishto"; that is, not to tie oneself to their soul-mate, but to be mdabek, to be one. The Torah says that Isha is named for being taken from Ish; "Ki m'Ish Lukacha", that man and woman are inherently one and separated into two different bodies, but they are not tied together. ChaZaL understood Hagar's tshuva as being tied to Hashem, but not nidbak (profoundly one'ed) like Tzadikim; there remained a layer of separation.
When the Torah says that Avraham gave Yitzchak everything, that means that Avraham gave Yitzchak Avraham. Inheritance is the parents infusing their essence to the progeny, it is an inner dimension of transfer, of union between Av and Ben. Not so by gifts. If A gives B a gift, so B has a gift, but it isn't atzmiyus (essence). The Vav is always the letter of chibur, of inner connection and shefa (spiritual influx into the world), and these gifts that Avraham gave to the children of Ketura were missing this Vav; they were missing this inner connection from Avraham, for they were outside. The union of Avraham and Ketura was a zivug of tosefet (additional union). It was not enough for Avraham to refine his mida of chesed through ridding his progeny of the extreme lack of gvul expressed in Yishmael, for there remained this aspect of chesed called matana. On a deepest level, giving a gift is not chesed, because it takes away from the person's life force; he now has something which he did not labor and invest in, he now has something which is not him. True chesed is "teaching a man to fish" as opposed to "giving a man a fish". Teaching is true chesed for it allows the student to take the information and develop it into his own ideas, his own chelek (unique vision) in Torah. Hearing and learning Torah from others, especially those who are levels beyond where one is at the moment, is not only about understanding someone else's Torah, not merely about moving in their direction. Rather, hearing and learning can be guiding lights and can be opportunities to touch one's makif (unactualized potential levels of self). Hearing and learning allow one to internalize and chew on his own until he has developed and refined his chelek, his nekuda and unique color in the rainbow of Torah. It would not be chesed for one to give a lot of information to someone; for all that remains someone else's will wilt away and be dry of any depth and meaning as long as it does not develop into one's own chelek in Torah.
This aspect of chesed is what Avaraham refined through being with Ketura. The result of being with she who is "tied" to Hashem (as opposed to being one with Hashem) is children who receive gifts and not the inheritance of Yitzchak. This parashah of the Life of Sarah that is coming down this Shabbos should infuse us all with the spiritual yearning to find each of our unique chalakim in Torah and Avodas Hashem (Relationship with God). We should all be blessed to develop the ways in which we unify with Hashem in the deepest of ways and never settle for a tie.
(Based on shiurim from R' Lopiansky.)