I
"'Avraham took a wife whose name was Keturah' (Breishis 25:1). This is Hagar, but she is called Keturah because her deeds were as beautiful as ketores (incense), and because she tied (kashra) her entrance, as she did not have relations with any man from the day she separated from Avraham" (Rashi). The Mizrachi says "Keturah refers to 'katra', which is Aramaic for 'kashra', tied" (Mizrachi).
It makes sense that ketores is etymologically connected to katar - tying, since the ketores represents tying all Jews together. We see this when the gemara (Kerisus 6b) says, "Any fast day that does not include the sinners is not a fast" and cites two proofs: first, that the foul-smelling chelbana (galabanum) is among the spices of the ketores, and second, that the navi (Amos 9:6) says, "Va'agudaso (when they are all tied together, Rashi) [then] He founded the earth." Once again we see that ketores is connected to tying.
On Yom Kippur the ketores was ground into especially thin particles (daka min ha'daka, ibid). This signifies that on the unique Torah fast day, all Jews must be enmeshed in even greater closeness. Yom Kippur is a "day of love and friendship, a day without jealousy and competition" (Mussaf). We begin Yom Kippur, right before Kol Nidrei, by allowing sinners, even those who are banned for the rest of the year, to join the community in prayer, as the ketores teaches.
The plague in the aftermath of Korach's rebellion was stopped by the ketores (Bamidbar 17:12, 13). The people had complained that the ketores is a deadly poison, since through it Nadav and Avihu and two hundred and fifty people died. Hashem said, "You will see that the ketores stops a plague and sin is what kills" (Rashi).
The sin that kills is machlokes - quarrelling, an act prohibited so as not to follow the behavior of Korach and his group (17:5, see Sanhedrin 110a). Moshe warned them (Rashi 16:16), "The ketores is the most beloved offering, but it contains a deadly ingredient. We have one Hashem, one Ark, one Torah, one Altar, and one Kohen Gadol." Despite the warning, Korach and the two hundred and fifty people offered an unauthorized ketores and perished, just like Nadav and Avihu. The deadly sin was separation from the community which is the precise opposite of the purpose of ketores, i.e. to tie all Jews together.
The ketores is beloved, and lifesaving, when Jews come together. Just as a parent's most fervent wish is that his children get along, so, as it were, it is Hashem's desire that we, His children, do so, and this unity will lead to our redemption. Thus the ketores is offered for nachas ru'ach (Metzudos, Yechezkel 20:40), paralleling a parent's nachas from his unified children.
This expression "one Hashem" in Rashi is puzzling. Why is machlokes a denial of Hashem? The answer lies in the idea expressed by the Sefer HaChinuch (241), that one who seeks revenge assumes that another person wronged him. In reality, however, it was Hashem who decreed that he suffer, and he should not seek revenge, which, in effect, denies Hashem's providence. Korach and his group, who fought for a status that Hashem gave to others, were also deniers of "one Hashem".
On Yom Kippur, the day that our one Kohen Gadol approached the one Ark and the one Altar and served the one Hashem based on the one Torah, the extra-thin ketores represents unity and inclusion. Kol Nidrei, which begins by allowing sinners to join in, concludes with a declaration that the entire nation is forgiven; they were misguided by serious rabbinic error (the Sanhedrin allowed an action which turned out to be avodah Zara), and their sin is deemed unintentional (Bamidbar 15:24-26). The implication for the sinners of our generation is clear and powerful.
The ketores is unique, separated from the rest of the offerings. The Netziv (Shemos 30:1) explains that ketores atones for lashon hara (Yoma 44a), the most serious interpersonal sin. Its main purpose is to accentuate gemilus chasadim, which is represented by Shilo (ibid 39b). While the other offerings were based on the Torah, which emerges from Yerushalayim (Tziyon), the ketores of Shilo actually merged with its idolatrous counterpart. Hashem accepted it because of the hospitality of Pesel Micha (Sanhedrin 103b). The value of interpersonal propriety, even in the absence of Torah, and even tainted by idolatry, may not be diminished.
II
The tying together of all Jews is found in the Medrash (Vayikra Raba 30:12) as well, which says that the four species represent four types of Jews: the esrog has taste and smell, as some Jews have Torah and good deeds (ma'asim tovim); the lulav has taste but not smell, as some Jews have Torah but no good deeds; the hadasim have smell but no taste, as some Jews have good deeds but no Torah; the aravos have neither taste nor smell, as some Jews have neither Torah nor good deeds. Hashem said "let them all be tied (yuksheru) into one bundle, and these atone for those." The command to take for ourselves (lachem) the four species means tie ourselves together.
The Etz Yosef interprets "massim tovim" in the aforementioned Medrash to be mitzvos. He asks since Torah is more abstract than mitzvos, shouldn't Torah be compared to the abstract smell rather than the physical taste? More troubling is the following question: what value does Torah have if the person does not perform its mitzvos? We must conclude that mitzvos are included in Torah. What, then, are ma'asim tovim?
The answer is that good deeds must be taken literally. Any act of kindness, of charity, of supporting charitable institutions of all types are ma'asim tovim. Again, the implication of this redefinition is enormous. The vast majority of non-observant Jews, according to the Etz Yosef, have neither Torah nor ma'asim tovim. According to our interpretation, nearly all have ma'asim tovim. Generally, secular Jews are far more charitable and concerned about social justice than non-Jews. As the Netziv notes, non-Torah, and even anti-Torah enterprises can contain gemilus chasadim of value.
The Etz Yosef, citing the Vilna Gaon, requires that those with neither Torah nor ma'asim tovim identify as Jews and as a part of the Jewish community. By denying idolatry, they acknowledge the entire Torah (Chulin 5a) and should be tied together with observant Jews. A significant majority of secular Jews meet these criteria.
Nonetheless, the proper practice of ma'asim tovim is far less defined than Torah and mitzvos. Some charities and social justice agendas are incompatible with Torah observance and/or values. Hence, ma'asim tovim are compared to the more abstract smell, while the more defined Torah and mitzvos are compared to taste.
The Etz Yosef, quoting the Radal, notes that the esrog is not tied with the three other species. So, too, a talmid chacham should be near all other Jews, but remain somewhat apart. In our analysis, all observant and ethical Jews have Torah and ma'asim Tovim, and, together with talmidei chachamim, are represented by the esrog. They should remain somewhat apart from the non-observant and the unethical.
As we read about Keturah, we should beautify our deeds like the ketores and tie ourselves together with all identifying Jews, bringing nachas, as it were, to Hashem and, by eliminating sinas chinam, which caused the churban, merit the ultimate redemption.