The number of months, with God, is 12 in the Book of God, the day that He created the heavens and the earth… The month postponed is an increase of unbelief whereby the unbelievers go astray; one year they make it profane, and hallow it another…
The media were ready for blood during the days leading up to Yom Kippur this year, as the holiday fell on the first day of the Muslim festival of Eid el-Adha. Given the fraught atmosphere between Jews and Arabs that was created during the Gaza war this summer, there was concern that the usual small-scale Yom Kippur violence would be exacerbated by the coincidence of the holy days. Celebrating Eid el-Adha often involves picnicking in the park; the sound of drums and the smell of the barbecue smoke were unlikely to be welcome to fasting Jewish neighbors…
However, for a change we were treated to good news on the morning after, when everyone agreed that the combination of educational efforts by communal and religious leaders and intense police presence in potential trouble spots led to a perfectly calm and joyous holiday for everyone (except, I guess, for the cops on duty). The best the newspapers could come up with was a catalog of all the incidents of people fainting during the fast, children injured in bicycle accidents (since there is no vehicular traffic in the Jewish cities, the roads are taken over by kids on bikes), and children injured by fireworks (part of Eid el-Adha festivities).
Hopefully this was good practice for next year, as the two holidays will coincide again - but then not for another 33 years. Remember, the Muslim calendar is purely lunar, and thus "gains" 11 days each year on the solar calendar. The Jewish calendar is lunar with a leap year correction of an extra month every two to three years so as not to fall out of synch with the seasons. The month of Dhul Hijjah (in which Eid el-Adha falls on the 10th) matched Cheshvan last year; 5774 was a leap year, so we added a month, bumping the Muslim month up to Tishrei this year (5775). Since this is not a leap year, the two months will coincide again next fall; but then 5776 will be a leap year, so Dhul Hijjah will move up to Elul for a couple of years…. and so on.
Interestingly, apparently the pre-Muslim Arab calendar also had a solar correction, as several of the months are the names of seasons which they must have matched. It seems that Muhammed rejected this practice as indicated in the above passage from the Quran (Who knows? Maybe as a way to distinguish his followers from the Jews, just as the church set the date of Easter so as not to coincide consistently with Passover, as a conscious sign of separation).
But wait, there's more: On Rosh HaShanah we read the Torah portion telling of the binding of Isaac, a story that is then referred to frequently in the Yom Kippur liturgy, suggesting that God judge us more favorably in view of the absolute obedience of our ancestor Abraham. The day before Rosh HaShanah, working in the garden, I happened to hear the sermon blaring from the village mosque across the valley. I know only rudimentary Arabic, but the words "Abraham" and "mountain" kept recurring. Ten days later, Eid el-Adha, the Festival of the Sacrifice, commemorates that same almost-sacrifice of Abraham's son (see Quran 37:102; note that the name of the son is not specified) as a test of faith. It is also the culmination of the Hajj, the pilgrimage to Mecca. Some Muslims who are not going on the Hajj fast for the 10 days; some fast just on day nine. Both religions make a point of giving tzedakah (charity) during this period. And note: we stuffed ourselves for three days on Rosh HaShanah/Shabbat, then repented for 10 days and fasted on Yom Kippur; our neighbors fasted for 10 days and then stuffed themselves for three.
In any case, it is interesting to see that this is not just a calendrical coincidence of two religious holidays falling on the same day, but a deeper correspondence of religious beliefs, stories, and images. Maybe if we weren't both so ignorant of each other's traditions, we might get along a bit better.