Nothing, they say, is a coincidence. It's a platitude so often that it has the ring of a truism, in the beginning of speeches, in casual conversations, implicit in the inspirationalness of a good 70% of inspirational stories. You happen to meet a stranger who ends up knowing your second cousin? Katrina strikes soon after disengagement? Parsha Mattos always falls during the three weeks*? All of them represent some sort of message from Hashem, whether as a specific instruction, a source of potential inspiration, or just a general statement registering His participation in the world.
I hear this quoted so often, in fact, leading into the main gist of some speech or other, than I tend to take it as a given. On further examination, however, this doesn't really tally entirely with my vision on the world. I mean, I believe that G-d is parsimonious in His direct intervention in the world. Indirect intervention is far trickier, but I am personally inclined towards Rambam's vision of Hashgacha. The Rambam maintains that G-d largely leaves the world to its own rules and devices. Hurricanes will, for the most part, hit because of meteorological conditions. Depending on a person's greatness, G-d will intervene in his life more or less, but in general, He stays out of the picture. In other words, coincidences often happen due solely to natural explanations or random fluctuations of chance.
On the other hand, I do not really reject the idea of Divine Intervention. I believe that G-d does have some interaction and direction over the randomness, to whatever degree or however directly. Many coincidences, then, may have some important message.
The problem with this otherwise balanced theory is that I have no way of determining which coincidences are which. It would be nice if one could compose a neat algorithm, based, perhaps, on the odds against this particular confluence of events. But that's mathematically silly and theologically ridiculous. So the most logical way to decide the issue seems to be to evaluate the cost of a miss and that of a false positive and determine the best course accordingly.
Which gives rise to a very interesting insight: This is little to no cost to a false positive, and there may even be some benefit. Because attributing Hashgacha rarely causes anyone to do anything that they wouldn't otherwise. When faced with a coincidence, people tend to interpret events based on their prior convictions. Which is natural, and perfectly logical. So nobody who thought that disengagement was a good idea would possibly say that Katrina must have been a punishment for it. No matter how likely or unlikely they consider the similarities between the events**, it would never occur to them to draw the link. Similarly, those who find a link between the Parsha and the week's events always use them to reinforce and/or inspire towards an ideal they had already had. So "wrongly" assuming coincidence tend to inspire people towards pretty noble goals- better interpersonal relationships, improving their midot, serving Hashem better and so forth.
A miss, on the other hand, has small to large negative. At best, you fail to be inspired towards the noble goals that you would otherwise attain. At worst, G-d has to continue to send more and more harsh messages to shape up until you get the hint.
Based on this analysis, I think I would come to the more complicated conclusion, "Many things may very well be a coincidence, but it may not be morally useful to believe so." It seems, I will admit, somewhat disingenuous, but I have very little problem lying to myself, as long as I know that I'm doing it. Or, to sound moderately less split-personality, I am willing to assume everything is Hashgacha in order to get myself to become better, as long as I do not let it murk up my theology.
This may not, in fact, be the best system. Perhaps it would be better for me to totally lose the theology that alerts me to the possibility of coincidence, so that I will be more likely to fall for my own attributions and thus be more inspired. Or perhaps it is disingenuous to suck false inspiration from anything and I should just be inspired by good old fortitude. Be that as it may. I find myself unable to fool myself any more than I do and unwilling to fool myelf any less.
*If you want to call this a coincidence instead of presuming some prior planning by the calender makers or some supernatural aura/power corresponding to certain times of the year
**This example, by the way, is based off of an e-mail that went around just after Katrina explaining it as punishment for America for pushing disengagement, as proven by the fact that it struck Condaleeza Rice's home state and other uncanny similarities