What a great essay. There are so many points and places to branch off of and explore. I'll limit myself to a question about the following quoted part, though. It does look like it was slightly explored in other discussions so maybe it's not that interesting, oh well.

"Like all digitally encoded information, it has unavoidably the uncomfortable property that the smallest possible perturbations —i.e. changes of a single bit— can have the most drastic consequences."

Is this really a unique fact about digital vs. analog systems? I'm not inclined to think so. He gives the example of pressing slightly harder on a pencil to get a slightly thicker line. Another possibility is that by pressing slightly harder, you cross the threshold of the paper's strength and wind up with an ugly hole. In the digital world, if I change the low-order bit of a single number in a single calculation, the result will be only slightly inaccurate. We can still get to the moon on inaccurate digital calculations. If I change the high-order bit it will be more inaccurate, and if I continue using the results then errors propagate. Similarly if I keep trying to draw over the hole in the paper I'll just wind up with a bigger hole. To put it shortly, initial conditions matter. Another way to put it, some small changes may indeed have large effects, some small changes may indeed have small effects, but you need to know what changed and in what environment the system is in in order to have any idea what to predict. Another way: any analog/continuous thing can be discretized, so is the problem with the discrete property itself so that only continuous systems that have been discretized will exhibit the problem, or is it fundamental to everything?

It seems to me that humans by default think that small changes can only have small consequences, whether those changes are to an analog or digital system. Small->Big is surprising when it happens. I'm sure there are lots of just-so evolutionary psych stories you could come up with to suggest how our brains got this way too. Imagining in great detail the huge effects made possible by such a small action as Stalin counter-factually being run over as a kid takes a lot of brain power that could be spent gathering food, consider how it might feel to have to imagine grand series of causes, effects, counter-factuals, and so on for 8 hours a day. (Or get back to doing it if you're a programmer at work.)

So I think Dijkstra is really getting at the fact that for the first time ever humans (programmers) have to be face-to-face with these hugely complicated systems, and they have to come to terms with the fact that tiny changes can and will cause big effects. In this sense, the second radical novelty of computing is just a special case of the first: dealing with the dynamics of fine-grained discrete systems like that of a digital computer is a big intellectual challenge for us when we're used to reasoning over Fuzzy or just large intervals.

After the section I quoted, Dijkstra points out that even with error correction the picture isn't changed. But I think error correction does significantly alleviate the problem--human bodies are also incredibly complicated but they're also robust and they have many error-correction features like an immune system. Computer programs on the other hand are extremely fragile. Nevertheless a single stupidly tiny virus with a simple DNA signature that is introduced to a human can cause that human to later die! In one of the other discussions someone mentioned that a tiny DNA change results in a lack of an iris. For all of our body's resistances to mitigate changes, we still can't escape the seemingly fundamental problem that small changes can cause big effects.

Edit: On the example Dijkstra gives later on with the board and the dominoes, I knew I had seen that problem before. I saw it first here where it has pictures: http://lesswrong.com/lw/rb/possibility_and_couldness/