How could it be possible? Let's assume that a "small effect" is something like a character change. Consider:
if (a == b) ...
And,
if (a != b) ...
One character difference, exactly opposite meaning. Is it possible for such behavior to not exist in programming languages? I can't prove it, but I doubt it. I suspect it's inherent.
Let me clarify. Consider if I instead chose equal and not equal as my operators. Now a "small change" probably won't even be a valid program (not wqual). Any small change that does result in a valid program is unlikely to result in an equally small behavior change for any interesting input. Changing a strictly-less-than to a less-than-or-equal-to is a small change that results in what seems like a small behavior change when viewed locally. But my own experience with programming is that a local change such as that will have huge consequences later on - often to the point that the program crashes.
Consider it this way: the space of valid programs is infinite. The space of valid programs that solve a particular problem is much smaller (in the physics << sense) than the space of valid programs. Any perturbation from a valid program that solves the problem is much more likely (>>) to land you on a valid program that does not solve your problem than one that does.
I agree with your intuition, but computer science is a mathematically founded discipline, so the kinds of claim Dijkstra was making about "robustness" require formalisation and mathematical proof if they are to be taken seriously.
Like you I find it very difficult to even envisage what a "robust" language would be in this sense. What I'd like is for someone to define the properties that one would have and then show that it can't exist :)
NB he is demonstrably incorrect on this point:
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.
>>> 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.
>> Error correcting codes do exist!
He acknowledged this explicitly immediately after, on the next sentence:
> [For the sake of completness I add that the picture is not essentially changed by the introduction of redundancy or error correction.]
Think of what happens if a single bit is changed in the error-correcting part of the program.
You could once-and-for-all prove the error correcting program correct and then use it again and again for every program. But that wouldn't actually help getting programs correct. For example if your error correcting program was to write every program three times, then if one of the three programs gives a different answer you use the answer of the other two. Now a human writing a program would probably just write the same bug in each of the three versions, i.e. the three versions are not independent. You could have the three versions written by three different humans. But that doesn't solve the problem either because some errors are just likely to be made by all three of them (for example forgetting to check some edge condition somewhere). So again the three versions are correlated. Or worse the problem could be in the specification all three of them got. I don't think there is any way out of this.
Human DNA is a "robust language." Everything is encoded redundantly, and most features "express" through multiple small, additive gates (e.g. changing one bit of your DNA will never take your hair all the way from blonde to black, only make it slightly lighter or darker.) We could make a programming language that works similarly, though it would likely be very unintuitive.
Not everything is encoded redundantly. Try changing CGA to TGA in one of the exons of PAX6. In humans, this change will result in aniridia, the lack of an iris, an unstable corneal epithelium, and other problems. This is just one example, the one I'm familiar with. There are many other single nucleotide polymorphisms that can cause big changes.
