This seems to be a recurring topic on HN. The "goats vs sheep" study cited in the link's "highest-voted answer" has appeared on the front page at least once before, recently.

I am more interested in the meta-question: what are the implications of this question? I.E. if we knew for certain that the answer is "yes," how would this change our behavior (and likewise if the answer is "no").

I would think: if we knew for certain that some people can program and some people just can't, we would focus more energy on sorting people early on, to avoid wasting everyone's time trying to teach the unteachable. By contrast, if we knew for certain that everyone could program given the right circumstances, we would focus more energy on devising better teaching methods, etc.

Because of this, I am inclined to maintain a deliberate bias toward "no" (I.e. I am inclined to behave as if anyone could learn to program). Even if the answer really is yes, there are sure to be some cases where a "programming-capable" individual struggles at first for some reason, and an "anyone can program" general attitude is more likely to save them from mis-categorization as a non-programming "goat."