It's neat to see James Hague write about APL/J/K, and the article makes an interesting historical observation about the point-free style of functional programming. But I think he does the APL strain of languages a bit of an injustice. They are certainly different, but not as utterly difficult as he makes out (or as first impressions invariably suggest). And while the community may be miniscule, it is far from moribund: it thrives in its niche, which is in fact quite lucrative.
Assuming x is a truth value--either 0 or 1--then !x gives the same result as these expressions:
1 - x
x ^ 1
(x + 1) & 1
In x ^ 1, ^ is exclusive or, not exponentiation. But exponentiation can also do the trick: