>They're (poorly) aping mathematical notation without the properties that give actual notations their power to augment thought using symbolic manipulation
Yeah, I'm not sure I agree with that. Both of these are some of the most eye-popping books I have ever read related to math and computing [0] [1] (note, both pdf files) Both are well-written (by the guy that created both APL and J) in extremely approachable language and the introduction of J into the mix is almost obvious compared to doing some of the common operations in any other non-array language. These two documents and Joe Armstrong's PhD thesis were ones that really made me "think different" about programming.