http://www.mathworks.com/company/newsletters/news_notes/clev...
which shows part of a 1983 plan for Matlab:
"Combining the technology of 1) mice and windows, 2) matrix and APL environments, and 3) direct manipulation, will do for engineers what Lotus 1-2-3 has done for the business world."
Ulf Grenander, the Brown University mathematician who invented statistical pattern theory, once used APL, but moved to Matlab for his expository book on pattern theory:
http://books.google.com/books?id=lxBDcFvFFvsC&pg=PA146&#...
I agree that the vectorized operations in Matlab are good at lifting computational ideas out of the fog of nested for loops. It is more compact to represent some matrix algebra in Matlab notation than in ordinary matrix notation, as anyone who has read Golub and van Loan knows.
It's weird to proclaim, but this concise notation can be as freeing for certain problems as Prolog's declarative transformations, and functional composition in Lisp.
(If you ask me, R/SPLUS is the inelegant language, especially when doing serious matrix -- yuck! But it's trendy....)
Matlab is a lot like SQL -- people love to hate on it because it isn't perfect and they know it really well (because it is ubiquitous and pragmatic).
And, the weird lack-of-speed issues. It used to be that you could implement a matrix multiply, in an m-file, that would be faster than the builtin *. I benchmarked this myself.
And my somewhat informed opinion is that J sucks ass. To start with, input/ output suck and it's hard to read and maintain -- it is the least pragmatic language I know. But what I really hate about it is the community -- full of true believers who think it's a cosmic language and "mathematical", even though you can't prove theorems in J (that's what would make it mathematical, duh), who babble about how they can calculate pi to 1000 digits in only 4 characters, as if that is remotely useful or profound (neither)
As for your other throwaway comments, any code, in any language is hard to read and maintain when you don't know what you are looking at. Or, as better stated by Whitehead (whose quote led off this thread), "Of course, nothing is more incomprehensible than a symbolism which we do not understand.".
Concerning the community you "hate" for some small-minded reason, my experience has been quite the opposite, I have not found a more informed, helpful or friendly group anywhere, and this also includes the APL/k/q/A+/NARS/SAC communities (all languages designed or influenced by Iverson).
As for pragmatism, Iverson was probably one of the most pragmatic language designers in history. Don't take my word for it though, here is what Dr. Fred Brooks has to say:
I once asked Kenneth Iverson, Turing Award winner and inventor of the APL programming language, "Why is APL so easy to use?" His answer spoke volumes: "It does what you expect it to do." APL epitomizes consistency, illustrating in detail orthogonality, propriety, and generality. It also epitomizes parsimony, providing many functions with few concepts. - Fred Brooks, "The Design of Design" page 72
I FAR prefer matlab for matrix work, as it is closer to actual math than any other language I know. For logic ish programming, Prolog or AMPL or SQL (I like SQL, even though people hate on it all the time).
But, in my humble, J and APL are interesting historically, but rather crappy in comparison to more recent languages