I generally hate videos, but this one is well worth the few minutes it takes (assuming you are not familiar with APL; read the examples on the linked page first, it will save you a couple of reviews of the videos until you get it all)
Quibble. The demo should allow use of the computer's keyboard and Alt key. Point and click with a graphical keyboard is nuts. It should support overstrike for APL's composite symbols. I did a whole lot of APL programming in the '60s and '70s at IBM and consider it IBM's bastard child. There need not have been Matlab.
I'm appalled by the authors enforcement of 1-origin indexing.
"Try typing backquote followed by another character."
I mean the text box at http://ngn.github.io/apl/web/index.html
If you type for instance `r in it, you will get a rho symbol, `i for iota, `a `w for alpha and omega, etc
I wouldn't describe it as obtuse, but I would describe it as concise.
I think that even people who are familiar with it could feel that its concision hurts readability. It's not such an unfair criticism as you may suggest.
Ken Iverson wrote an interesting document, "Notation as a tool of thought", which covers his thoughts on what a concise/efficient notation provides: http://www.jsoftware.com/papers/tot.htm
The one worry I have with APL and its descendants is that its conciseness will encourage people to make overly long expressions.
One possibly beneficial side-effect of more verbose languages is that it tends to encourage the use of additional identifiers to hold sub-expressions. The act of naming things is often a good thing for both the authors and readers of a program. More abstractly, it allows the program to carry intentional semantics alongside operational semantics.
This is also a problem I have with mathematics -- mathematical notation often uses context-dependent single-letter variable names for semantic information, which is terrible from an outsider's perspective (and by outsider I really mean anyone who isn't working in the exact field of the mathematician).
Edit: I should mention that I'm still pretty enamored with J for numerical computation, even though I never do any of it :)
I've observed two reasons people perceive APL code as unreadable:
1. They are not familiar with the symbols. It's the equivalent of trying to read a label in a foreign language. The text may seem unreadable to you, but if you learn the alphabet/hieroglyphs and some vocab, it makes sense.
2. They aren't used to brevity of notation. An APL program is to be read character by character, the way one reads a Java program line by line. Brevity is an advantage because it allows you to see more of a program's structure at a glance.
I generally hate videos, but this one is well worth the few minutes it takes (assuming you are not familiar with APL; read the examples on the linked page first, it will save you a couple of reviews of the videos until you get it all)