One possible reason for me not thinking APL is a good notation is that it seems to avoid assigning names to things. I believe good names are a vital tool for a thinking notation. In my bilinear upscaler example, I was initially struggling to understand the code I had found on the web. The variable names were all things like "x1a", "x2". I changed them to things like "srcX" and "weightX". That helped a lot.
And another: types. They seem to be under emphasised in APL. In my bilinear example the original code had lots of "(pixel >> 8) & 0xff" kinds of things to access the colour components. I created a type to allow those to become "pixel.g". That immediately made the code feel easier to understand. (Pleasingly it made the code run faster too).
Prominent APLers think it doesn't need one. I agree, because APL tries to be close to math, and you don't write types when doing math. You use alternate and overloaded operators.
In math, not only are you dealing with an expectation of a multi year commitment among participants in an academic conversation, but people also either define the terms they use or rely on established culture.
The single-letter variable names and the lack of types (beyond some duck-typing using bold and uppercase) is what makes math so difficult to read (for me). There must be tons of errors in math papers that go undetected just because there’s no type checking.
Also, any halfway decent math writers (including those writing for domains that use math, but are not strictly done by mathematicians) also define their terms or provide a context. If you're doing physics, the following is perfectly comprehensible (and is useless if you haven't studied at least a bit of physics):
x(t) = x_0 + v_0 * t + 1/2 * a * t^2
In a physics book, all of those terms would have been defined prior to that statement, but you wouldn't exclude that equation because it's so useful later on (to actually do calculations with, or to solve for the other elements).
If you take any arbitrary APL program or mathematical statement out of context, it's going to be mostly meaningless. I mean, I can tell you what that does above if I've taken algebra but haven't taken the first couple weeks of Physics 101, but I don't know what it means so it's not useful. That's not the fault of the equation and it shouldn't be discarded just because it needs context to fully understand (either context fully stated with it, or an expectation that you've already studied the topic and so a minimal context can be provided and you can fill in the gaps).
