All other things being equal (they're not, but let's pretend), APL will always have a cult of appreciation because it represents really the only time programming has said "we need our own alphabet." But I don't think APL symbols are really that evocative. Where does ⍳ come from? It looks kind of like a little i—it's the index function, after all.
i. seems just as legitimate and I can type that.
Some of them have some nice caché. ⌈ and ⌊ are min and max from mathematics, and J doesn't have those. On the other hand, every other programming language on earth uses something besides × and ÷ for multiplication and division, and while learning APL there were plenty of times I used * when I meant ×, so I'm not sure this is especially significant. In actual math, I would probably just nestle two things next to each other for multiplication or use a dot, and division would be a whole huge thing. It doesn't seem that hard to use
>. for min and max.
⋆ and ⍟ for exponent and logarithm come from where exactly? Nowhere. Now, ⊥ has an actual meaning in math that has nothing to do with decoding. ⊤ has a nice symmetry with ⊥ because it is visually inverted and is the inverse function. But J has many operators whose inverse is the same operator with a
:; this set is
#:, but head/tail, behead/curtail, and exponent/log all follow a rule like this.
What does the symbol ⍕ have to do with formatting? There's nothing it's standing for here, it's just meant to look a bit like encode and be typeable with an IBM Selectric using overstrike. Really. There were more APL symbols than spots on the typeball, so you'd back up and hit another key. That's how they came up with ⌹ for matrix inverse. It's a box around a division sign!
I'm not saying there are not nice symmetries with APL's symbolry. There definitely are. But J also has nice symmetries. APL's symbolry is closer to mathematics really only for multiplication and division, min and max, which you're already accustomed to writing another way on a computer. The rest of APL's symbolry is a total fabrication—just like J!
Let's also note that in A Programming Language, Iverson proposes lots of syntax that you can't do in APL or any other language. The inner product syntax, which is amazing, isn't available anywhere but that book!