Come on. It's totally obvious that the shapes of * and + are much simpler and much more distinct than "sum" and "mul" (which by the way are relatively short and simple examples for words).
Humans have excellent shape recognition -- recognizing (and differentiating) a tree and a person happens subconsciously, effortlessly. Interpreting the words "person" and "tree" takes way more effort.
Similarly, humans have usually very good spatial sense. If there are persons to the left and to the right of a tree, it is effortless to recognize that they are "separated".
> You're talking GUI, which is different than writing and reading code.
No. I'm talking perception.
> There are, for instance, much less GUI elements visible on the screen than there are identifiers
That depends. There are very complex GUIs out there. But let's assume it for a moment.
(By the way that typically that means the code is not good (weak cohesion)).
> there is much more context available for deduction in the code than in the GUI.
That is not supportive of your previous argument: The more identifiers, the less context per identifier.
> I don't think the two situations - recognizing GUI features and recognizing and understanding identifiers in the code - are comparable.
It's both about perception. It's very, very important that programmers can focus on their work instead of wasting energy building parse trees in their minds, incurring severe "cache misses". Again, take this simple commonplace example:
(sum (mul a (minus (b c)) d)
a*(b-c) + d
If you don't think there's a huge difference I can't help you. I'm sure I need about three seconds to parse the sexp as a tree and figure out what goes with what. Then I have to go back and interpret the operators.
Conversely, the infix/symbol operators example I can map out with minimal, and linear, movement of the eyes. In most cases I don't even need to parse it as a tree -- it's almost a sequence. On a good day, it costs me maybe a second to parse the thing and extract the information I need.
Another advantage of symbols for arithmetic is that they give a sense of security, because one can intuitively infer that they have "static" meaning. While usually words are reserved for things that change, i.e. mutable variables. Being able to infer non-mutability based on shape alone gives a huge advantage.