3 ms·

The more 'objectively' is used here, the less meaning it seems to have. If people have trouble using the notation, it's a subjective issue that cuts into the ut

The more 'objectively' is used here, the less meaning it seems to have. If people have trouble using the notation, it's a subjective issue that cuts into the utility of the language. Even after getting used to it myself, I sometimes get tied up translating infix formulas to RPN or PN. There doesn't need to be one notation/language to handle everything.

qsort 4y ago
The point is why people have more trouble parsing (+ 2 3) than they have parsing (2 + 3). I agree with you (contra GP) that path dependency is a fine reason to prefer infix. Continuing with what we're used to is very often the preferable choice where the costs of switching are high and the benefits unclear. I actually think that infix notation has some advantages, especially for associative operations {e.g. if (G, +) is a group and a, b, c \in G, it's much more natural to write a + b + c than to choose between the equivalent (+ (+ a b) c) and (+ a (+ b c))}. But undeniably S-expressions are superior from a teaching point of view as they don't hide the "true" structure. Even though I don't dislike infix at all, it's hard to argue the reason most people prefer it isn't that they're just used to it.
- hayley-patton 4y ago
  Then don't choose, write (+ a b c).
  - qsort 4y ago
    Yeah, but what's the difference then?
- consilient 4y ago
  > I actually think that infix notation has some advantages, especially for associative operations {e.g. if (G, +) is a group and a, b, c \in G, it's much more natural to write a + b + c than to choose between the equivalent (+ (+ a b) c) and (+ a (+ b c))}. > But undeniably S-expressions are superior from a teaching point of view as they don't hide the "true" structure. That's exactly what they do though. A group G is not the same as a particular choice of presentation, and an element of g is not a particular tree of generators. Linear transformations aren't matrices, numbers aren't decimal expansions, polygons aren't lines on a chalkboard - and internalizing this is extremely important for beginning math students.
  - qsort 4y ago
    > That's exactly what they do though. > and internalizing this is extremely important for beginning math students. I'm not saying that you're wrong, because, well, you aren't. But does the choice of notation help here? Understanding that a matrix isn't a linear transformation but only a representation of it is something that's inherently hard and requires a certain level of mathematical maturity. At that point in a sense notation doesn't really matter any longer.

qsort 4y ago

The point is why people have more trouble parsing (+ 2 3) than they have parsing (2 + 3). I agree with you (contra GP) that path dependency is a fine reason to prefer infix. Continuing with what we're used to is very often the preferable choice where the costs of switching are high and the benefits unclear. I actually think that infix notation has some advantages, especially for associative operations {e.g. if (G, +) is a group and a, b, c \in G, it's much more natural to write a + b + c than to choose between the equivalent (+ (+ a b) c) and (+ a (+ b c))}. But undeniably S-expressions are superior from a teaching point of view as they don't hide the "true" structure. Even though I don't dislike infix at all, it's hard to argue the reason most people prefer it isn't that they're just used to it.

hayley-patton 4y ago
Then don't choose, write (+ a b c).
- qsort 4y ago
  Yeah, but what's the difference then?
consilient 4y ago
> I actually think that infix notation has some advantages, especially for associative operations {e.g. if (G, +) is a group and a, b, c \in G, it's much more natural to write a + b + c than to choose between the equivalent (+ (+ a b) c) and (+ a (+ b c))}. > But undeniably S-expressions are superior from a teaching point of view as they don't hide the "true" structure. That's exactly what they do though. A group G is not the same as a particular choice of presentation, and an element of g is not a particular tree of generators. Linear transformations aren't matrices, numbers aren't decimal expansions, polygons aren't lines on a chalkboard - and internalizing this is extremely important for beginning math students.
- qsort 4y ago
  > That's exactly what they do though. > and internalizing this is extremely important for beginning math students. I'm not saying that you're wrong, because, well, you aren't. But does the choice of notation help here? Understanding that a matrix isn't a linear transformation but only a representation of it is something that's inherently hard and requires a certain level of mathematical maturity. At that point in a sense notation doesn't really matter any longer.