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There is a certain pleasing physicality to function notion, in the sense that empty parens make a circle into which you put things. () -> (1). Look, I put a 1 i

There is a certain pleasing physicality to function notion, in the sense that empty parens make a circle into which you put things. () -> (1). Look, I put a 1 in there! f(x) is a notation that is strictly speaking only good for the author of f because they know how to access their independent data; any utility to the caller, by inferring what "x" should be, is purely conventional/accidental. Function notion in this sense mirrors our counting system, which begins with an empty circle, 0, which we replace with a succession of symbols, until we hit 9, and then 10. It's interesting to imagine what "10" means if you're treating each symbol as a function. But this requires defining some sort of analog to "counting" with functions, which I'm not sure makes much sense in any general way. What is the "successor" to a function? It seems that we have a lot of options. One simple example would be to let f return a function based on an integer input, with the understanding that this is a simple function from 0-9 but then at 10 we return the composition of f_1 and f_0. In this way we describe the composition of 9 functions in any order using only a natural number. Anyway, back to writing CRUD webapps.

thaumasiotes 11y ago
> There is a certain pleasing physicality to function notion, in the sense that empty parens make a circle into which you put things. () -> (1). Look, I put a 1 in there! This gets dropped as you go further in math, though. Take the function that reflects across the x,y plane, f(x,y,z) = (x,y,-z). Interpreting the notation your way, you'd want to write f((x,y,z)) = (x,y,-z), but that isn't done.
- taeric 11y ago
  Doesn't matter. Often affordances are only relevant to get you thinking at the start. Once a concept is fully established, the affordance no longer matters. Consider the use of a disk to indicate that something can be saved. The fact that you no longer save to disk is ultimately irrelevant.
- javajosh 11y ago
  I didn't talk about how to implement (or represent) the body of the function! And besides, Church seemed to like single arguments, so actually he would write something like that. :) Physicists wouldn't (my degree is in physics). Programmers would write f(x,y,z){return {x,y,-z};}. But actually, I would say that this is nasty because of asymmetry - it can't consume it's own output. f(p){return {p.x,p.y,-p.z}} where p = {x,y,z}

thaumasiotes 11y ago

> There is a certain pleasing physicality to function notion, in the sense that empty parens make a circle into which you put things. () -> (1). Look, I put a 1 in there! This gets dropped as you go further in math, though. Take the function that reflects across the x,y plane, f(x,y,z) = (x,y,-z). Interpreting the notation your way, you'd want to write f((x,y,z)) = (x,y,-z), but that isn't done.

taeric 11y ago
Doesn't matter. Often affordances are only relevant to get you thinking at the start. Once a concept is fully established, the affordance no longer matters. Consider the use of a disk to indicate that something can be saved. The fact that you no longer save to disk is ultimately irrelevant.
javajosh 11y ago
I didn't talk about how to implement (or represent) the body of the function! And besides, Church seemed to like single arguments, so actually he would write something like that. :) Physicists wouldn't (my degree is in physics). Programmers would write f(x,y,z){return {x,y,-z};}. But actually, I would say that this is nasty because of asymmetry - it can't consume it's own output. f(p){return {p.x,p.y,-p.z}} where p = {x,y,z}