Nobody wants to write proofs as English prose like they did when first proving basic algebraic properties. Yet those proofs are much easier to guess at the meaning of, even if you don't fully get it, than using our standard mathematical notation. Of course, it just so happens that our mathematical notation allows middle schoolers and high schoolers to think of these proofs as obvious and trivial, whereas they would have no idea what to make of the English proofs that are more "natural" to the English speaker. Of course, that notation that they use with such facility (even if they aren't particularly competent with it and just learned it last week) has no relation and no intuition at all to the English language, and makes no attempt to do so.
Yet, I challenge you to back up your statement about character counting by showing me a Computer Scientist and a Software Engineer who no longer writes or uses traditional mathematical notation for anything, but has systematically moved over to the more intuitive and natural programming language of their choice, such as Scheme, C, or Haskell.
APL is a suitable replacement for Mathematical notation and was designed as such. Other programming languages are not. That's a very important element.
It's not about character counting. See Iverson's Notation as a Tool of Thought Turing Award lecture.
You might have a stronger case if, since the advent of computing programming languages, which are demonstrably capable of representing a whole host of mathematical ideas and concepts directly, people have begun flocking to programming languages to replace their mathematical notation in the communication of ideas in non-computer science contexts.
However, people rarely consider a programming language equivalent to be better/superior to traditional mathematical notation when they are talking amongst themselves in front of a whiteboard.
>Nobody wants to write proofs as English prose like they did when first proving basic algebraic properties.
You'd be surprised. Mathematical proofs contain lots of "english prose".
>Yet, I challenge you to back up your statement about character counting by showing me a Computer Scientist and a Software Engineer who no longer writes or uses traditional mathematical notation for anything, but has systematically moved over to the more intuitive and natural programming language of their choice, such as Scheme, C, or Haskell.
That's irrelevant. Best tool for the job et al.
>APL is a suitable replacement for Mathematical notation and was designed as such.
That doesn't make it suitable for programming in general.
And mathematical notation is much richer than APL, it's not constrained by mere sequential characters on a line.
Some mathematical proofs contain lots of "english prose", but not in fields that have nailed down the semantics; and no field that did even goes back to prose.
mathematical notation is not automatically suitable for programming in general, but is not automatically unsuitable.
APL was devised as a notation for algorithms, not for general math; Iverson noticed that at the time (1950s), everyone was inventing their own algorithm specification when give mathematical proof, and tried to unify that. And since it was well enough specified, someone later wrote an interpreter, and that's how APL came to be more than notation. I urge everyone to read Iverson's "notation as a tool of thought".
> Best tool for the job et al.
Best tool depends on context. No programming language is the best tool if the person reading/writing/mainting it does not know the basics of how to program.
APL is suitable for programming in general for people who take the time to learn it, and is often the best tool for the job, as long as the context is "to be read/maintained by other people who know APL". IMHO, this is an unfortunately rare context.
No software development in any language should be undertaken by people who don't understand the language and surrounding tooling and libraries. No program in any language should be written with the expectation that it can be maintained by people who don't know the language. This is not some APL predicament.
Yet, I challenge you to back up your statement about character counting by showing me a Computer Scientist and a Software Engineer who no longer writes or uses traditional mathematical notation for anything, but has systematically moved over to the more intuitive and natural programming language of their choice, such as Scheme, C, or Haskell.
APL is a suitable replacement for Mathematical notation and was designed as such. Other programming languages are not. That's a very important element.
It's not about character counting. See Iverson's Notation as a Tool of Thought Turing Award lecture.
You might have a stronger case if, since the advent of computing programming languages, which are demonstrably capable of representing a whole host of mathematical ideas and concepts directly, people have begun flocking to programming languages to replace their mathematical notation in the communication of ideas in non-computer science contexts.
However, people rarely consider a programming language equivalent to be better/superior to traditional mathematical notation when they are talking amongst themselves in front of a whiteboard.