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To be fair, fields have conventions that help quite a bit. Matrices are almost always (I have seen exceptions) capital letters. I used to be an advocate for so

To be fair, fields have conventions that help quite a bit. Matrices are almost always (I have seen exceptions) capital letters. I used to be an advocate for some kind of universal notation, but honestly it is not practical. A useful notation for one paper can be incredibly cumbersome in another paper in the same field. This gets worse if you’re paper is at the border of two fields and their notational conventions are mutually inconsistent. It’s best to just have a notation section that sets forth your convention in the document and stick to it. Ultimately, if you’re reading a paper in an area in which you are knowledgeable and can’t parse the notation quickly, the author failed to write the paper well. As Whitehead said, “By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.”

hoosieree 3y ago
I agree with the Whitehead quote. Ken Iverson opened his 1979 Turing award lecture ("Notation as a Tool of Thought") with it. And APL would be a suitable replacement for 90% of the bespoke pseudo-notations I've seen in hundreds of academic papers in my domain (machine learning and reverse engineering). Contrast this with 2 papers I've read recently which independently defined a "function" that returns 1 when its argument is true, and 0 when its argument is false. In both cases, the purpose of this function was to either keep or cancel part of an arithmetic expression by multiplying by either 1 or 0. Each paper defined this function with different notation (one used prefix notation: "Fn(condition)", the other used brackets: "[[condition]]"). Each paper spent several sentences defining the meaning of this notation and the associated function. Meanwhile in APL, true and false are 1 and 0. If these authors had used APL, they could both have used the same notation, and neither would need to explain beyond saying something like "we use APL notation here". This behavior is not unique to APL - JavaScript, C, Python, and many others have "truthy" values which can be treated as 1 or 0 for the purpose of multiplication. I don't care if authors use APL (or Python, or Idris, or whatever). I just would prefer that (when possible) they use an existing language which is actually learnable. If it's acceptable to not define your notation (relying instead on tacit conventions and context) why not use an existing language?

hoosieree 3y ago

I agree with the Whitehead quote. Ken Iverson opened his 1979 Turing award lecture ("Notation as a Tool of Thought") with it. And APL would be a suitable replacement for 90% of the bespoke pseudo-notations I've seen in hundreds of academic papers in my domain (machine learning and reverse engineering). Contrast this with 2 papers I've read recently which independently defined a "function" that returns 1 when its argument is true, and 0 when its argument is false. In both cases, the purpose of this function was to either keep or cancel part of an arithmetic expression by multiplying by either 1 or 0. Each paper defined this function with different notation (one used prefix notation: "Fn(condition)", the other used brackets: "[[condition]]"). Each paper spent several sentences defining the meaning of this notation and the associated function. Meanwhile in APL, true and false are 1 and 0. If these authors had used APL, they could both have used the same notation, and neither would need to explain beyond saying something like "we use APL notation here". This behavior is not unique to APL - JavaScript, C, Python, and many others have "truthy" values which can be treated as 1 or 0 for the purpose of multiplication. I don't care if authors use APL (or Python, or Idris, or whatever). I just would prefer that (when possible) they use an existing language which is actually learnable. If it's acceptable to not define your notation (relying instead on tacit conventions and context) why not use an existing language?