Math is a great example of how notation is sooo important. Doing math with roman numerals is.... possible, sure. But for pretty much any math that's worth anything, it's just a bad notation. It obscures what's going on and makes it harder to mentally deal with. Notation is a critical tool of thought.
Absolutely. The same is also true of programming, music, and natural languages. Probably nearly every discipline that uses its own notation and significantly divergent (from the primary natural language) nomenclature sees a major boost in understanding and expressivity by using custom notations and language.
Re programming: Some languages are simply better at expressing certain types of programs than others, C may be great, but it gets pretty hairy when you try to use it in certain parallel/concurrent coding contexts (i.e., you're probably using a lot of extra libraries and tooling).
Re music: Could you imagine expressing any piece of significant length or complexity in plain English? Even a mathematical (concise and precise) symbolic language would prove difficult, compared to the visual and multi-dimensional notation customarily used. (At least for reading, a case could possibly be made for more expressive and concise notations for writing musical pieces.)
Re natural languages: This is why we borrow so many words in English (and other languages, I'm sure) from elsewhere. A larger set of words allows us to produce more expressive and nuanced statements and questions.
Comments
Math is a great example of how notation is sooo important. Doing math with roman numerals is.... possible, sure. But for pretty much any math that's worth anything, it's just a bad notation. It obscures what's going on and makes it harder to mentally deal with. Notation is a critical tool of thought.
Absolutely. The same is also true of programming, music, and natural languages. Probably nearly every discipline that uses its own notation and significantly divergent (from the primary natural language) nomenclature sees a major boost in understanding and expressivity by using custom notations and language.
Re programming: Some languages are simply better at expressing certain types of programs than others, C may be great, but it gets pretty hairy when you try to use it in certain parallel/concurrent coding contexts (i.e., you're probably using a lot of extra libraries and tooling).
Re music: Could you imagine expressing any piece of significant length or complexity in plain English? Even a mathematical (concise and precise) symbolic language would prove difficult, compared to the visual and multi-dimensional notation customarily used. (At least for reading, a case could possibly be made for more expressive and concise notations for writing musical pieces.)
Re natural languages: This is why we borrow so many words in English (and other languages, I'm sure) from elsewhere. A larger set of words allows us to produce more expressive and nuanced statements and questions.