While I understand and largely agree with the point- it is worth saying that like so many man made concepts, mathematic notation is a system of evolution and consensus. That is to say that the symbols and conventions to note a concept aren’t some natural law but the process by which individuals simply used what was intuitive or made the most sense to them, and as individuals desired to work together and share information, a standardization emerged.
A comparison is the common metric/standard debate. Each system has benefits and draw backs but one of the major arguments for metric adoption is that metric is default fr most of the world. Conversely one of the greatest hurdles to metric adoption in standard system countries has been that in those countries and to their people that standard has been the default.
We can look at language as another example- we have definitive spellings and punctuation or structure rules so that it is easy to understand a language. There is no particular reason that we have to use these rules and these rules and spellings or definitions etc. can change over time by usage and consensus. In other words- the rules of English don’t really matter in value because languages which use completely different rules and structures and basic Characters and phonetics like Chinese fr example are perfectly functional. The important thing is that they have some set of rules which allows them to function, not the specific rules themselves.
So I’m (hopefully) clearly by saying these people are correct- but I am saying that if enough people agree they are correct they become correct. With specific words we see their meaning change over time. “Curiosity killed the cat” is an English saying which generally is used to mean don’t poke where you shouldn’t. Cats aren’t particularly known for their curiosity, they posses it but by nature tend to be relatively cautious. The word “curiosity” was used in place of the word “care.” care killed the cat originally- a message saying that excessive worrying or cautiousness wasn’t good. The cord care changed meanings and so the saying changed and in the next change of definitions it lost its original meaning.
We can see this across many languages. Using English as an example- silent letters- letters that aren’t pronounced when speaking a word like the “b” in “debt” which is originally pronounced: “Det” and in older English was spelled as “det.” Many silent letters were actually added by academics and the like to give words a more “Latin look” on the page. There are other reasons for silent letters as well- but the changes to language or convention aren’t always organic or for a practical and general good. Sometimes they are by certain interests and serve those interests. Math and notation change with time too- even CNC pets existing to antiquity, one can’t simply hope to take a modern understanding of math and step in to understanding problems across cultures or time. So there is a case to be made that we can’t view such things as absolutes, though at the end of the day however one notes the operation or concepts; adding two and two is four or generally “wrong,” and when communicating…
.. with others a failure of understanding can be factored in to a judgment to understand the situation, but results speak ultimately. Or in other words by example- it is common for non native speakers or those with little native language skill to be perceived as less intelligent anywhere in the world. The reason is simple and intuitive- even if you are an accomplished physicist or philosopher if you lack the ability to communicate those concepts to others in a way they can understand your brilliance, your ideas only exist in your head. If you can’t find a shared method to communicate then your ideas can’t be communicated. It’s that simple. These conventions like the widely accepted notation of mathematical operations are a frame work to shared communication. Music is perhaps a perfect example for those familiar. While there is fair standardization in notation there are different ways to write the same thing. A sharp may be be written as a flat of another note for example.
Different groups tend to have established their own standards- that a certain note be written as a flat for ease of reading unless there is a practical reason otherwise. However one doesn’t need to be able to read and write sheet music to play or compose. “By ear” or numerous other systems like tabs exist so that people who don’t read and wrote sheet music can share in information. In digital tools you can use file names and specific parameters and filters vs. giving things like notes or chords etc. people or other entities even have their own systems- on many child or beginner instruments specific keys etc. are often color coded, and music is played through a sheet telling you colors to press. More modern electronic interfaces simply show you where to press your fingers on a screen or using lights on the instrument etc.
While an individual can play and share musical compositions without understanding the common standard of notation, and an individual can be brilliant and gifted at playing or composing while using a system they devised themselves- those who don’t know their system and are used to communicating in standard sheet notation probably couldn’t understand their writing easily or at all. When looking for new music or working with others the person with unique notation would likely find themselves lost. In the case presented above I doubt the individuals are campaigning for a new system of notation so much as they do not understand the standard system of notation. In such a case we don’t really have a discussion of opinion because we aren’t talking about the same thing.
The thing about opinions is that to discuss them we must agree on certain fundamental things. We can’t discuss our opinions on “Animal Farm” if you refuse to believe the book/story exist right? And if I’m talking about the book and you’re talking about a film version we may still not be able to have a productive discussion because we aren’t talking about the same thing.
This is a case that clearly illustrates the concept. Opinions are what they are, but to share them with others there has to be some level of common understanding and agreement.
A comparison is the common metric/standard debate. Each system has benefits and draw backs but one of the major arguments for metric adoption is that metric is default fr most of the world. Conversely one of the greatest hurdles to metric adoption in standard system countries has been that in those countries and to their people that standard has been the default.
This is a case that clearly illustrates the concept. Opinions are what they are, but to share them with others there has to be some level of common understanding and agreement.