# How to cope with the abuse of notation in the literature? [closed]

In mathematics or (mostly) in computer science, there is a much gap between the literature and the standard textbooks.

Many good research papers are also abusing the notations either with or without mentioning it explicitly.

Is there any standardised mechanism or authoritative body that deals with this issue? If not, how to deal with it?

• In which sense are they abusing notation? Can you make any concrete example? – Massimo Ortolano Feb 3 '19 at 10:15
• @SolarMike That's a nonsense comparison. c is a constant representing a particular, fixed velocity. It's not even in the ballpark of making sense to suggest we should use v instead. – zibadawa timmy Feb 3 '19 at 10:30
• @SolarMike You don't seem to comprehend. v is standard notation for a velocity variable. c is standard notation for the constant known as the speed of light. Completely different. That we invariably hit overloaded notation is a valid statement, you just picked such an egregiously bad non-example that it boggles the mind. – zibadawa timmy Feb 3 '19 at 10:35
• NO. There is no authoritative body that enforces mathematical terminology. For example, when a physicist says "delta function" and a mathematician answers "it is not a function", there is no referee to decide which is right. – GEdgar Feb 3 '19 at 13:34
• Not an answer: 1) Abusing notation often helps understanding at an advanced level. 2) There is much more abuse of notation than you may be aware of, even in first year textbooks. – Dirk Feb 3 '19 at 16:20

## 2 Answers

What is notation? It's really just a way to say things, in much the same way as we use words to express concepts in sentences.

Now, think about how we use language. Charley Owens said "Say it ain't so" to Shoeless Joe Jackson, which is not correct English but everyone understands what he was saying. Jaz-Z says "And I ain't tryin' to see no highway chase" and gets told "Well, you was doing 55 in a 54", neither of which is correct Oxford English. But everyone knows what he's tellin' us!

Notation is the same way: We use it to communicate, but it is not necessary to stick to a rigid use of it to make ourselves clear to our readers. What is necessary is that every educated reader understands what we're saying, but this allows for some "abuse" of notation, which is really typically just a convenient way of expressing things without having to go into great formal detail that does not actually illuminate anything.

I am not sure if you are really looking for a way to cope with varying notations, but mostly these are necessary to name all the values involved in a document. Often, different topics deal with different sizes, all of which need a unique identifier.

The best way to cope with this is to adapt to it. In my field it is common to introduce every variable explicitely before using it, so when I fully read a document, I just need to make sure to not miss these introductions.

If you have trouble remembering, it may help to write them down for each publication etc. you are considering.

I had a problem where an author used M and N the other way round than I would have. I failed to reproduce some results, only to realize I had not properly read the paper. This was my fault though, the author is free to define their own notation as long as they tell the reader.