# “namespace clutter” in mathematics

In programming, if you had a lot of functions and variables defined such that loading new functions / variables overwrites existing ones, you'd call it namespace clutter (or at least, that's one term for it).

In mathematics (or science disciplines), is there a similar term? e.g., the constant h could be used for both the height of an object and Planck's constant in the same document (or formula).

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I would try asking about math jargon at Mathematics. –  MετάEd Feb 17 '13 at 3:49
The mathematician's term for such a document is "badly written". All notations that could be ambiguous to the intended readership should be clearly defined. –  Gerry Myerson Feb 17 '13 at 12:47
@Gerry: Agreed, but we do allow some overloading, mostly of operation symbols whose operands disambiguate them, e.g., $+$ in $(a+b)(\vec u+\vec v)$. –  Brian M. Scott Feb 17 '13 at 12:53
@GerryMyerson - agreed, every symbol use ought to be clear and well explained. But if you were to talk about a paper with a lot of overlapping symbol use (e.g., if a paper crosses two sub-fields that conventionally use the same symbol in different ways), how would you refer to the issue? Maybe there's no term for it, but that's the situation I'm referring to. –  keflavich Feb 17 '13 at 21:14
Sorry, I can't recall ever hearing a term for it. –  Gerry Myerson Feb 17 '13 at 22:17

I don't think there is any standard term for it.

In general, mathematicians try their best to be precise and unambiguous (this is not to say that they always succeed). It is considered bad practice to "overload" terminology and notation if it can be potential causes for confusion, and in publishing papers those are often considered to be "errors" that referees and/or editors would want the author(s) to fix before accepting a paper for publication.

A side effect of this being that if a paper spans two fields with overlapping notation, for the sake of clarity the paper will most likely "go against convention" used in one, if not both, of the fields.

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So maybe we call it 'overlapping notation' or 'overloaded notation'? –  Tara B Feb 22 '13 at 11:43
Since there doesn't seem to be a standard term, you are welcome to call it whatever you want. I will preferentially follow Gerry's suggestion. –  Willie Wong Feb 22 '13 at 11:45
Well, the thing is that you would call it 'badly written' in programming too, it's just that there's a specific name for the kind of badly written. –  Tara B Feb 22 '13 at 11:47
@TaraB seems to be right - this shows up in the literature as 'overloaded notation': johndcook.com/blog/2014/03/04/nomenclatural-abomination, specifically referencing arxiv.org/abs/1205.4446v1 –  keflavich Mar 4 '14 at 16:45

Unlike a computer, who can't tell the difference between identically named variables, humans are generally a lot better at using contextual information.

Therefore, in mathematics and other sciences this is rarely if ever a problem. For instance, it is not rare to see the letter $i$ used both as an index as well as $\sqrt{-1}$ in the same equation.

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I think it can be a problem sometimes, though. I've seen more than one example on this site of people using the same letter for two different things and it can cause confusion. –  Tara B Feb 22 '13 at 11:40
The index / imaginary number example is one that I had in mind. While I agree that it is not a problem in the sense that people can figure it out, on a quick read (and for academic papers, that's all they ever really get) it can be quite confusing. –  keflavich Feb 22 '13 at 15:55

In English this is called Homonyms, same spelling, same pronunciation but different meaning.

A good example is the Mathematical $i$ in electrical engineering becoming $j$ to avoid confusion with the same symbol for current.

They are examples of context sensitive/dependent symbols.

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