1

This is not a mathematical question as such, but more about the correct grammatical way to describe the mathematical terms that are being introduced in a sentence.

I am used to writing sentences in this way:

A deterministic policy, $\pi$, is a function, $\pi: S \rightarrow A$, that selects an action, $a \in A$, for a state, $s \in S$.

But a reviewer for one of my paper submissions came back with a comment that I use too many commas around my variables. I used to think that my way is the correct way, since there is a pause when introducing the respective mathematical term.

I have seen papers that use either my approach, or a single comma after the term, or no commas at all.

What is the correct grammatical way to introduce mathematical terms in these kinds of sentences?

jbx
  • 383
  • 1
    Your sample sentence has a lot of appositives – J. W. Tanner Aug 13 '23 at 14:35
  • compare the answer at https://ai.stackexchange.com/questions/12274/what-is-the-difference-between-a-stochastic-and-a-deterministic-policy I would expect more detail when explaining to students, less when reporting to peers. – Will Jagy Aug 13 '23 at 14:55
  • @KurtG. not really, I am referring to terms defined in English sentences themselves, that are not directly the subject or object of the sentence. – jbx Aug 13 '23 at 15:53
  • @WillJagy so the style of the answer you quoted seems to use my approach. So what is the reviewer complaining about? – jbx Aug 13 '23 at 15:54
  • 1
    @J.W.Tanner yes, just to illustrate the example. So it seems that is the correct grammatical approach to punctuation? (Whether they should be used too much or not is another story). – jbx Aug 13 '23 at 15:56
  • 1
    Recommendation: don't argue with a reviewer of your papers about "correct" punctuation. If that's all they criticise get it published by sacrificing a few commas. – Kurt G. Aug 13 '23 at 15:59
  • 1
    A deterministic policy is a function $\pi: S \rightarrow A$, where $S$ is the set of states and $A$ is the set of actions. – Will Jagy Aug 13 '23 at 16:10
  • @WillJagy well this was just a simple example to illustrate the problem. I am not asking about restructuring this sentence, I am asking if commas should be there or not. – jbx Aug 14 '23 at 17:33

1 Answers1

-1

In English, appositives should generally be set off by commas: "Jack, my brother, stood six feet tall." rather than "Jack my brother stood six feet tall."

In mathematical writing, however, they're often omitted: "The indicator function $\chi_A$ for the set $A$ is defined as ..."

I personally don't like that choice, but your reviewer does. @Will Jagy has suggested a restructuring that may work in some situations if the lack of commas irritates you. And @Kurt G. has a good point: don't sweat the small stuff in reviews.

John Hughes
  • 93,729
  • 1
    That distinction between plain and mathematical English is a false dichotomy: a more pertinent comparison is "My brother, Jack, stood..." and "The indication function, $\chi_A,$ for..." (with commas, both definitely correct) $\quad$ versus $\quad$ "My brother Jack stood..." and "The indication function $\chi_A$ for..." (without commas, both acceptable as a stylistic variation by authors who prefer fewer pauses). $\quad$ To be clear: "Jack my brother stood..." is indeed an incorrect substitute for "Jack, my brother, stood...". – ryang Aug 14 '23 at 00:53
  • Scratch 'false dichotomy' above: I meant to just say that the two examples aren't really analogous. – ryang Aug 14 '23 at 23:48
  • Fair enough. Your comment made me consider that appositives of the form "description, name, verb-phrase" seem to be different from those of the form "name, description, verb-phrase" in the way we treat them. I still believe that commas offsetting a name are less frequent in mathematics than in most other writing, but I don't have actual data to support that. – John Hughes Aug 14 '23 at 23:52