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A comma before that seems to be very uncommon 1,2. But I am quite unsure about the following sentence:

For each state and word, we calculate its orbit, that is, the set [... a mathematical formula defining the term orbit appears here ...].

Are the commas here valid (I am also unsure about the other ones to be honest)? According to the ''pause of speech''-rule they seem valid, but they also seem to be "to much".

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  • It's a matter of style. That punctuation is common. But it could certainly be rephrased: We calculate the orbit of each state and word … It's unclear how the rest of the sentence goes, so I can't say how the set part might be rephrased. (And without the rest of the text, I also can't tell what the set is referring to specifically.) But I don't think it needs to be part of the same sentence. (Even without knowing the rest of the text, I get the impression it will make the single sentence a bit too wordy.) Commented Jul 20, 2020 at 15:01
  • @JasonBassford Thanks for your answer. What appears after "the set" is a mathematical formula. I edited my question. Hence, there is a dependence between the term orbit and what follows. So, for me, it would feel quite unnatural to form two sentences.
    – StefanH
    Commented Jul 20, 2020 at 15:07
  • Ah. Then, expanding on my last comment, you could remove all commas: We calculate the orbit of each state and word (with / by using) the set [formula]. In fact, if that's the context of the sentence, I'd say the sentence is arguably ungrammatical in its original form. At least in terms of general use, you can't really say that a formula is a synonym for a word. In that sense of the sentence, I would put the formula in parentheses—or have it follow a colon—after the first part of the sentence, and leave out that is altogether. Commented Jul 20, 2020 at 15:11
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    It depends which first comma you're talking about. ;) The one after word is optional. If that is is a parenthetical phrase, then both the comma before and after it are required. The problem with the analysis is that I'm not sure if it is a parenthetical phrase—given the discussion in comments and how calculates is being used in conjunction with the formula. The interpretation of the overall sentence changes the interpretation of the function of that is, as well as the punctuation around it. Commented Jul 20, 2020 at 16:36
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    For example: My ride (that is, my car) is red.My ride, that is, my car, is red. In that sentence, that is, my car is parenthetical—as the parentheses explicitly demonstrate. When replacing the parentheses with commas, you need both the opening and closing commas (and the one in the middle of the phrase, in this case). When I didn't know how your particular sentence finished, it at least seemed possible that the use of that is was acting as parenthetical information. With the clarification, it no longer seems that's the case—but I'm still hung up on the other issue with the sentence. Commented Jul 20, 2020 at 16:48

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The reference you provide concerns "that" as a conjunction and a comma is never used before this "that".

In your example "that" is a demonstrative used in the turn "that is" meaning "i.e."; the commas are always necessary but sometimes the last one is omitted. The first comma can sometimes be replaced by a dash. The same principe is valid for the synonymous turn "that is to say" excepted for short phrases.

Examples from Google Books

that is

  • In the same way, both one who is making use of the instrument for willing by intending what he wills, and one who is not making use of it but has an affection (that is, an aptitude) for willing, are said to will. One can thereby recognize that there ...

  • We know that the order of this group is φ(n), so any such p would be a generator for the group (Z/n)×. That is, the group would be cyclic.

  • Professor Mothers: That is a very interesting area and there is very active research going on at the moment. There is a lot of evidence that early life nutrition — that is nutrition in the womb as well as nutrition in the first year of life“can affect ...(Here a dash has been used in place of a comma and the second comma has been omitted)

  • It assumes or at least suggests that rational insight is always genuine , that is , that the claim that is apprehended to be necessary always is in fact necessary ,

that is to say

  • That is to say, to add a price, a new state of the market-world, to the existing prices. Possibility and probability and stochastic processes, all these constructs, are themselves derivative concepts, that is to say secondary. They came later.

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