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I am unsure about the first three commas in the following sentence:

In this paper, I will explain, on the intuitive level, how to use different methods of light polarisation to obtain interesting physical phenomena.

Is it the right usage?

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    The 2nd and third must go together (either both in or both out). Stylistically, I don't think you really want any of them. You don't really need to parenthesize the 'on the intuitive level'. And the first one isn't really needed. – Mitch Apr 11 '14 at 12:41
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In this paper, I will explain, on the intuitive level, how to use different methods of light polarisation to obtain interesting physical phenomena.

Each comma in your example is correct in the sense that they would be correct if the rest of the sentence wasn't so hard to read. But this particular sentence is very awkward to read because of the commas and, therefore, many writers would modify the sentence to one of these options:

In this paper I will explain, on the intuitive level, how to use different methods of light polarisation to obtain interesting physical phenomena.

In this paper, I will explain on the intuitive level how to use different methods of light polarisation to obtain interesting physical phenomena.

In this paper, I will explain how to use different methods of light polarisation to obtain interesting physical phenomena.

I will explain, on the intuitive level, how to use different methods of light polarisation to obtain interesting physical phenomena.

This type of editing is a stylistic choice, however, so there is no single "correct" answer or opinion. Commas are often removed purely for the sake of readability.

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In this paper I will explain on the intuitive level how to use different methods of light polarisation to obtain interesting physical phenomena.

Works fine with no commas. Works best with no commas.

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  1. First Comma: There is nothing wrong with it. As comma denotes a short pause, and that is what it is doing here.
  2. Second Comma: Well, I don't think so that a comma is needed here. There is no pause between I will explain and on the intuitive level. But if you want to enforce a pause for your readers, you are welcome to have a comma here.
  3. Third Comma: Sure. You need a comma here as the context of what you are saying changes a little bit here - in other words, you do need to have a pause here.

Again, a comma represents a pause. So sometimes, it becomes optional. First and third ones are necessary but the second one is up to you that how you want your readers to read you.

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    I'd say that the second and third commas set of a parenthetical and so are both advisable. – Edwin Ashworth Apr 11 '14 at 12:38
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People rarely agree about commas. See the book Eats, Shoots and Leaves by Lynne Truss.

FWIW I suggest you take out "on the intuitive level" and then you will need no commas at all.

I'm not sure what you mean by "I will explain on the intuitive level" with or without a comma. It doesn't sound English to me, in fact it sounds French au niveau intuitif which, in French, is a way of avoiding a clumsy adverb. But if you can perhaps explain it better, such that a layman like myself can understand, it might be better in a second sentence.

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