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As you say, replied ,Polemarchus: besides, there will be a night-festival, which it will be worth while to look at. We will rise after dinner, and go out to see this festival; and there we shall meet with many of our young men, with whom we can converse. Therefore stay, and do not refuse us. - The Republic of Plato

I've never seen a sentence which has no verb after conjunction while. Is it okay grammatically? And what's the meaning?

I presume it means "during looking at"

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    See this – user178049 Mar 30 '17 at 8:42
  • @user178049 Thank you. Why is there a space there? – Ting Choe Mar 30 '17 at 8:46
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    All these versions are fine: worthwhile, worth-while, and worth while. You can read more about it in Cambridge Guide to English Usage on page 583. – user178049 Mar 30 '17 at 8:49
  • You are welcome, but can you access that book? – user178049 Mar 30 '17 at 9:17
  • @user178049 I got a pdf file easily from Google. – Ting Choe Mar 30 '17 at 9:24
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There's no phrase like "while to". Nor is the while a conjunction in the sentence presented. In fact, the "to" is part of the to-infinitive "to look". The phrase "worth while" has been used in place of the adjective "worthwhile"

You can use either the adjective worthwhile + to do something or the phrase worth while + to do something, without any difference in meaning. However, the former is far more common.

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