China bhai I know about the visibility issue. This again is a tradition that has no Quranic basis. Moon is there for precise calculation. It doesn't matter whether we can see the new moon or not. Once new moon is born a new month has started.
If the birth of the new moon is before the sunset then new month starts right after the sunset and next day will be the first day of the month. If the birth takes place after the sunset then new month starts after the following day sunset. In lunar system a new "day" starts at night (after sunset).
God tells us that both sun and moon is there for calculation. And one cannot calculate anything precisely if input is left to subjective data as "visibility".
Quote:
[Quran 10:5] He is the One who rendered the sun radiant, and the moon a light, and He designed its phases that you may learn to count the years and to calculate. GOD did not create all this, except for a specific purpose. He explains the revelations for people who know.
[Quran 17:12] We rendered the night and the day two signs. We made the night dark, and the day lighted, that you may seek provisions from your Lord therein. This also establishes for you a timing system, and the means of calculation. We thus explain everything in detail.
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It is quite understandable that previous generations used the visibility because of lack of precise calculation. But now we possess the ability and thus visiblity of moon has no value.