Ive been researching about the moon for quite some time now and i have been told by a few that the new moon was not viewable because the moon phase was at 4 percent which was deemed not viewable to the naked eye. google calculator cat formoon phase

It was stressed that the percentage shown on this page was the percentage of circumference and not the area and it wouldnt be viewable unto 10 to 15 percent of it showed at the least. Everywhere I research I dont see anything about the percentage so Im confused. I really need as much info you can give me about the phases of the moon in relation to naked eye visibility. What are the optimal conditions and is 15 percent ever viewable at the start of a new month?