I've often seen Lord Shiva with 'half-moon' on his head which, I was told, as the timelessness of Lord Shiva; meaning Lord Shiva is beyond 'time' or he's the master of time and space as per Hindu sources.
But why does specifically the 'half-moon' symbolize this?
The crescent moon symbolizes the time cycle and not timelessness. The moon goes from the new moon to the full moon and back. Hence it symbolizes a cycle.
The crescent moon is shown on the side of the Lord's head as an
ornament and not an integral part of His countenance. The waxing and
waning phenomenon of the moon symbolizes the time cycle through which
creation evolves from the beginning to the end. Since Lord is the
Eternal Reality, the crescent moon is only one of His ornaments and
not an integral part of Him.
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