@SW-User haha you can interpret it as such if you want!
It's kinda confusing since there's several stories behind it, in one he supposedly broke one off to write when his writing stylus broke while taking non-stop dictation from a sage. In the other an avatar of another God called Vishnu struck him with an axe because he wouldn't let him pass and meet his parents. The third theory is that it's supposed to depict a union between the physical reality (with the intact tusk, called shakti or power) and the spiritual reality.
