"I invented this later but independently" isn't a valid defense, even if you can prove it. So it's not actions (like copying or plagiarism) that is prohibited, it's the result.

That's the problem with IP law.

In effect you give people monopoly on numbers. When the numbers are big nobody is bothered by this, because chance of arriving at the exact same one is effectively zero. But for songs the numbers are pretty small (depending on the encoding used to compare the songs), and the absurdity is evident.

That's not correct in the case of copyright. Independent invention can be used as a defense to a copyright infringement claim.

> Generally, a plaintiff proves copying through circumstantial evidence, showing that the defendant had access to the copyrighted work [...] > > [...] unlike in patent law, if a defendant independently creates the substantially similar work, he is not liable to the copyright holder.

https://www.finnegan.com/en/insights/copying-copyright-s-wil...

s/song/music/

i.e. sans lyrics