Conversely then, how does the DMCA not violate the first amendment by silencing speech? Is there actually any difference in the direction of application of this regulation?
The DMCA takedown system is an exemption to copyright law; violate it, and you lose its safe harbor and go back under ordinary copyright law. Copyright law does not violate the First Amendment because the Constitution specifically allows for it:
> To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries
and the First Amendment does not override it; it is specifically worded "Congress shall make no law".
> To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries
and the First Amendment does not override it; it is specifically worded "Congress shall make no law".