Re: internet freedom @Ole re: alternate root
Whilst it is true you can do this for DNS for a DNS alternative, it is not possible with the numeric IP4 or IP6 address spaces. This is because a single organization does not control the routing tables outside of their own networks. You certainly could give your network any IP address you wanted, but persuading an upstream ISP to route to that set of addresses without it being properly registered isn't going to happen (and the problem only gets worse as you get further from your network).
It would be possible to use VPNs across the current Internet proper to tunnel a private address space, but you could not really call that an alternative Internet. At best, you would regard it as a parasitic network. relying on the thing you want to replace for it's existence.
To really set up an alternative Internet, you would need an alternative global router network, which would be very expensive to set up. But some global companies do run trans-national intranets, like most of the owners of the class A and many of the class B address ranges. But these are (again) not really an alternative to The Internet.