"Air gapping". https://en.wikipedia.org/wiki/Air_gap_(networking)
It's common practice in classified environments, as a necessary security precaution. But it's a true productivity killer imho. Better to just install an extension that blocks twitter/facebook etc, than completely cripple your ability to search for technical information as you need it.
Also - good luck installing tools and plugins when you have to start copying things from the internet computer to the classified computer.