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The European centre for high energy physics is one of the world's finest temples to classical Big Science. That it's also the birthplace of the web is one of those accidents of time and place that will always haunt those who try and fund research. But being a pure research institute, there was no commercial reason for Tim Berners-Lee or CERN to keep the idea to themselves, and as with TCP/IP this gave the open standard an unassailable advantage. The rest is history.
Real-life visiting potential: 7/10. Not the easiest place to visit outside a group, and you should move quickly if you want to sort something out. Next November they turn on the experiment, so lots of stuff will be closed to the public that isn't now.