Chinese government censorship of social media constitutes the largest selective suppression of human communication in recorded history. In three ways, we show, paradoxically, that this large system also leaves large footprints that reveal a great deal about itself and the intentions of the government. First is an observational study where we download all social media posts before the Chinese government can read and censor those they deem objectionable, and then detect from a network of computers all over the world which are censored. Second, we conduct a large scale randomized experiment by creating accounts on numerous social media sites spread throughout the country, submitting different randomly assigned types of social media texts, and then detecting which types are censored. And finally, we supplement the current approach of conducting uncertain (and potentially unsafe) confidential interviews with insiders via participant observation by setting up our own social media site in China, contracting with Chinese firms to install the same censoring technologies as existing sites, and -- with direct access to their software, documentation, and even customer service help desk support -- reverse engineering how it all works. Our results demonstrate, contrary to prior understandings, that criticism of the state, its leaders, and their policies are routinely published whereas posts with collective action potential are much more likely to be censored (regardless of whether they are for or against the state). We are also able to clarify the internal mechanisms of the Chinese censorship apparatus, and show how changes in censorship behavior reveal government intent by presaging their action on the ground. This talk is based on two papers, joint with with Jennifer Pan and Margaret Roberts, available at http://j.mp/ChinaExp and http://j.mp/ChinaObs.