"That is, in let’s say a drug testing experiment, you give some people the drug and they recover. That doesn’t tell you much until you give some other people a placebo drug you know doesn’t work – but which they themselves believe in – and see how many of them recover."

There is actually a science of studying Placebos. It is not as simple as most think. For example the strong the drug in many trials, the stronger the Placebo effect is. Things like the total number of trials of the drug become relative. Spatial Separation does not necessary imply Independence.