Scientific ESP

There's a recent article in the New York Times describing the latest controversy in the scientific community. It looks like someone has done research on ESP, and a paper about their research has been accepted into a respected scientific journal. Psychic scientists everywhere love it, rigorous physics-loving scientists say that it's a joke.

I especially liked this part of the article:

In his version, Dr. Bem gave 100 college students a memory test ... and found they were significantly more likely to remember words that they practiced later. “The results show that practicing a set of words after the recall test does, in fact, reach back in time to facilitate the recall of those words,” the paper concludes.

This feels like the very thing statisticians warn everyone against. Correlation vs causation. In other words, "I don't think those numbers mean what you think it means"

Suppose for a second that whatever scientific methods this guy used are legit. He gives you a memory test, and scoring higher on that test is highly correlated by the amount of studying you do after the test. Aside from giving a bunch of underprepared college students yet another reason to not study for finals, he also makes a big leap. Stating that this test implies a causal link would infer that there are statistical analysis methods that are independent of the flow of time.

This interests me more than the ESP. It's pretty easy to show things are correlated if they are. But to say that one causes another is another matter entirely. Usually you have to do some experiments with two nearly identical groups, one in which you inject what you believe to be the causal element, and one in which you do not. In some cases, the latter needs to be tricked into thinking they have been given something so that knowledge isn't another difference between the groups. Then you watch, and wait, and only after time has passed can you conclusively say if that one causal element that you used is wholly responsible for the differences between the two groups.

Time must have passed. You can't have a causal link that is independent of the flow of time. That's not how physics works, that's not how chemistry works, and that's certainly not something that current statistical methods allow.

But let's suppose that there are causal links that aren't dependent on time. That right now, the outcome of something is dependent on what I do in the future. How could we prove that in a statistical context?

I don't have any real answer, but it's interesting to think about.