I think that what Davies is saying here is that we think that we can control what is going to happen to us by practicing superstitions. This makes sense to me. When people do superstitious things, they are trying to bring themselves luck (or at least avoid bad luck). You can see this in things like baseball players jumping over the foul lines when going on or off the field.
In the article you cite, Davies mentions his mother and the Italian scientist. Both of them are trying to affect the future -- to have some control over what will happen to them (or to others, in him mom's case).