Is There an Infinite Number of Needles in a Haystack?

There's an infinite number of needles, because there's all these correlations that can look significant in a data set of large size. They're not replicable, they're not going to replicate it. So statistical significance has very little discriminating ability to tell you which ones are the real needles and which are just looks. That summarizes my worry about big data. What do you think about it?