Less is more. Stay pure. Stay poor.
So if I simulate a bunch of random independent variables and select one as the DV and the rest as IVs, I should expect 1 in 20 will be significant at p value </= 0.05 as the number of terms increases toward infinity, right? By chance, the number of significant terms may be higher than 1\20 at first but should settle into 5% after awhile. This seems like the Law of Large Numbers, right? Am I missing anything?