A couple of years ago my workplace was running one of those guess-the-number-of-jellybeans-in-the-jar competitions. I don't even like jellybeans all that much, but nonetheless, I held aloft my nonmagic calculator and said "by the power of Galton!" Taking the mean of all the previous guesses, I put that down as my answer. I was out by one bean, and won the jar. I don't think my colleagues have ever been so interested in statistics as they were that afternoon, and I doubt they ever will be again.
I'm going to admit something a bit silly and embarrassing now: that made me feel like a wizard. Not because of the scope of what I'd done, since it was an utterly trivial piece of arithmetic, but because of the reaction it got. I had drawn on arcane lore unknown to my colleagues, and used it to exercise power over the world.
Personally, I think something like solid state semiconductor technology is about as impressive a real-world miracle as one could ever want by way of demonstrating the whole Science Works/Rationality Is Systematised Winning/Maths Has Manifold Real-World Applications thing, but for most people it will never have the impact of intentionally winning a jar full of jellybeans.
So I ask you, LW-readership: what other impressive nonmagical powers do we have, that we can casually demonstrate to everyday people in everyday circumstances?