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?
Memories are more easily accessed, in humans, when contextual information is brought to mind. When making observations that lead to memories, if the context is relevant to the questions that you will attempt to answer in the future, you will not have to artificially call forth the contextual info. The solution is to approach new situations critically.
So, if you explore a neighborhood, before you set out determine what you will look for. For instance, ask yourself: Are architectural features related to the relative affluence of the area at the time of each building's construction.
Or, in math classes, consider what the lessons build upon and where they may lead.
Consider new situations with conscious consideration of previous knowledge. "Blankness" is not appropriate when approaching an experience in which you have previous expertise. Calling to mind relevant experiences helps to ensure that memories attain relevant associations.
So basically, instead of just trying to collect facts, try to organize them in some way?