# Intuition is fallible

There is no good reason to believe in the supernatural. There is no evidence that forces exist, or ever existed, outside of the universe. All religions are bunk. People will often believe something if they feel it must be true. But intuition is fallible. One of the great benefits of a good math education, is that it becomes obvious that intuition is a tool which must be weilded carefully. Using concrete objects, pictures, and intuition, can help make concepts more palettable, and can often motivate us to learn something in the first place, but nothing beats a good proof. If a proof stands in opposition to your intuition, it must be that your intuition was incorrect. How can we get this idea across, that intuition is error-prone? Certainly, illusions can be used at an early age. Illusions come in visual, auditory, and tactile form. When someone recounts a brush with the supernatural, they will often say "I saw," "I heard," or "I felt." I have yet to hear anyone smelling or tasting the supernatural, but that would be funny.

Math offers lots of opportunities to defy one's intuition. The earliest point at which we can defy a student's intuition, is when they're learning how to measure using rulers. We can show visual illusions which make two lengths appear equal when they aren't, or unequal when they are. The next opportunity for defying the student's intuition, is just after the student learns that the area of a triangle is \((1/2)bh.\) At this point, we can show Curry's paradox. Once the student is learning about probability in high-school, there are lots of counterintuitive probability puzzles we can give the student, such as the Monty Hall problem, or the Boy-Girl paradox.