Against expectaion

You can't just know. You have to know that you know that you know something. But do you believe it? At pre-teen camp this year, we had a bit of free time at canoeing with the red girls (7-10 years), so we decided to "test" the life jackets with them. Everybody knows the purpose of a life jacket isn't fashion accessory or for comfort, but to keep you bobbing around at the surface of the water. And they know that they know this. So, the girls waded out to about hip-deep into the water and splashed about. The daring ones ventured out to maybe chest-deep with their toes just barely touching the mucky mud bottom, but none went further. At this point, I took it upon myself to grab them by their jacket straps and send them sailing out into deeper water where even I could not touch. The reaction was hilarious. "No! No, I can't touch. I can't swim... Don't let go of...." This was followed by a second of shocked silence, then giggles and shouts of delight as they found themselves suspended in the water, not sinking.

Another example: In Physics, we were learning about Newton's laws, and how things fall at the same rate, and air resistance and such. So the teacher takes a big heavy ball, and a little light ball and drops them. No surprise that they hit at the same time. Then, the big ball and a piece of paper. The ball falls, and the paper wafts slowly to the ground; but when the paper is crumpled, of course, air resistance is gone, and it is affected by gravity just the same as the ball. So, the question is, what happens to a feather on the moon when you drop it? There is no air on the moon, so there is no air resistance. Logic tells us that it would fall just like anything else, and we all know this, and we know that we know it. It would fall just like the crumpled piece of paper. The teacher then plays for us the video of the astronauts on the moon where they have a hammer and an eagle's feather. The guy holds them both up, and then lets them go. Even though I knew what would happen, I had every expectation for the feather to float gently down to the ground. Instead, to my amazement, it fell just like the hammer. Around the classroom, there were gasps of surprise and quiet laughs of astonishment.

I guess my question from all this is: What do you know that you know that you know, but still fail to believe?