My ten-year-old niece and her father came to stay with us this weekend. She’s smart, inquisitive, and a lot of fun to talk to. Ten is a great age, because you know so much already, but there are so many horizons left.
I showed her the Spinning Dancer optical illusion. You can see it at the top of this page. The dancer on the left is spinning clockwise, the one on the right, counterclockwise. But the one in the middle is ambiguous – it can be perceived as spinning in either direction, and you can “switch” it by looking at the left or right image. (Actually you can “switch” it without the help of the other images, but it’s harder.) Here’s some more information.
This is pretty cool for a lot of people the first time they see it. But I showed it to my niece, and it blew her mind. She spent five minutes staring at the screen, trying to figure out what was going on. For her, the illusion wasn’t just new or different. It conflicted with her understanding of reality on a fundamental level. I could almost see her mind adjusting its rules to accommodate a universe where this sort of thing is possible.
I imagine this kind of feeling happens to almost everyone. It certainly happens to me.
I still remember the high school math class where I learned that 0.999… is precisely equal to 1. (Multiply both sides of ⅓ = 0.333… by 3 for an easy proof.) I didn’t believe it at first – it was just so foreign to the way my brain worked. I think it took me a full day of thinking it over before I could accept the truth. Apparently skepticism about this particular equation is very common.
Truly world-altering revelations like this seem to get rarer the older you get, but I hope they still happen once in a while. You need a good mental revolution every so often to keep you honest.
Has something like this happened to you?
Brian D. Buckley 
The different degrees of infinity is the one that still bothers me.
Yes! I think that’s weird too. Math is mind-expanding in general.
There is no purple wavelength of light. Purple is instead the combination of red and blue wavelengths. After years of believing purple and violet to be synonyms, it blew my mind that they were so fundamentally different.
Whoa, I never knew that. Very cool. 🙂
When I first discovered that BBSs existed, that I could get by writing out to people for free (this was before their was a world wide web).
Up to then I was making little chapbooks, but they were so expensive to make that I lost a little money on every one I sold. I didn’t care if I ever made money writing, but I couldn’t really afford to lose any.
But BBSs, and then the web? It was exactly what I was waiting for.
Oh,and the first time I saw a color TV. I had just assumed that TV programs were all in black and white.
And when my obsessively inseparable best buddy ended up in my bed, despite all her claims (and all the evidence) that she was gay. That was certainly world-altering for me.
I imagine that last one would be world-altering for just about anyone. 🙂