Control of our brain switches sides, apparently. Says Dr. Pettigrew in Australia.
His test is quite simple (it's available online in that article): Draw three dots to form the points of an isosceles or equilateral triangle. If you stare at one of those points, you'll notice that eventually the other two points will disappear. Then they reappear. Have someone time you for 30 seconds while you stare at one of those points. On a piece of scrap paper, make a check mark every time you see the two peripheral points reappear. It's called Bonneh's Illusion, after Yoram Bonneh.
Every time the two peripheral points reappear is when the control of your brain switches back. The rate at which you switch is theoretically indicative of the skills you're good at. It can also be controlled with training. Buddhist Monks can apparently make the dots disappear for hundreds of seconds at a time.
What's exciting to me, though, is that I noticed this before I was 10 that I could stare at something and make everything else turn white or disappear around it. And I knew that if I held my eyes reallyreally still, the white haze would stay as long as my eyes didn't move and I didn't blink. It was a game that I never told anyone about (I WAS AN ONLY CHILD, UH-KAY?). This could be why sometimes I got reprimanded for "daydreaming" or "staring off into space". I think I did try to tell others about it but I didn't explain it well and no one knew what I was talking about, I was laughed at, told I was stupid, etc.
For me, the two dots fade very very slowly and they will reappear every time I twitched or moved my eyes. So, I'm not sure if I counted the dot reappearances correctly. If I waited until the other dots completely disappeared, then I only get 2 switches in 30 seconds (like Mathematicians). If I didn't wait, I just counted it when they became bright again, I get 5 switches (4-6 is the Average Joe rate; 6+ is the Dancer/Musician rate).
I'm decent in Math, but not fantastic. I can keep up with senior undergraduate level Math curricula (which is nowhere near "being a Mathematician"), but I think I'd struggle going any further.