I started attending a dance aerobics class about eight years ago. For the first few weeks I had considerable trouble because I copied what the instructor did, and everyone else copied the mirror image of what the instructor did. When she raised her right arm I raised my right arm and everyone else raised their left arms.
Pretty soon I learned to do what everyone else did, except for occasional lapses. This morning I thought about mentioning this idiosyncrasy on this blog and got confused enough that I had to stop dead and start over — and then it took me starting over twice to get back into the exercise.
I thought smugly that this was all because I am a Mathematician and understand Coordinate Systems intuitively. Or at least because I am a Boy and can Read Maps Intuitively. However, none of the other mathematicians and scientists in the class were doing this.
Two people occasionally reverse what they do on purpose and pretend to bump into other people. They do this very skillfully. One is an English Professor and the other is a botanist. They are both much better at this dancing thing than I am.
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I wonder if this is due to which brain hemisphere is dominant. I understand that for most (but not all) right-handed people, the left hemisphere is dominant, and for most (but not all) left-handed people the right hemisphere is dominant.
There may also be commonalities for mathematicians, or at least for most mathematicians. It has been shown, for instance, that most right-handed, non-musicians process sounds and music in their right hemisphere, but for trained, right-handed musicians, music is processed in the left. It could be the case that mathematical training results in one hemisphere becoming dominant for mathematical thinking. Because the left hemisphere in right-handed people typically processes language I would guess that mathematicians mostly process math in that hemisphere (although this may be more true of algebraists than for others, I suppose).