The Right Way to be Wrong
Rhett Alain is an Associate Professor of Physics at Southeastern Louisiana University. He is one of many physics educators who has impressed me by being insightful and funny on Twitter (@rjallain), and at Wired.com Science Blogs.
Recently, Rhett wrote about a brain teaser. Then people on Twitter and in the comments section of his blog told Rhett that he was wrong, and he responded in the way we all should – he admitted he was wrong. I suspect that most people think they would be honest and forthright when their errors are pointed out, but I don’t know that most people actually do that. I always appreciate it when somebody does it correctly.
But that’s not exactly what prompted me to reflect here. The puzzler Rhett wrote about reminds me a bit of another that I heard a long time ago (I have no idea the source):
A man starts at the bottom of a mountain at sunrise and takes all day to hike to the top, arriving at the summit exactly at sunset. He camps at the peak overnight. The next day he starts down the exact same path from the peak, beginning at sunrise and arriving at the bottom exactly at sunset.
Keeping in mind that he’s on the same trail, does it have to be true that at some point, he will be at the exact same place and time on the second day as he was on the first day?
Years ago when I first heard this, I figured the answer would have to be “no”. I’m not sure why – it was just a gut response. Probably the reason I remember the question years later is that my gut response was wrong, and the reason it is wrong was explained very clearly. If I change the way the question is asked, it should become very clear.
One day, a man walks up a trail from the bottom of a mountain to the top. During the same day, a woman walks down from the top of the mountain to the bottom, using the same trail. Does it have to be true that at some point, they will be at the exact same place and time?
Clearly the answer is yes. The rewording of the question didn’t just tell me that the answer is yes – it allowed me to see clearly that the answer must be yes. I think this experience is one of the best parts of learning and of teaching, and I relish every time I am able to help a student see why their gut response is incorrect. It’s almost as good a feeling as when somebody does that for me.