The Sciences

The Power of 17

Cosmic VarianceBy John ConwayJan 31, 2007 3:00 AM


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Some years ago I heard a fascinating talk by the magician and pseudoscience debunker James Randi, in which he spoke of many interesting things ranging from ESP and UFOs to medical quackery. One thing he talked about was a strange phenomenon involving, of all things, the number 17. In the advanced undergrad lab course I am teaching this term, my students and I today were talking about random numbers. At one point, the memory of Randi's talk bubbled up in my head and I said "Hey, did you know that if you ask people to choose a random number between 1 and 20, inclusive, and record their answers, there is a big excess at 17?" Ordinarily, if you ask 100 people to do this, you would think that would get about 5 responses for any given number like 6 or 12 or 15. Of course it will vary statisticaly, but there should be no real preponderance of any particular number. Right? My students thought this 17 stuff was nonsense, and saw an opportunity to see if I was just teasing them. So, with about 30 people to attack in the class, they started recording real data, asking first the students that had arrived, and then students who filtered in for the next 20 minutes or so. The result? Well, to my own great surprise the number of people who answered 17 was an early favorite: three out of the first 12 or so! And then a string of four people ALL answered "17" as they were asked the second they came through the door! We were actually shocked by the prepomderance of 17's. The students have the data sheet, and I think are continuing to ask their other freinds and roommates this evening. We of course tried to explain this really odd phenomenon, but so far have no good theories. Clearly 17 is a number that's not to far away from the maximum allowed, 20, and it's one that you don't often encounter like the small integers, or 10, 12, 15, 16, etc. So perhaps it seems more "random" to people. But still it's quite weird. I wonder if it would still work if asked for a number between 1 and 100, for example. I know there are a lot of readers out there who might find this intriguing and want to do their own experiment. I am willing to try to compile the data that folks send me via email - just send a message with one line per integer, and one frequency: 1 5 2 4 3 8 4 3 . . . et cetera, so I can put them into a program and make a combined histogram which I will show here in a week or so if I get data. Make sure you don't tip off the group you are in as to the nature of the test, and don't give your victims more than a second or two to think about it. Have fun! (Okay, it's a bit nerdy...)

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