The Power of…7 ?

By John Conway | February 9, 2007 11:54 am

Well, the results are in, and here they are:

As you recall, I asked people to send in their results from asking people to choose a random number between 1 and 20 inclusive. I got several responses, and the results show a clear preference for 17 as predicted, or at least as observed by others. But in this sample, we also see that 7 was equally popular! Perhaps there is some affinity to 7 in this context…

I also got an email from Dom DeStefano, pointing out that a similar article had appeared in Cognitive Daily, inspired by ours a few days before. Their data as well show the 17 effect as awell as a preference for 7. The go on to examine odd versus even, prime and non-prime, etc.

Dom hypothesized to me that the “first guess” of an individual can never be considered “true random”, and that subsequent guesses become more random and less motivated by deductive reasoning. This would make a vey interesting study for psychologists or sociologists.

Even more interesting – the Cognitive Daily piece got 40k hits! Apparently, this has been a lot of fun for school children in particular. It’s good to learn about randomness…there seems to be a lot of it in the world.

We use tons of random numbers in my own field, when we do computer simulations of high energy particle collisions and the response of our detectors to them. At the core, the computer software that generates random numbers is called a “pseudo-random number generator” because, since it’s a computer program, the numbers are not truly random. In fact, if you run such a generator over and over again, starting from the same “seed” values, you get the same sequence. That is useful, especially if you are trying to debug your program!

There is a whole minor industry in the computer science world dedicated to figuring out how to tell if a random sequence is truly random, and developing procedures to test them. There are random number generators available on the web that are truly random, and use digitized atmospheric radio noise or radioactive decays to generate the numbers. Take a look at for more on that.

Well, my original post was inspired at least in part by the subtitle of this site – we ought to be saying just what randomness is after all. Which leads me to end on a question, one which plagued Einstein himself: is the world truly random? Quantum mechanics certainly seems to imply that. But like Einstein, I have never found that satisfying. If you ponder these things, immediately you can get bogged down in the philosophical morass of free will and determinism, and the role of consciousness in making reality. Good luck getting out…


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