Pick a Number between Zero and Infinity...

David J. Chalmers

From: [email protected] (David Chalmers)
Newsgroups: sci.math,sci.math.num-analysis
Subject: Re: call for votes: most & least boring numbers
Date: 17 Jan 90 20:40:02 GMT

In article <[email protected]> [email protected] writes:

Reminds me of a friend of mine who claims that the number 17 is "the most random" number. His proof ran as follows: pick a number. It's not really as good a random number as 17, is it? (Invariable Answer: "Umm, well, no...")

This reminds me of a little experiment I did a couple of years ago. I stood on a busy street-corner in Oxford, and asked passers-by to "name a random number between zero and infinity." I was wondering what this "random" distribution would look like.

The results: (most common numbers first, out of about 150 responses in all):

• 3 (11 people)
• 7 (9 people)
• 5 (8 people)
• 12 (6 people)
• 1, 4, 10, 77 (5 people each)
• 2, 47, infinity-1 (4 people each)
• 15, 17, 20, 27 (3 people each)
• 18, 23, 26, 30, 42, 99 (2 people each)
• 6, 13, 14, 19, 21, 22, 25, thirteen more 2-digit numbers, twenty 3-digit numbers, twelve 4-digit numbers, one 5-digit number, one 6-digit number, four 7-digit numbers, one 8-digit number, one non-integer (328.39), one huge number (9.265.10^10^10). (1 person each)

Of course a uniform distribution is a priori impossible so I couldn't have expected that :-). Even a logarithmic distribution is impossible (it has infinite integral). Interestingly enough, this distribution, taken coarsely, was quite close to logarithmic up to 1000 or so. There were roughly the same number of 2-digit responses as 1-digit responses, and a few less 3-digit reponses. Then things fell off sharply, however.

Other interesting features:

• 17 wasn't quite as "random" as might have been predicted.
• Extreme frequency of the digit "7" all round.
• Especially notable are the good performances of 77 and 47.
• Poor performance of digit "8", also "6" and "9".
• Both "very prime" (e.g. 17) and "very composite" (e.g. 12) numbers did well.

Then I could tell you about the "random word" experiment I did on Sydney harbour...perhaps another time.