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 random.org 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…
February 9th, 2007 at 1:42 pm
i did a similar poll in my livejournal. the results are here:
1 = 0
2 = 0
3 = 4
4 = 0
5 = 0
6 = 1
7 = 1
8 = 2
9 = 1
10 = 0
11 = 1
12 = 3
13 = 2
14 = 1
15 = 1
16 = 2
17 = 7
18 = 2
19 = 2
20 = 1
February 9th, 2007 at 2:05 pm
I’m very surprised that “9″ is the least frequent response, behind “10″ (which I would have guessed to be least frequent among those pressed to pick a “random” number). When I played this game in my head the first number (outside 17, which was mentioned) to come to mind was 9.
Incidentally, I always thought my affinity for the number 17 was because I was born on the 17th. Now I wonder whether other people have an affinity for numbers in their birthdates, or if I was rationalizing an affinity that was based on something else about this number.
February 9th, 2007 at 2:22 pm
wow, stragne, because for what ever inexplicable connections my brain makes, 7 seems to be least random because of its “lucky number” status and 17 seems to be most random. no ryme or reason for this at all that i can think of.
February 9th, 2007 at 2:28 pm
Before I really believe the “17 effect”, I’d like to see the following far more difficult experiment: Ask M-9 independent groups of “random individuals” the following question: Pick a number between 1 and N, with N=10,11,12, … , M. I’d like to see M at least 100 or even more. Then what happens? Question being, is the “17 effect” purely an artefact of the arbitrary choice M=20?
And what other mysterious “patterns” arise with increasing M? Can it be shown that the least favoured numbers are near 1, M/2 and M?
February 9th, 2007 at 2:32 pm
I keep hearing the question,Is the world truly random?, again and again, but never figured out what the person expects the answer to be. Do they mean by this that, we can’t predict the outcomes of all physical processes? This could be answered by saying that, no – we cannot do that , because we cannot gain all the necessary information about every physical system in the first place – and hence the world is random. But this is like a typical definition of pseudorandomness you see in computer science. For instance, you can see the physical process of measurement as a test for randomness and all that we are asking in this version of the question is to say that the process fools this test. So, this in fact this argues only for `pseudorandomness’, and I really can’t think of any other conclusion being reachable. So, I’d really like some physicist to tell me what they mean or what they expect in an answer when asking ‘Is the world truly random?’
February 9th, 2007 at 2:36 pm
Quantum mechanical uncertainty goes beyond a mere lack of infinite precision in the initial conditions but is inherent.
February 9th, 2007 at 2:38 pm
Maybe 7 and 17 are most popular because they are really the easiest to write, at least cursively… along with a 1. My wife wants to choose an address for our new house. She says it has to have a 7 in it, preferably more than 1. She complains that our existing address is hard to write – 360. Try it. Much easier to dash off 7’s or 1’s than any other number.
John
February 9th, 2007 at 5:16 pm
I remember reading somewhere (Feynman perhaps?) that in the old days before computers were widely available there were books full of random numbers that you could use for manual calculations. In one of these books, a wag had pasted an erratum with corrections to the random numbers in the book. Made me laugh.
February 9th, 2007 at 5:30 pm
pick a number from 1 to 10 and people pick 7. pick a number from 1 to 20, people think ‘ah that;s two groups of ten’. so then they have to decide to pick from the first group of ten or the second. if they flip to the 1st then its 7, if the second then its 17 (7 in the second group). so the real question then is why 7, is it not? 17 is actually irrelevant, though it would be interesting to see if the effect extends up through further powers of 10, eg. 27, 37 etc.
February 9th, 2007 at 5:41 pm
Maybe a marginal thing is the ‘twenty’ in the question
putting the ‘eh’ sound of seven and seventeen into people’s heads as they scrabble around for a random number. Would there be a trend if it was a random number between one and 30?
February 9th, 2007 at 6:32 pm
I think one of the issues is that there are certain numbers that you’re never going to choose when asked to pick a “random” number. 1, 5, 10, 15, and 20 are definitely out. Even numbers just don’t seem as random, so you’re left with 3,7,9,11,13,17, and 19. 3 is a “common” number, so doesn’t seem as random, and 9’s a square, so it’s special. 19 and 11 are too close to 10 and 20, so seem less random (guilt by association). This leaves 7, 13, and 17. As you’ll notice, the third largest spike is 13.
February 9th, 2007 at 7:20 pm
Quantum mechanics isn’t random: any state evolves determistically in time by the action of the operator e^(iHt).
(Wave function collapse? What’s that?)
February 9th, 2007 at 9:01 pm
Oh, no! Introduce worms to can, then aquaint can with tin opener. Also, 9 is one less than the fourth power of two minus six (insert brackets where appropriate (like here)) and is therefore special.
February 9th, 2007 at 10:26 pm
The results are certainly mysterious in many ways, not just a pronounced affinity to 17 but the lowest frequency of 9 over 1 or 20. Both lucky 7 and sometimes ominous 13 are the second and the third ‘random’ choices. It would be interesting to compare with different schemes:
1. What if the numbers range from ,for example,4-29 or odd-odd/even-even range other than starting with 1 and ending with multiples of 10?
2. How do other cultures respond with their lucky/unlucky numbers and different sets of rhyming sound?
3. If 17 happens to be the most frequent across cultures, how do you explain it?
4. Which appears consistently higher, odd or even number? Any cultural difference there?
5. Quote: ‘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.’
If you give them a second and third chances in 10sec./1min…., would the answer be different? Would 17 still stand out as the second and the third choices among those who opted for other numbers initially?
Very interesting.
February 10th, 2007 at 2:03 am
I think Julianne makes a good point. Computers would obviously not favor 17 over other numbers. This points to the human mind not considering all numbers equally random.Our mind most likely perceives prime numbers as more random since they don’t evoke any particular pattern. The 3 most chosen numbers 17,13 and 7 are all prime numbers. I think random number for the brain does not equate to: all outcomes are equiprobable but rather to: not showing any pattern.
February 10th, 2007 at 4:49 am
Emphasising kapakapa’s point No 2, it would be really interesting to conduct this experiment not only among speakers of different languages, but also among users of different number representations. In other words, is this presumptive predilection based upon how we write the number, how we internally vocalise the number, or how we perceive the number itself?
February 10th, 2007 at 9:56 am
Why not just have a sheet of paper with twenty identical hashmarks on it and ask people to check the one they felt the best about? It might eliminate some bias.
February 10th, 2007 at 10:25 am
Matt, that is a different experiment. Isn’t the whole point that we want to know how people perceive numbers?
February 10th, 2007 at 11:14 am
Today’s xkcd:
http://xkcd.com/c221.html
February 11th, 2007 at 1:40 pm
—Andy on Feb 9th, 2007 at 2:36 pm
—Quantum mechanical uncertainty goes beyond a mere lack —of infinite precision in the initial conditions but is —inherent.
That’s my main question, what do you mean by inherent? I’d like to see a rigorous definition of this inherent randomness that you are talking about. And since it seems to be a property that we are claiming physical systems/processes to have, the definition, should allow for certifiability (by this I mean being able to test if the system/process is ‘inherently’ random by some measurements), else it’s unlikely it’ll make much sense.
February 11th, 2007 at 5:11 pm
I mentioned this to a friend who is in PR. His ‘explanation’ was that
people tend towards 17 as being ‘not too good’ but still good; ie people are viewing the range as if it were the results of a test and wish to ‘do well’ but still be somewhat ‘humble’.
I would like to see two further tests: 100-120 and 40-60 or 60-80.
In the latter, if there were still a bias towards ‘17′ (57 or 77) his idea
might have credence.
February 12th, 2007 at 3:56 am
“How do other cultures respond with their lucky/unlucky numbers and different sets of rhyming sound?” kapakapa
Below are results of my small poll made in Russia.
7 (2)
11(1)
13(1)
15(1)
17(3)
19(1)