# Think of a number…

…between one and twenty.

Then go read this article on Cosmic Variance (although I think it was a mistake to reveal the answer in the first paragraph and the title, so I stole my approach from present simple).

1. David Livesay says

Weird. The first number I thought of was 17, but before I clicked the link I thought, no, too obvious, 6, which turned out to be the very next number they mentioned after 17.

I’m glad I always went to great lengths to persuade my students that there is a world of difference between random and arbitrary, but I wish I’d had this example back then.

2. sally says

i case you’re keeping track here… no number came to mind, but i decided i best come up with one before i continued with the post. after a few seconds thought, i chose 17 thinking it would not be the featured number. i feel so… ordinary.

3. Carlie says

Damn. Now I feel so… ordinary.

I do something vaguely analagous when talking about random distribution. I tell all the students to draw a box and randomly put dots in it for about 20 seconds, then we look at them all and see how they’re all beautifully non-random.

4. Carlie says

Whoa! Sally and I had the same response at the same time! What non-randomness! Eek!

I wonder if it has to do with our tendency to split things in half, being dualistic and all. Split 1-20 in half for 10, too obvious, go halfsies again to 15 and again, and you’re at 17. It seemed from the examples in the article and comments that no matter what number range you choose, the most common number is just over 3/4 of the range.

5. sally says

i’m not quite that mathy Carlie. must be some other explaination.
:)

6. says

Well, when I thought of a number, I came up with 11.

I think there’s a whole slew of biases: you’re going to avoid 5, 10, 15, and 20, and even numbers don’t seem “random” enough, and numbers that are prime seem especially odd. It’s a kind of forced choice.

There was an interesting comment over on CV that it might also be shaped by language — that when you hear the “enty” in “twenty” it biases you to think of something with an “enteen” in it, too.

Brains are weird and messy things.

7. David Livesay says

Whoa! Sally and I had the same response at the same time! What non-randomness! Eek!

Why would you expect your responses to be random? The human brain is a lousy random-number generator. That’s why we need random number generators.

It is freaky that you both chose the same phrase–ellipses and all–to express yourselves, but I’m not surprised that you both felt that way. I did too. :)

8. amph says

I confess, I thought of 17.
Somehow, I feel like caught red-handed, or as if I made a fool of myself.
I would expect a preference for prime numbers, and the popularity of 6 comes as a surprise.

9. David Livesay says

Brains are weird and messy things.

Tasty too! ;-)

10. says

I’m weird: I picked one of the numbers I was supposed to avoid: 15.

11. MYOB says

I don’t know about you guys but this sounds like something the ID creationists would use as proof of design.

By the way, I picked 10 and I know why.
It’s entirely psychological.

Picking a number between 1 and 20 suggests a game, a contest between you and another. There is a subconscious assumption on your part that the other person has also picked a number. There is also a subconscious assumption that influences this selection dealing with how close you are to another number or to either end of the scale. There is also a subconscious assumption that piling on works thus the larger the number is better than the smaller number which plays on people’s(mainly men’s) sexual insecurities.

There are all kinds of reasons why a person might jump on a number first. What is important is that if you find the right reasons to explain away a particular number of trend towards a number you find out something about that person.

I chose ten because I was hedging my bets and was trying to maximize my distance from whatever number I subconsciously thought the other person might have chosen. It’s like the Price is Right game on tv. Guess a price as close to the real price without going over. In this case there is no price but I knew that no matter what number the other person chooses or I assume he or she chooses, I will be closer to it on either end of the scale than had I chosen something closer to one end or the other.

Of course all of this on my part is pure hypothesis and not substantiated by any documented facts that I am aware of.

MYOB’
.

12. David Livesay says

There was an interesting comment over on CV that it might also be shaped by language — that when you hear the “enty” in “twenty” it biases you to think of something with an “enteen” in it, too.

That is interesting, but I don’t think I thought “seventeen.” When I think of a number I have more of a visual representation of “17.” How about the rest of you? What goes through your mind when you think of a number? Do you hear the way the word sounds, visualize the way the number looks or perhaps something else?

13. says

Yeah, Munger, but you do this kind of stuff all the time — it must bias your brain away from the common answers. I know now that if ever I get this question again, my brain will be thinking “any number but 17, any number but 17″.

14. Joe Shelby says

What, nobody but me picks “13”? I tend to think of that first because it’s so famously avoided in public superstitious circles, and just like black cats (I have one), walking under ladders, occasionally breaking a mirror (by accident), and not throwing spilled salt over my shoulder, i tend to thumb my noise at the “bad luck” doomsayers.

even today there are still buildings being built without a 13th floor, and I was just last month in a hotel room that didn’t have an n13 room on ANY floor. The odds side just skipped from 11 to 15 on each.

15. sally says

I also have a more visual representations of numbers. i blame it on poor math skills.

16. says

I picked 2, believe it or not. Not sure why — it’s just the one that flashed through my head.

17. Nance Confer says

I picked 18.

Hurray! I win! :)

Nance

18. folderol says

I’ve ruined that, of course.

19. Richard Harris, FCD says

Joe, “even today there are still buildings being built without a 13th floor”.

No, the floor’s there all right. It’s just called the 14th. :¬)

20. Michael Kremer says

I tested the 5 people in my family. Answers:
7 (me, as soon as I saw the question)
4
20
15
17 (my wife)

Not exactly a preponderance of 17. But my wife did say she was thinking about the question as I asked everyone else (I asked her last) and had concluded that the most common answer would be 17.

21. sally says

michael, looks like your wife doesnt know the family too well
;)

22. says

Well, I picked 6, but my dad picked 17!!

23. George says

17! [Kidding. 11…. My second choice would be 9. I do not pretend to know why. Maybe it’s aesthetics. 11 has a nice symmetry. I consider 9 quite beautiful. 3 would be a nice choice, too. So… round. We have such fine looking numbers, don’t we?]

24. Randall says

I picked 2, but I’ve encountered 17 in this sort of context before. I once knew a girl who lived in Random House at MIT (one of their student residences), and she said that the house’s official number is 17, because it’s the most random number. Upon a moment’s reflection, I couldn’t help but agree.

25. Crudely Wrott says

I chose, I clicked, looked away to attend to some trifle, turned back and there was my number – 17. Thing is, I can remember the process of choosing 17, but can’t fully describe it. I could mention the line of glowing numbers and me flying along it. Or the string of rapid-fire judgments of the way I observe people relating to certain integers. What made the choice for me was that 17 is a prime and, here’s the odd thing, that I realized that I hadn’t considered it as an interesting number for a long time. That tiny sense of something wanting, something undone, was sufficient to halt the search then and there. I took no consideration of 18, 19 or 20. And all this within 2 seconds. On top of this, I got a 93 on the Bible quiz. Haven’t cracked the covers in years. This is an ominous beginning to my weekend.

26. George says

My partner picked 17. Yikes!

27. David Livesay says

she said that the house’s official number is 17, because it’s the most random number. Upon a moment’s reflection, I couldn’t help but agree.

I hope on further reflection you’ll agree that there is no such thing as a “most random number.”

My father used to tell a joke about how a mathematician tried to divide numbers into the interesting numbers (like pi, the square root of two, the first prime number, etc.) and the dull numbers (numbers which had nothing especially interesting about them), but the problem was, there would have to be a first dull number, and that would make it interesting….

Apparently you would be rolling on the floor laughing right now if you were a mathematician.

28. Impish says

There were exactly 17 comments when I encountered this blog entry, so I’m adding one.

BTW, I chose 17.

29. Joe says

I chose 4. Now I feel left out.

30. bPer says

I picked 4.

That’s a number that has always appealed to me, probably because it was the example given when I learned about square numbers in elementary school, and I lived in apartment number 4 at the time. Sure, that isn’t really random, but my thinking (in a flash during the process of picking) was that in the group of us who are all picking a number, who else would have the same reason for picking 4? If we all picked numbers that had some personal story like mine, wouldn’t we have a better chance to end up with a somewhat random distribution? And if not, at least it was as good a reason for picking it as any, IMO.

31. says

It seems pretty clear (i.e., I have no evidence, but it makes so much sense ;)) that most people will choose a number in the range 11-20. We’re so often asked to pick a number in the range 1-10 that we will naturally avoid that range when offered more choice. Variety is the spice of life.

So most people are choosing a number 10+n, where n is in the range 1-10. It then reduces to the well-known question of why people choose 7 from that range.

32. Dylan Llyr says

I asked my father to choose a number and he immediately said 17. Hmm.

Though I admit I myself chose 6.

It’d be really interesting to see how many would say 10. It’d probably be far more disproportionately low than 17 is high.

33. says

hey i thought of 17 without thinking!

now, obviously, the only people who are going to come and post a comment on this blog are those who were happily surprized to have been right with their choice of 17…

34. Susan says

Joe, I picked 13 as well, for similar reasons. I was born on the 13th, and have always embraced that number – particularly because of everyone else’s aversion and superstition.

35. Rand Careaga says

Dang! 17!

36. says

Well, at first I picked 3, but then I decided that it was too small. So I subtracted it from 20 to get …… 17! Wow, that’s pretty weird.

37. Hank Fox says

18 here.

Once again the universe finds a way to tell me I’m not normal.

Darned universe.

38. says

You missed ‘random’ out of the blog title, and I can’t figure out whether it’s important or not, since people seem to be choosing 17 anyway in disproportionate numbers.

My theory (which is sort of exploded by you missing the ‘random’) is that when you say ‘random number’ people think random means ‘not connected with other numbers’ or ‘not relevant to anything, or associated with anything,’ and so they automatically disqualify even numbers. (I’ve noticed that when the number is not 17, it’s usually odd.) Then they disqualify divisible numbers, because they’re somehow relevant to other numbers. Your ‘choice’ is therefore suddenly down to eight numbers, 1, 3, 5, 7, 11, 13, 17, and 19.

1 is not random (in non-geeky heads) because it’s the first number. That’s out. 7 is a ‘lucky number’, therefore special, so that’s out. 13 is unlucky, out. ‘Things happen in 3s’ (plus there are other associations with 3 – the Trinity for one if you’re religious), and 11 is a double number so that might get discarded, too, and now you are down to three numbers, and things aren’t looking quite so random. Often people will discard 19 because it’s too close to 20, so then you have a choice of 5 or 17. And 5 might be associated with the number of fingers on your hand, and not quite so random-feeling…

I’m not saying that people actually think all these things, but 17 has no associations at all that I can think of and maybe that’s why we choose it.

39. says

This kind of bias can be very useful. There was a contest on moleskinerie.com a while ago, where people picked a number between 1 and 5000, and after a few days of picking (1000 entries or so), a random number was picked and whoever got closest without going over would win some notebooks. After 633 entries I took all the answers and sorted and plotted them…it’s a pretty interesting distribution. I gave myself a slightly better chance by picking a number near the beginning of the largest un-picked interval (a gap of 75; average gap size was about 7). Numbers corresponding to recent years were highly overrepresented, and in general higher numbers were more likely to be picked.

I won the first prize. (okay, I know my pick had very little to do with it, but still..)

40. David Livesay says

BadAunt, I don’t think you know what random means. A given number is neither random or nonrandom. Any given number can be selected either randomly or arbitrarily. Randomization is all about how a number is selected, not the numbers themselves, and human beings can’t reliably pick numbers at random because we tend to pick things for arbitrary reasons. While these reasons are not always evident, they exist, and the preference for 17 in the article referenced is one example of this.

41. says

Yes, I do understand what random means, but I’m talking about the general perception of the meaning of random, not the actual meaning. I suspect this sort of trick works best on a non-geeky audience.

42. says

I thought of 12.

Prime numbers do seem to have a certain charisma to them – I’m guessing that “pick a random number between 1 and 100” probably also generates a lot of 23s and 37s. I suspect the posters above are correct, that “pick a random number” translates in people’s brains as “pick an obscure or uncommon number” and then primes automatically have the advantage. Though that doesn’t explain why 6 and 12 would be runners-up.

For my part, I think my brain gave me visual representations of the numbers 1 and 20 and rearranged the digits, yielding 12. Though I couldn’t prove that.

43. A lemur says

Well, I thought of the #’s between 1 and 21, felt drawn towards the upper end of the scale (that male thing? Has anyone broken this down between men and women?) thought briefly about 17 but felt 19 was more in a ‘pocket’ of being close to 21 but not quite and a prime to boot. So I went with that. I confess that part of my thought process was to avoid what I suspected would be a ‘common’ choice, hence I picked a number near but not quite at the end of the scale.

17 also seems to be one of those ‘loaded’ numbers. In this culture 18 is the age of majority, but 17 is being ‘not quite there’ so it carries penultimate weight. Janis Ian based a song around being 17. There may also be a linguistic basis, it starts with a soft consonant, a good ‘sss’ sound, goes consonant vowel, consonant vowel. It aliterates nicely with ‘teen’ and usually takes an uptick in accent at the end of seven so it sounds positive. Plus it’s a prime, which makes it ‘interesting’.

Now the question would be, does this preference for 17 extend across different lanquages, or even; do our British cousins display the same preference?

44. says

David Livesay; Jeremy Avigad (philosophy dept., CMU) tells a similar joke, only “formalizes” it by using the least number principle …

Now, as for the request, am I the only one who did something as screwball as picking e squared? (Who said the number had to be an integer?)

45. David Livesay says

Keith,

My father may have told it the same way, but the subtlety went right over my head. Math ability is clearly an X-linked trait.

46. says

Am I the only one who whipped out a calculator and used the random integer function? I ‘picked’ 4 :)

Seventeen is an unlucky number in Italy.

Interesting, seeing that 17 is rather common as old swedish negative emotion markers. (“fy 17!”, “vad 17?”, “17 också!”, “för 17 gubbar”, “det vete 17!”, and many more; all roughly meaning ‘damn!’.) Also as marker for slyness. (“full i 17” := ‘being sly’.)

I can’t get to an etymology for any of these variants on a theme.

I think picking 7 (from 1-10) or 17 (from 1-20 or 10-20) are rather language independent ‘odd numbers’. Could be cultural dependent though.

Seventeen is an unlucky number in Italy.

Interesting, seeing that 17 is rather common as old swedish negative emotion markers. (“fy 17!”, “vad 17?”, “17 också!”, “för 17 gubbar”, “det vete 17!”, and many more; all roughly meaning ‘damn!’.) Also as marker for slyness. (“full i 17” := ‘being sly’.)

I can’t get to an etymology for any of these variants on a theme.

I think picking 7 (from 1-10) or 17 (from 1-20 or 10-20) are rather language independent ‘odd numbers’. Could be cultural dependent though.

49. says

Well, it’s obviously the law of 23 coming to play. Take 17 and add it together to get 8, which is 2 to the 3rd power, hence 23! The law of 23 is always true.

I thought of 5.

50. says

The book Catch 22 was originally going to be Catch 17, but since Stalag 17 had just come out, Heller was convinced to change the number. I understand it took some (figurative) kicking and screaming, because he felt no other number would roll off the tongue as well as “Catch Seventeen.”

51. Captain C says

I picked 17. In my case, it has to do with it being associated with the Discordians in several of Robert Anton Wilson’s book…now I wonder if he knew of this phenomenon.

Interesting side note: several years ago, a friend of mine offered some afghans to me and another friend. We both wanted the same one, so she said “pick a number between 1 and 20.” I immediately said, “17!” She said, “you got it.” And so, I got a really cool afghan.

52. Bill LaLonde says

I answered 17, and I can tell you why. I specifically chose it because I thought that it *wouldn’t* be popular… my first thought was 7, but I thought “Everyone likes 7,” so I added 10 to it in a (failed) attempt to make it less predictable.

53. AndreasB says

I picked 19.

The number that came to my mind first, however, was 17. I thought, nah, that looks like a “random bias” question and 17 looks like a popular number, so I changed numbers before clicking the link.

Why 17? People asked to pick any number/position choose something apparantly not obvious in a desire to make a random choice. So the borders and center ­- 1, 10, 20 ­- are right out. 5 and 15 as centers on each half are likely also biased against.

17 is in the middle between biased against numbers and is not an even number ­- it’s feeling attractively random. Why it’s not 3, 7 or 13 is probably because of people tending to the larger end in general. After all you could have picked 3 when asked a number between 1 and 10 or 1 and 5, so it isn’t “unique” enough to be random.

Or it’s because people barely register the 1 (after all they’re always asked for a number between 1 and something) and pay more attention to the upper limit and thereby choose a number in that region. I wonder wether it would be more interesting to ask for a number between, say, 14 and 29.

54. says

I tried to buck the system by not going for a random number, but going with my birthdate. Unfortunately, I was born on the 17th…

55. says

So, uh, do I lose? I picked one, thinking it would be the most obvious … I mean, c’mon, it’s number one!

56. David Marjanović says

Being a wise-ass nerd, I knew that most people would pick a prime number because they look more “random” — 1 is among the numbers least commonly guessed in lotteries –, so I deliberately chose 10 for aesthetic symmetry reasons. MWA HA HA HA HAAAAAH…

(Still, I was normal enough to assume it had to be an integer.)

I agree wholeheartedly that 17 is the Most Random Number: not too close to the borders or the center, odd, prime, and without cultural connotations outside of Italy.

Rearranging the letters in the Roman numerals for 17 spells “VIXI” or “I lived” (past tense) in Italian.

GAH! No! That’s not Italian, it’s Classical Latin!!!

(Incidentally, 13 is my lucky number. Most of the time anyway.)

57. David Marjanović says

Being a wise-ass nerd, I knew that most people would pick a prime number because they look more “random” — 1 is among the numbers least commonly guessed in lotteries –, so I deliberately chose 10 for aesthetic symmetry reasons. MWA HA HA HA HAAAAAH…

(Still, I was normal enough to assume it had to be an integer.)

I agree wholeheartedly that 17 is the Most Random Number: not too close to the borders or the center, odd, prime, and without cultural connotations outside of Italy.

Rearranging the letters in the Roman numerals for 17 spells “VIXI” or “I lived” (past tense) in Italian.

GAH! No! That’s not Italian, it’s Classical Latin!!!

(Incidentally, 13 is my lucky number. Most of the time anyway.)

58. 17 has been my favorite number for most of my life. It was a joy to me as a child to find out that it was a Fermat prime. But 6, well, 6 is perfect!

A trick to achieve randomization could be to increment the number each time asked, with wrappings to fit the number space. Assuming each questioner is independent (and they better be or they will get a completely different answer :-), they should get something that looks sufficiently randomized to them.

Now, where did I put my eidetic memory?

A trick to achieve randomization could be to increment the number each time asked, with wrappings to fit the number space. Assuming each questioner is independent (and they better be or they will get a completely different answer :-), they should get something that looks sufficiently randomized to them.

Now, where did I put my eidetic memory?

6 is perfect

Most of the time, but it can also depend on if 1, 2, 3 or more are involved. :-)

6 is perfect

Most of the time, but it can also depend on if 1, 2, 3 or more are involved. :-)

63. Baratos says

My first thought was “a number between one and twenty? To stand out, I pick thirty!”

64. says

I picked 17, because my birthday is on the 17th :)

My husband picked 18.

I was still surprised to see 17 in the link.

65. TAW says

5 was the first number that came to mind, so that’s what I picked.

I asked 4 people, and here’s what they said- 5, 7, 7, 13.

66. CCP says

Hey, Cap’n C! Me too! I picked 17 intentionally because of its importance (along, of course, with 23 and 5) in Shea & Wilson’s Illuminatus! trilogy.

67. rubberband says

I choose pi. I do this often when asked to pick a number, just to make people think. (Or maybe because I’m an incurable smartass)
If asked for an integer greater than zero and less than twenty-one, I suppose I might pick 17.
Why? Well, it’s kinda like rock-paper-scissors. I’m gonna choose a number that I think the other person will pick to avoid the number s/he thinks I’m gonna pick. So, I figure that the other person will figure that the ‘logical’ choice is 10 ’cause it’s equally far from both extremes, so the other person will NOT pick 10. Then I need to commit to either the upper or lower range. If I’m committing to the upper range as a guess, but don’t think that the very top is likely, then 17 just seems within ‘striking distance’ of the entire upper range. (If the other person is thinking of a number below 10 I’m screwed, but hell, it’s just a game)
This is far less logical than it seems. Stuff like this is why some folks believe in numerology.

. . . .I need some sleep.

68. Noah says

I picked twenty. Then I realized you hadn’t said to pick an integer, so I picked pi.

69. Chinchillazilla says

I picked seventeen. But I think that may be because I just turned seventeen.

I was disappointed to realize it wasn’t some kind of awesome mind-reading internet thing; I was going to go back and try again with a different number.

70. says

After reading just the title, I picked 42. After I read the rest of the post, I picked 1.

In regards to his further experiment, where he wants to have people pick a number between 1 and 100, considering that the people conducting these polls are likely to be nerds, with nerd friends, I wonder how common 42 will be.

71. says

Re: PZ Myers’ “that it might also be shaped by language”.

This is called priming, probably of the phonetic variety, something (as a linguist) I have studied more than in passing but not in great detail. I agree that this is a very plausible explanation for why most people who use this “halfing rule” don’t half to the lower part of the range, something I’d had trouble reasoning.

Intriguing.

A few other simple tests could be done to see if the choice is range-based (halfing rule, or some other operation on the highest and lowest values) by increasing the range, banning odds, banning primes, etc.