The Power of 17

By John Conway | January 30, 2007 10:00 pm

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…)

CATEGORIZED UNDER: Humor, Science
  • http://enceladus.wordpress.com/ Babbler

    May it have something to do with it being a prime?

  • http://char1y.blogspot.com Charly

    In the street magic world, there are a couple of other tendencies that are often exploited to make you look like a mind reader.

    1) Think of a number between 50 and a 100, even different digits.

    2) Think of any card.

    ————————

    The common answer to 1) is 68. The common answers to 2) are the Queen of Hearts, the Ace of Spades, the Six of Clubs and the Nine of Diamonds.

    I had never heard of the “17″ tendency, but I will definitely try it.

  • http://char1y.blogspot.com Charly

    Oh, and James Randi is my hero as well (for debunking Uri Geller, among other things).

  • D
  • BillyK

    You may know about the trick where you write 1, 2, 3, 4 on one side of a paper and write “Why did you choose 3?” on the other side. You then show the front of the paper and ask the participant to pick a number. A very large number of people choose 3 and you then hand them the paper to turn over and walk away. It’s amazing how often this works and it’s a nice effect. Something about the ordering of the numbers.

  • Nobody

    Listen to the way the words sound: “between one and twenty”…
    The last two syllables: “twenty”
    Last two syllables of seventeen: “enteen”
    Same sequence of vowel sounds….. whatever neurons get paid to notice that pattern are already firing when your brain starts to look for a new number. The only permitted number other than twenty that closes with the same vowel pattern is seventeen. Presumably people don’t pick twenty or one since they feel that’s non-random for some reason, so they tend to pick seventeen, because that little part of their brain is already “turned on”. Maybe if you restated the intructions so that you never said “between one and twenty”, the pattern would change… maybe try saying “name a number no greater than twenty and no smaller than one”

    First Hypothesis: the pattern will vanish if you rephrase the instructions in the suggested way.

    Second Hypothesis: if you tell people to “pick a number no smaller than one and no greater than eleven”, they will usually choose seven, for the same reasons.

  • Scott

    If you ask 1-10 it is 7 thats chosen.

  • http://www.stud.uni-graz.at/~04schlie/ Jürgen Schlieber

    Interesting point, Nobody. To further investigate that, one could make the test in Austria, where I happen to live. The numbers 20 and 17 sound very different in German.
    20 = Zwanzig
    17 = Siebzehn
    It’s bad I won’t meet enough people until monday to conduct a test where say at least 40 people participate. But it would be certainly interesting to see whether the result differs.

  • http://kasperolsen.wordpress.com Kasper Olsen

    John,

    nice fun fact; I guess this is well-known, at least a math teacher once told me, that “17 is the most random number”; with tongue-in-cheek?

    PS: I think your experiment is too biased to work, but let’s see…. :-)

    -Kasper

  • http://www.valdostamuseum.org/hamsmith/ Tony Smith

    William Feller (his wikipedia entry has a link to a St. Andrews biography) was born in Zagreb in 1906, got his Ph.D at Gottingen (studying under Hilbert and Courant) in 1926, and moved to Princeton in 1950, where he told his students two things that stand out in my memory:

    1 – You always need to have in mind a concrete example to understand abstract concepts, and his favorite was the harmonic functions on the unit disk. It, and its generalizations, do exemplify MANY abstract math structures.

    2 – It is good to have a random number to plug into equations to check out how they work numerically.
    The best such number is 17.
    17 is prime, bigger than 12, not unlucky like 13, and not too big like 19.

    Since the math genealogy site shows that he had 17 (of course) students and 614 descendants,
    maybe “The Power of 17″ is due to him.
    At least, his spirit is doubless happy to see that nowadays people are likely to pick his favorite number, 17.

    Tony Smith

  • http://theeternaluniverse.blogspot.com Joseph Smidt

    My favorite game with primes goes like this:

    I ask a group of people to tell me 5 of prime numbers.(Any number of them works) I then say I will give $20 to the first person who can multiply the the first four together in any combination to give me something divisible by the fifth. Since prime factorization is unique, they’ll never do it, but some try for hours.

    It is great! :)

  • Tom Renbarger

    I assume that the fourth root of the unused prime is not allowed? ;)

  • Uncle Enzo

    Who cares. Who cares. Who cares.

  • http://www.savory.de/blog.htm Stu Savory

    @Josef,
    you ARE aware that there are algebraic rings to which prime factorisation does not apply?

  • Ambitwistor

    I read this same observation some years ago in the science section of, I think, the Washington Post. They did an experiment with the numbers 1-100. There, the most common “random” number was 37.

  • Pierre

    This makes me think of the following test : basically you ask someone to several simple additions (a dozen for instance ala :
    17+42
    27+32
    45+64
    23+23
    25+9

    Think immediately of a tool and a color !

    It’s said 98% people think of a red hammer…

  • Bob

    A “random” number won’t be even, or divisible by 5 — those numbers don’t appear to be “random” enough, nor is 1. 37 (in 1 to 100) is a good choice because each of its digits satisfies those rules — 77 would also be good, except that both digits are the same, obviously not “random”! ;-)

  • http://theeternaluniverse.blogspot.com/index.html Joseph Smidt

    @ Stu

    Your right, this kind of game wouldn’t work with you all. After you’ve taken some abstract algebra you know there’s all kinds of counterexamples you can use.

  • http://www.mikepeel.net/ Mike Peel

    Humans are hopeless when it comes to randomness in general. Another fun thing to try is to tell a group of people to space themselves out randomly in a room. They will tend to spread themselves out equidistantly.

  • http://backreaction.blogspot.com/ B

    Does it matter whether one asks people to choose a random number between 20 and 1?

  • Z

    Also, what happens when you ask people for a random number between -Pi and +Pi or, better, between the mathematical constant e and and the complex conjugate i?

  • Tom Allen

    The point is that there is no such thing as a “random” number. Once you choose a number, it’s no longer random. It’s the chosen number. Randomness is a property of a set of numbers.
    So it’s essentially a nonsensical request to ask someone for a random number.

  • http://name99.org/blog99 Maynard Handley

    This is clearly a numberist observation. The other numbers have just as much ability to be popular as 17, excuses about widths of distributions notwithstanding. They just choose to use their time otherwise. A program to encourage the other numbers to be less shy should remedy the situation.

  • http://musingandmoaning.blogspot.com/ Mr Knightley

    Pierre: that’s impressive. I did indeed think of a red hammer, though it’s possible that’s because I subconciously saw your last line. But even withstanding that it’s weird. Do you happen to know why so many people say red hammer?

  • http://mollishka.blogspot.com mollishka

    As an alum, I feel obligated to at least mention that the number 17 has been … claimed … by the dorm Random Hall at MIT. Seventeen isn’t just random, it’s Random.

  • Nonnormalizable

    I should let you know that 17 is also by far the most common “random” number used in examples by David Griffiths, who I’m sure is known to many readers of this blog.

  • http://backreaction.blogspot.com/ B

    Hi Pierre,

    Think immediately of a tool and a color !

    That’s what I thought of:

    Screwdriver for Girls only ;-)

    seen in an home depot last week.

    -B.

  • http://saber-taylor.livejournal.com/ saber

    I once read a book where a pseudoscience practicioner had become so popular that a spacecraft mission to investigate life on Europa had to include him.

    Irrelevant. Anyway, the stage magician asks a crowd of people to think of a number 1-100. 32 is the most popular but he claims maybe it was 35 not sure. So that’s the 2nd number. By then you’d have a good mass of the crowd.

    I see an above comment with 37. I think primeness is a good characteristic. You have to ask what is the motivation. The provider of the “random” number wants to impress you. So a number that’s not trivial like one of the boundaries, but not being obvious about that criterion. Very Princess Bride. Primeness is useful in numbers when I try to remember algebra rules by testing them with arithmetic so that an accidental factoring doesn’t confuse me.

    I think I remember reading that in choosing a bathroom stall, the most common stall was the 2nd to last one. The motivation there would be to choose the least used stall.

    Seems like an arms race of randomness.

  • anon

    Tried with a class of 15 liberal arts people. I told them to write down their answer within five seconds of my giving them the instructions because I didn’t want them affected by others’ answers. I then went around the room and wrote what they said on the board. I didn’t copy the data down, but very strange. Lots of 12s and 6s, and only two odd numbers (7 and 11). Not *one* 17. I wonder if they don’t have a “good” sense of a random number (or perhaps they have a better one than more mathematically inclined students).

    Anyway, interesting.

  • Paul Schmit

    anon, recall what Nobody (#6) said, which I believe carries some weight. I tried asking one of my fellow physics majors “pick a number between one and twenty” with that exact wording at lunch yesterday, and he blurted out 17 (and I know he doesn’t peruse this blog, though he should…he was completely confused when my friend and i started cracking up at his response). When you ask your classmates to write their response down on paper, they might not be connecting the hearing/verbal-response centers of their brains nearly as effectively, even if they’re thinking quickly, and that “entee” stimulus might not play such a big role. That’s why John’s method of asking each person as they walk in a room makes so much sense…you don’t get biased answers, and everyone answers verbally.

  • Lee Smolin

    Some time back some playful mathematicians in Berkeley worshipped the Yellow Pig by contemplating a theorem each day at 17:17 and celebrating Yellow Pig Day each July 17th. If you asked them why they said that “17 is the most random number.” You can see signs of this if you look carefully at the illustrations in Michael Spivak’s Great American Differential Geometry Book.

  • http://backreaction.blogspot.com/ B

    my office mate said 20. here’s why: he thought I tried to schedule him for a seminar and he’d smartly pick the last possible date.

    besides this, a completely representative survey resulted in lots of 6-s and 12-s from Germans, all Americans picked 17 (there was only one, see above), the Italians were confused, the Austrians were suspicious and requested further information before answering.

    -B.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    That’s what we call a “systematic error.”

  • Carlie

    Perhaps it has to do with our somewhat dualistic way of thinking. People go at half between 1 and 20 for 10, quickly decide that’s too obvious, then go half again and a little over, and you get 17.

  • http://astore.amazon.com/grommel-20 Daldianus

    I’ve said 15.

  • Michael Kremer

    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.

  • llewelly

    Think immediately of a tool and a color !
    It’s said 98% people think of a red hammer…

    That’s funny. I thought of emacs. And dark slate gray.

  • http://onwardsandforwards.wordpress.com/ eenauk

    think of a number of US soldiers happily sitting at home right now between 1,000 and 20,000 …

  • hf

    They did an experiment with the numbers 1-100. There, the most common “random” number was 37.

    Amusingly, both 17 and 37 are important numbers in some Cabala. Probably we could find a common psychological explanation. Cabala (this kind, anyway) pays attention to primes because it interprets numbers as combinations or extensions of other numbers.

  • http://industrialrelations.typepad.com/ride_lots/ Mathias

    Maybe 17 is the average age people lost their virginity so its the most common number they pick since it was eventful.

  • http://www.myspace.com/3n7r0py JL Wallace

    17 is a Full Reptend Prime. 17 = 0.5882352941176470

  • antonio

    The 68, red hammer, 17 and 7 tricks work the same in spanish.

  • Pingback: Glúon /blog » É provável que tenha escolhido 17!

  • Pingback: Not so Random Numbers « Lifer On Earth

  • http://www.ranma.pl ranma

    17 in binary is 10001
    in hexadecimal it’s 11

    17 is the age at which one may donate blood and join the military voluntarily, the age at which one may view R-rated movies without a parent’s accompaniment according to MPAA standards and it is the age at which one may purchase M-rated video games according to ESRB ratings.

    There is a magazine called “seventeen”.

    In the Harry Potter universe, 17 is the coming of age for wizards. It is equivalent to the usual coming of age at 18 ;)

    The fictional city in the video game Half Life 2 is called City 17.

    17 is the number of guns in a 17-gun salute to U.S. Army, Air Force and Marine Corps Generals, and Navy and Coast Guard Admirals.

    Seventeen is also the number of syllables in a haiku poem (5+7+5).

    Research done on wikipedia.

  • http://www.ranma.pl ranma

    something more, 2² + 3² + 5² + 7² + 11² + 13² + 17² = 666 (although it is said, that “the new number of the beast” is 616, not 666 ;)

  • http://www.ranma.pl ranma

    I found something more interesting, in Bible, the word “seventeen” is used seventeen times.

    Genesis 7:11, 8:4, 37:2, 47:28; 1 Kings 14:21, 22:52; 2 Kings 13:1, 16:1; 1 Chronicles 24:15, 25:24; 2 Chronicles 12:13; Jeremiah 32:9; Judith 1:13; Judges 8:14; 1 Chronicles 7:11; Ezra 2:39; Nehemiah 7:42.

    take look at http://www.vinc17.org/d17_eng.html also.

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