This week's Casual Fridays study was inspired by this comment on the Random Number thread:

When a freshman at Penn State too many years ago to count, the intro psychology prof did an amazing demonstration. I wonder if anyone knows the answer to this which I have long forgotten.

He said he had written the numbers 1 through 5 in random order on a piece of paper. He then asked the very large class to read his mind and write down his number order.

When the class compiled the answers, more than 50% of the class had his order, and so proved that telepathy was possible!!!

The class was ecstatic, until he then told us that humans more often than not arrange those numbers in that particular sequence that he had.

Does anyone know what that sequence order is?

I have puzzled over this for years since.

I thought we might do Bobbysoxer a favor by uncovering the number sequence, if indeed it exists. I was skeptical: half the class? A sequence of five items, in random order? Since there are 120 possible unique sequences of the numbers 1 through 5, a random distribution of responses would mean fewer than one percent of answers would be in any given order. Chances that HALF the responses would be the same seem remote.

That's not to say that responses will be truly randomly distributed. But I doubted that any single combination of digits would even approach 50 percent.

Our survey asked respondents to randomly arrange the digits 1 through 5 -- and also 1 through 4, and 1 through 3. Perhaps with a smaller range of choices we'd get something approaching Bobbysoxer's memory of the event.

First let's take a look at the distribution of responses for the digits 1 through 5. How "random" were our answers?

The most popular response was "12345", selected by 5.3 percent of our 1,409 respondents. Yes, technically, sometimes a "random" arrangement of those digits would come out in that order, but I suspect this reflects the percentage of our readers who are cheeky and want to make a point about "randomness," not the amazing mystery number Bobbysoxer remembers from college. Second most popular was "54321" with 3 percent of the responses. The next three sequences were tied: "34251", "53421", and "52314", each with 1.8 percent of the total response. That's hardly the 50 percent response that would have been so impressive to a class of intro psych students.

I suspect either the professor did something else to lead the students to respond in the way they did, or Bobbysoxer's memory isn't entirely accurate. What's clear from our study is that there's no "particular sequence" that most people arrange a sequence of five digits in.

That said, there were still some interesting patterns in the data. Take a look at this:

This shows the percent of people choosing each possible first digit in the sequence. They were significantly more likely to choose 3 or 5 than the other digits.

What about four-digit sequences? Were there any trends there? Once again, nothing as dramatic as what Bobbysoxer recalled. The most common response was "4231", with 6.7 percent of responses. This isn't anywhere near 50 percent, and only 2.5 percent above the expected 4.2 percent in a random sample. Was there a pattern with first digits?

This time, 1 was the least common first digit, with just 18.9 percent of an expected 25 percent responses. Interestingly, if you subtract out the 6 percent of respondents who answered "1234", answers starting with 1 sink to a very low 12.9 percent of the total -- about half of what would be expected due to chance.

What about 3-digit sequences? Here we see a bit more of a pattern to the answers.

With just six possible combinations, "231" garnered 22.6 percent of responses, and answers starting with 2 accounted for 43 percent of answers. But still, even with only three digits to arrange, no one answer accounts for anything near the 50 percent Bobbysoxer recalls.

But as with four-digit numbers, there seems to be a definite reluctance to start with the number 1.

So is it possible that Bobbysoxer's teacher somehow led his students to pick a particular sequence? It might be, although I'm having a hard time coming up with exactly how it might have been done. Perhaps the class had to fill out a form with a course number or some other numeric item before responding to the "mind-reading" challenge.

I didn't try to lead the respondents in a particular direction with this study, but another part of our study may have revealed just how suggestible people can be. We also asked respondents to "pick a random word and type it below."

Out of 1,409 responses, you wouldn't expect many repeats, given the fact that there are over 70,000 words in frequent use in the English language (math/stats whizzes: can you compute the expected number of repeats?). Yet there were in fact 409 repeats, including several words that were produced ten or more times. The most common word was "random," repeated 40 times (and of course, that word appeared immediately above the answer box). Next most popular was "pickle", with 20 repetitions ("pick" was also in the instructions for the question). Other common choices were "banana" and "monkey" (we use Survey Monkey to host our surveys). Food items were chosen dozens of times (we had previously asked how often readers went to the grocery store).

And take a look at this graph showing how frequently words were chosen starting with each letter:

The red bars show our survey responses, while blue shows the average incidence of starting letters in the English language. As you can see, our respondents chose words starting with B, C, and P significantly more frequently than those words actually appear in English. The discrepancy may again be due to our prompt -- it starts with a "P" word, "pick," and ends with a "B" word, "below."

I didn't find any correlation between the responses to the other "random" questions and how random the number sequences were, but in case you're interested, here are some of those results:

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This was a great fun survey. Putting numbers in a 'random' sequence is a hard thing to try and do, especially when (along with 80% of respondants) I don't believe I'm a random number generator. The order of the keys at the top of the keyboard makes you painfully aware of the decisions you're making with each keypress.

I entirely believe this story. For example: https://www.blogger.com/comment.g?blogID=11522380&postID=11244578374304… - this really works on most people (we checked it).

I saw a conference presentation by Allen Neuringer where he presented his work (which has been extensively published) where he reinforces participants for behaving in a random way on computer tasks. He taught them to produce number sequences that a computer could not distinguish from random generation. Whether that accounts to humans being "truly random" seems to me like it depends on your definition of truly random.

Alex:

We checked that one too. Our results weren't so impressive.

powers of suggestion are quite incredible, and can influence all sorts of choices. I don't doubt there is a way to bias the selection of numbers. Maybe when you are explaining the task, you say out loud one or two combination which then people will tend to suppress as 'non-random' biasing their choice to something the most orthogonal to the stated selections *shrug*

ohh, or maybe the class starts at 3:15 in room 24!

I recall reading an explanation of a "psychic" trick; the explanation claimed that if you ask a group to pick an odd number between one and 99 inclusive, more than half will choose 35 or 37. It was quite an odd claim, and in my classes afterward I was never able to get those sorts of results.

Then I saw a "psychic" do this particular trick--of course, there was quite a bit more patter than just the "odd number between 0 and 100"; there was the "two different numbers--not 11 or 55 or 77" and the obligatory "and don't choose something easy like 69", and a few more subtle prompts. The upshot was, a member of the audience might remember it as being a free choice among 50 possibilities, but in truth it had been narrowed down to a handful. Among that handful, yes--35 and 37 were the most commonly chosen.

So yeah, I suspect something more to the 12345 problem.

Two things: first, I actually consciously associate "banana" with the idea of randomness because my friends in high school would always use it as an example of being random (which is why I didn't choose it).

Second is something that may have affected the patterns for the four- and five-numbered sequences. I noticed on the survey that the pages were numbered. So the first page of questions was labeled 1-1 at the top, the second page 2-1, and so on. The page with the question about a four-number sequence was labeled 4-1, and the five-number sequence was labeled 5-1. I noticed that, thought you were doing it on purpose, and deliberately tried not to use those numbers at the beginning, but it may have had an effect on people who didn't notice it.

Dave:

We've tried the 'red hammer' trick in Russian. It worked much better, we got around 70% of 'red hammer' responses. The other significant answers were "black computer" and "yellow drill". Maybe it's also culture dependent.

Oh, and another test - pick a prime number less than 100 with two different digits.

The most frequent answer: sqrt(1369).

Just something I noticed. In your survey, we had to type the response. Now, for the random number order, I literally closed my eyes and punched keys blindly. This resulted in some repeats and some numbers outside the appropriate range, so I deleted the invalid numbers and for the appropriate numbers, deleted anything after the first appearance to get my random sequence.

In the experiment you described, the respondents had to write the answers. It's a lot harder to come up with a random sequence that you have to pull out of your head then it is to blindly push a bunch of keys on a keyboard. It might be interesting to see what happens if you stipulate that you must come up with the sequence in your head vs. trying some other random approach.

I've generally found that people mistake 'random' for 'equally distributed'. So if you ask someone to select 5 random people in a room they will choose one or two from the middle of the room (usually different sides), one from the front, one from the back and the last one will be from an area of the room so far unrepresented. They will also make the sex distribution as equal as possible, regardless of the proportion of males/females present.

I used random number generator for these (Mathematica)

Isn't there a central difference in the experiment above? The professor asked the students to try and guess his number not to try and write down a random number. This could lead to a significant change in the number chosen by the students (probably eliminating the choice of 12345 - because it would be to "easy")...

I believe that this is generally true, given enough of a sample size, but I highly doubt you can achieve 50%. With 5 digits, each selected once, the random odds of picking a sequence is 1/5! which is 1/120. So each sequence has a .83% chance of being picked by a truly random picker. I suspect we have a an "ordinal bias" where we can't help but take into account the ordinal value of a number, where a computer, choosing randomly doesn't. In other words, humans aren't capable of choosing a random order of a set of things if they already use the set of things in their every day life. An alternate experiment for comparison would be to present students 5 unknown symbols, and to present those symbols in a random order to each student (so each student sees the same set, but in a randomized order), then compare those answers to the 12345 experiment, and I'm sure you'll see a much more random distribution.

Surely we've all heard of various researchers (sometimes even in the social sciences!) who attempt to fake their data and of course upon analysis it becomes apparent that the data doesn't follow the expected distributions....

If humans were truly random then behavior would be completely unpredictable and there would be no "science" around how people act and react. While there are individual differences that are more difficult to account for, there is great overlap in behavior as well.

I believe there is more to this psychology professors mind-boggling demonstration story, then the freshman has let us know. People tend to lose the details of the situation, when represented an extraordinary effect such as this one.

I used to do lot of magic trick in my past and later days, when I've listened people who brought back the effects of my tricks, similar quotations arise: "He just told me to think of the number and...", when in reality the situation was much more controlled, usually involved a book or a deck of cards :)

http://rubbishfromthebalcony.blogspot.com/2008/01/why-we-do-not-play-ra…

Wish I could remember numbers. Have no idea what my answers to the survey were...sigh.

As for being random when I wanted to naturalize a lawn I got a whole bunch of golf balls, threw them onto the lawn from various spots in the street, and planted the plants and bulbs where they landed. It was the only way to make the garden have no pattern.

Why anyone thinks he could think random? It is just wishful thinking that you can act or think random.

When a person is asked for generating random sequence of numbers, what he can do? He could just try to recall some numbers (or generate them out by some algorithm/recipe) and, maybe, check the imagined numbers for looking random and reject "not random looking sequences".

Why to think that recalling is random? It is not! You can pick associations (which are not random, but learned) or generate mental objects by a method.

What brings a bit of randomness into human brain? These factors:

1) "content" of "short-term memory" (=certain neural paths being sensitized by a recent utilization)

2) associations, as result of experience (de-facto long term memory)

3) some borderline effects, like: possible exhaustion of certain neural paths (depleted neurotransmitters, glucose, oxygen etc.), tumors mechanically stimulating neurons, onset of psychoactive drugs or hormones...

The short term memory could be deliberately filled with anything commonly known (by requesting to imagine it or perform it).

Then you can largely depend on knowledge (associations) typical in population, eg.:

Question for quick recall of white thing would probably be answered with "milk", if the man was thinking about cows recently.

Brain works not random, but in accordance with physical laws of this universe. Quantum effects are too subtle to bring randomness into cognition.

"Its random" means "I don't know how it comes."

I'm surprised that so many chose 12345 as "random." Of course that sequence could be generated randomly, but i would think people would consciously avoid it as sequential and therefore not random.

It won't necessarily help you on this one...but my first day of Social Psychology class, the teacher said it was so powerful that it gave a practitioner like him almost psychic abilities to read people. To "prove" it, he feigned that he was studying each person and then handed that person a piece of paper with a paragraph that supposedly would describe them. He then asked everyone to raise their hand if they felt they agreed with the description he chose. Don't remember the exact % but definitely more than half raised their hands. And then he explained that everyone got the *same* paragraph. It was, of course, written in general enough terms by someone who knows what most college freshman think about themselves.

http://www.youtube.com/watch?v=gxJtlJ4eze4

Derren Brown is an amazing illusionist/entertainer who uses his knowledge of psychology and the human body to do all sorts of crazy stuff. In this video he uses dialogue and hand signals to manipulate people into thinking the numbers he wants them to think. (his other videos are pretty trippy as well.) I'd love to hear what you think about this guy!