diamond geezer

 Wednesday, May 08, 2019

The new exhibition at the Wellcome Collection is called Smoke and Mirrors: The Psychology of Magic. A cracking idea, and a decent show. Part 1 looks at mediums and spiritualism, part 2 ventures into the psychology of misdirection and the final part covers mind reading and mind control. I quite enjoyed it, and it made me think, but it was quite busy, and I didn't have the patience to stand and watch all the looping videos. Londonist enjoyed it more. The exhibition's free, and open until mid-September so no need to rush.

One of the displays in the final section includes a set of Zener cards, created in the 1930s to test for extra-sensory perception (ESP). The cards show one of five symbols - a yellow circle, a red cross, three blue vertical wavy lines, a black square or a green five-pointed star. A pack includes 25 cards, five of each design. In the original experiment one person shuffles the pack and looks at each symbol in turn. The other person, who can't see the cards, records what they think each of the 25 cards are. The higher their score the stronger their ESP (or their luck, depending).

And this reminded me that I used to have a pack of Zener cards. It came with The Unexplained, which was one of those partworks much beloved in pre-internet Britain where you went down the newsagents to buy the next set of pages every few weeks. I didn't buy all 157 volumes, because I recognised it was a con, but I did get as far as volume 8 which is when the Zener cards appeared. I cut out the cards and made a little box for them, then took them into school and did some ESP experiments with my friends. Obviously none of them proved psychic, but it passed some time in the corner of a 1980s playground.

And this encouraged me to dive into my spare room and find that pack of cards. Yup, still got it, 39 years later. And here are the cards...

So I thought we'd try an ESP experiment with Zener cards today.... on the hour, every hour from 8am to 12 noon.

I've shuffled my pack, and I'd like you to guess what the top card is. For clairvoyant purposes it's important that I'm looking at the card while you're guessing it, so let's do the first experiment at 8am precisely. I will stare at my card for two minutes, and then I'll give you until quarter past to enter your guess in this special comments box. To keep things easy, just write the word CIRCLE, CROSS, WAVE, SQUARE or STAR. Guess before you look to see what other people have written. Also, please leave a name or initials or alias of some kind for identification purposes.

Starts 08:00, Ends 08:15
your guesses
CIRCLE 2 (8%)
CROSS 4 (15%)
WAVE 6 (23%)
SQUARE 12 (46%)
STAR 2 (8%)
The card was

Thanks for all your guesses. Almost half of you thought my card was SQUARE, which is a particularly strong showing. The totals for CROSS and WAVE were close to the expected average (5) if everyone were guessing purely at random. Only two of you thought it was CIRCLE or STAR. None of the first twenty guesses were CIRCLE. Unfortunately the first card was CIRCLE. This has not been an excellent start for the theories of ESP. So let's try again at 9am.

Starts 09:00, Ends 09:15
your guesses
CIRCLE 3 (12%)
CROSS 4 (16%)
WAVE 9 (36%)
SQUARE 2 (8%)
STAR 7 (28%)
The card was

This time the most popular choice was WAVE, with just over a third of the votes, followed by STAR. At the bottom of the heap were CIRCLE with three votes and SQUARE with only two. It's interesting that CIRCLE and SQUARE were the most prominent results of the first experiment - the card chosen and the card most guessed - but you turned away from those this time. The actual result of the second experiment was STAR, which was your second-placed guess. Better, but let's try again at 10am.

Starts 10:00, Ends 10:15
your guesses
CIRCLE 6 (29%)
CROSS 3 (14%)
WAVE 3 (14%)
SQUARE 6 (29%)
STAR 3 (14%)
The card was

A bit more of an even spread this time, with CIRCLE and SQUARE getting six votes each and CROSS, WAVE and STAR three apiece. It's interesting that CIRCLE and SQUARE were the least popular choices in the second experiment but the most popular in the third. In fact the third card was CROSS. So far nobody has guessed all three cards correctly, but Kevin and QSP have guessed two out of three. The total number of guesses is down a bit this time, and you can't prove anything from a small sample. But let's have another go at 11am.

Starts 11:00, Ends 11:15
your guesses
CIRCLE 5 (23%)
CROSS 0 (0%)
WAVE 9 (41%)
SQUARE 6 (27%)
STAR 2 (9%)
The card was

Now that's interesting. The most popular choice was WAVE, followed by SQUARE. Between them WAVE and SQUARE had over two-thirds of the votes. This is very likely because WAVE and SQUARE are the only cards which haven't appeared yet. Statistically they were your best choices, because there were still five WAVEs and five SQUAREs in my Zener pack but only four of the other symbols. Absolutely nobody chose CROSS, which was the result of the previous experiment. Unfortunately the card was CROSS again. In my randomly shuffled pack, nobody's ESP skills are coming across particularly strongly. But maybe you can do better with the final card at noon.

Starts 12:00, Ends 12:15
your guesses
CIRCLE 3 (16%)
CROSS 2 (11%)
WAVE 8 (42%)
SQUARE 3 (16%)
STAR 3 (16%)
The card was

One strong performer stands out here, and that's WAVE. Over 40% of you chose it, and it received more than double the votes of any other option. Statistically your best choices were WAVE and SQUARE, because they hadn't been drawn yet, but only three of you went for SQUARE while eight chose WAVE. And the correct answer was WAVE, so well done, you got one right. But don't conclude that this is ESP at play. As a group you'd expect to get one of the five experiments right, on average, and this is the one that you got.


Altogether 66 different people had a guess. Only one person participated in every experiment, and he scored zero. Sorry Ken. The best score was three cards correct (out of four), so congratulations to QSP. Run a random experiment with a large enough set of people and somebody's bound to do well.

Altogether, across all five experiments, you made 113 guesses. The expected number of correct guesses is one-fifth of that total, i.e. 23, but in fact you only guessed correctly 20 times. That's an 18% success rate, below the expected average of 20% but not significantly so.

If ESP were really a thing you'd expect to be scoring over 20%. But of course ESP isn't a thing, indeed trying to read the mind of a blogger you've probably never met is total balderdash.

Instead what we've been experimenting on here is which cards people tend to pick when asked to pick from a selection of five cards. They quite like to pick the 'interesting' symbols, so WAVE does better than it should. They quite like to pick names from the centre of the list rather than the extremes. And in particular their choices are often biased by what's come up recently, shying away from those and instinctively choosing cards that haven't appeared.

I've now had a look through my pack and the first SQUARE didn't appear until the ninth card. Randomness is generally quirkier than the subjective guesses people instinctively make. And a ninth experiment wouldn't have happened until 4pm, and I think you'd all have lost interest by then.

With such a small group taking part, and relatively few people able to participate in more than one experiment, we have effectively proved nothing at all. But we don't need proof to know that ESP isn't real, and that the psychology of how people go about making 'random' choices is far more interesting.

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