Nazis, Sunken Ships, and a 67 Year-Old Game of Telephone

This is a guest post by Jeff Mosenkis, a freelance producer with Freakonomics Radio who holds a Ph.D. in psychology and comparative human development.

Nazis, Sunken Ships, And a 60 Year-Old Game of Telephone
By Jeff Mosenkis

Did you hear the one about the two statisticians who go deer hunting? The first one misses his shot ten feet to the right of the deer; the second one misses ten feet to the left of the deer. They then high five each other and shout “Got him!”

While the quantitative method might not work for hunting, it apparently does for finding sunken warships. NPR’s Alix Spiegel reported this remarkable story about two Australian cognitive psychologists who used a statistical distribution to find two sunken World War II ships, 67 years after they were lost.

On the evening of November 19, 1941, the HMAS Sydney was off the coast of Western Australia when it exchanged fire with the German HSK Kormoran, and sunk with all 645 crewmen aboard. It was a national tragedy, particularly because nobody knew exactly what happened to the ship and why it sunk. The German crew scuttled their damaged ship, and 317 surviving German sailors were picked up in lifeboats at sea or on shore and interrogated. Seventy offered a last location of the ships (including the captain) but the locations varied by as much as 100 miles, so most assumed they were lying, and none of the expeditions over the years were able to find the sunken ships.

But recently, psychologists John Dunn and Kim Kirsner took another look (paper here) and mapped out a statistical distribution of the locations given. They discovered that it conformed to a hyperbolic, or “lazy J-curve” distribution often found in natural phenomena. The distribution of species within an ecosystem takes this shape, so do genome sequences, and crucially, information reconstructed from memory.

Memory, both inside us and when shared between people, works a lot like that old “telephone” game. Every time a story is retold (even one person retelling the same story) the content shifts a little bit.  When Dunn and Kirsner mapped out all the pieces of information, they found that it mirrored classic studies of story retelling. Knowing this, they statistically modeled the pattern and error, factored in other information (like location of drifting debris) and proposed a search area. A new expedition found the Sydney about 3 miles from the location that Dunn & Kirsner had estimated.

So the statistical method might not work on deer, but who knows, maybe the History Channel will start airing “Quantitative Treasure Hunters” soon.

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  1. David Clayton says:

    Where’s Surowiecki when you need him?

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  2. Eric M. Jones. says:

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    • Nico says:

      It’s psychology, yes. But this is a pretty impressive use of statistics, so we can forgive them for that.
      I had heard the joke before, but it was about econometricians.

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    • Matthew says:

      I’m not so ready to dismiss it. If one assumes that the survivors roughly knew the location, but with some added random factor of error, combining the guesses would allow the error factors to cancel each other out. A plot of the guesses would reveal a center of mass, so to speak, that would point to the most likely actual location.

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      • Steevn says:

        Good news is, it would be incredibly easy to perform a test of this:

        Draw a grid of 100+ squares, mark one at random, show it to a group of people for a short period, then poll them later on where the marked square was located, average out their results and see how accurate it is.

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      • robyn ann goldstein says:

        As an introduction to sociology, I would play the game telephone with my students. Then separated boys and girls to see what happens. The boys generally were the poorest listeners of a false and really funny message that went something like the president and sarah p. were having a baby. I tried it many, many times over the years– different presidents…different names. Did not keep records, but the girls did not alter the message as much as the boys (wherein it often became incomprehensible and was lost) . I do have reason now and thanks to Freud, to think that this is a learned phenomenon that, with training, can be changed. So let me know if you find similar results.

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  3. Peter says:

    If you look at the little infograph in the story, the spot where the psychologists “predicted” it would be, 26S 111E, has about 90% of the mentions by the Germans. A 3rd grader could have done just as well.

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    • Steevn says:

      How about… remove all guesses of that specific area, and what do the rest average out to?

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    • Joshua Northey says:

      Yeah I don’t really see what psychology has to do with looking at a bunch of reports and recommending an area that 90% of the reports identify.

      10 people saw the robber. 9 of them reported he was wearing blue pants.

      I predict his pants will be somewhere between purple and green.

      I was right!

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  4. robyn ann goldstein says:

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    • robyn ann goldstein says:

      It is true that there are three individuals who made it possible for me to claim Social Science as `inevitable’ thanks to their rediscovery i.e., remembering my discovery of the concept of the derivative. The first taught me the real meaning of the word patience- so thank you for the “time.” And the other taught me the real `economic’ importance of expediency.

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  5. mannyvel says:

    Actually, this is pretty impressive. Before they waded into the reports, nobody knew where these ships were. What they showed is a formal process for doing what presumably reporters (and policemen, detectives, etc) do when they try and dig for information about an event.

    Everyone sees an event differently. Reconstructing what happened is usually based on the reliability of a given source. With this process, no reliable source is needed. Apparently for some cases all you need to do is determine and distill the common data points from the descriptions of the event in question.

    Will this work for all cases? No.

    Was it a lucky guess? Well, the people who originally interviewed all these survivors were highly motivated to find the wreck, and were unable to even find a place to start given the noise in the original interviews. The ocean is a big place. Many times the goal isn’t to find the item in question, it’s to exclude the 99.9999% of the other locations from the search area.

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