Duncker’s Radiation Problem

Duncker’s radiation problem reads:

Suppose you are a doctor faced with a patient who has a malignant tumour in his stomach.It is impossible to operate on the patient; but unless the tumour is destroyed the patient will die. There is a kind of ray that can be used to destroy the tumour. If the rays are directed at the tumour at a sufficiently high intensity the tumour will be destroyed. Unfortunately, at this intensity the healthy tissue that the rays pass through on the way to the tumour will also be destroyed. At lower intensities the rays are harmless to the healthy tissue but they will not affect the tumour either. What type of procedure might be used to destroy the tumour with the rays, and at the same time avoid destroying the healthy tissue? (Duncker; 1945; Gick & Holyoak, 1980, 1983; Keane, 1985)

One roadblock to successful performance, even with analogical hints, is understanding how radiation works (Helfenstein & Saariluoma, 2006)

Superficial similarity between analogies, while present in more difficult problems (Reed, 1987; Ross, 1987, 1989) is not found in the Duncker radition problem (Holyoak & Koh, 1987). In general, surface similarity does not effect the number of correct answers, it positively impacts the quality of answers (Heydenbluth & Hesse, 1996)

A story that analogously solves the problem brings a 30% success rate, while no clue provides a 10% success rate (Gick & Holyoak, 1980)

(A bibliography is below the fold)

Duncker, K. (1945). On problem solving. Psychological Monogrpahs, 58. Whole no. 270.

Gick, M. & Holyoak, K.J. (1980). Analogical problem solving. Cognitive Psychology, 12, 306-355.

Gick, M. & Holyoak, K.J. (1983). Structure-mapping. A theoretical framework for analogy. Cognitive Psychology, 15, 1-38.

Helfenstein, S. & Saariluoma, P. (2006). Mental contents in transfer. Psychological Research, 70(4), 293-303.

Heydenbluth, C. & Hesse, F.W. (1996). Impact of superficial similarity in the application phase of analogical problem solving. The American Journal of Psychology, 109(1), 37-57.

Holyoak, K. J., & Koh, K. (1987). Surface and structural similarity in analogical
transfer. Memory & Cognition, 15, 332-340.

Keane, M. (1985). On drawing analogies when solving poblems: A theory and test of solution generation in an analogical problem-solving task. British Journal of Psychology, 76, 449-458.

Reed, S. K. (1987). A structure-mapping model for word problems. Journal of Experimental Psychology: Learning, Memory, and Cognition, 13, 124-139.

Ross, B. H. (1987). This is like that: The use of earlier problems and the separation
of similarity effects. Journal of Experimental Psychology: Learning, Memory, and Cognition, 13,629-639.

Ross, B. H. (1989). Distinguishing types of superficial similarities: Different effects on the access and use of earlier problems. Journal of Experimental

Psychology: Learning, Memory, and Cognition, 15, 456-468.

9 thoughts on “Duncker’s Radiation Problem”

  1. Isn't the solution to this one to use multiple, focused rays that converge on the tumor but pass through different healthy tissues, delivering the needed radiation in sum, but not separately?

    Of course, you didn't ask, so I'm just blabbering…

  2. To this very day, a throat cancer is likely, for instance, to result in severely damaged salivary glands. It's a little better than the stone ages, but radiation therapy destroys a lot of healthy tissue. That would be the case whether you're getting therapy in the Dakotas or at a place like MD Anderson.

    Proton radiation, which requires a very expensive machine and facility, is touted as less harmful to surrounding tissues, but may not be as effective in killing some tumor tissue. To me it looks promising. MD Anderson just started using theirs.

  3. I've seen this problem before in my ed psych courses, and while I can partially recall the analogical situation offered (with the army being broken up, I believe), I couldn't recall the solution to the problem. Interesting how memory works.

  4. I had 8 weeks of radiation treatment for prostate cancer. Unfortunately it didn’t work and fortunately other treatment got me in remission, but I was certainly introduced to this problem very thoroughly, so wouldn’t need the analogies, much as I like them.
    I had to lie in the exact same spot confirmed by CT scan every time, to reduce the risk of damaging other tissue or organs. I guess the technology isn’t quite there because it did damage some other parts. Nevertheless, I do really like the use of analogy to help solve problems like this.

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