Over at OmniBrain, Steve has a great summary of a recent article by Thomas and Lleras(1 on embodied cognition/perceptual symbol systems and problem solving. I recommend reading Steve’s summary before going on with this post, but in case you’re really lazy, here’s the abstract:
Grant and Spivey (2003) proposed that eye movement trajectories can influence spatial reasoning by way of an implicit eye-movement-to-cognition link. We tested this proposal and investigated the nature of this link by continuously monitoring eye movements and asking participants to perform a problem-solving task under free-viewing conditions while occasionally guiding their eye movements (via an unrelated tracking task), either in a pattern related to the problem’s solution or in unrelated patterns. Although participants reported that they were not aware of any relationship between the tracking task and the problem, those who moved their eyes in a pattern related to the problem’s solution were the most successful problem solvers. Our results support the existence of an implicit compatibility between spatial cognition and the eye movement patterns that people use to examine a scene.
I find this study’s results fascinating, and more than a bit surprising, for several reasons, which I’ll get to in a moment, but first let me tell you a bit about the problem they used. It’s a problem that those of us who spend a significant portion of our time studying analogy are intimately familiar with — the Duncker radiation problem, which, as originally formulated, read like this(2):
Your problem is to find out how to aply a certain kind of x-rays, with high intensities of which destroy organic tissue, in order to cure a man from a tumor within his body (for instance, in his stomach. (p. 669)
Or more recently(3):
A tumor was located in the interior of a patient’s body. A doctor wanted to destroy the tumor with rays. The doctor wanted to prevent the rays from destroying healthy tissue. As a result the high-intensity rays could not be applied to the tumor along one path. However, high-intensity rays were needed to destroy the tumor. So applying one low-intensity ray would not succeed. (p. 311)
This is an incredibly difficult problem for most people to solve spontaneously (i.e., without being given any sort of hint). Duncker identified three spontaneously produced solutions, but most researchers have focused on one, and as it’s the solution that Thomas and Lleras use in their study, I’ll just describe it. The solution involves using more than one (in Duncker’s example, 2, but in most examples, more than 2) weak rays from different directions that meet in the middle. The idea is that as they pass through the healthy tissue on their way to the tumor from different directions, they will be too weak to do any harm, but when they meat in the middle, their concentrated effect will kill the tumor cells. In Duncker’s most comprehensive study(4), only two out of forty-two partipants, or 4.8%, spontaneously produced this solution.
In a classic study on analogical reasoning, Gick and Holyoak gave people an analogous story to help them solve the problem. The story involved a general who wanted to attack a the fortress of a ruthless dictator. The fortress had many roads radiating out of it in several directions, but the dictator had the roads mined. The mines would explode if a large force walked over them, but if a small force walked over them, they wouldn’t explode. The general felt he needed his entire large force to take the fort, but couldn’t send the force down one road without setting off the mines. So he divided his forces into several small forces, and sent each one down one of the many roads leading to the fortress. They all met at the fortress, and were able to take it.
The idea was that if participants read the radiation problem after reading the story about the general taking the fortress, they would recognize the two problems were analogous, and use the general’s solution to solve the radiation problem. In Gick and Holyoak’s study, participants spontaneously (i.e., without reading the story about the general) produced the weaker rays on multiple routes solution between between 0 and 20% of the time. When they were given the analogy without being told that it could be used to help solve the radiation problem, they solved it between 30 and 40% of the time. That’s a pretty nice improvement, but still the majority of the participants couldn’t come up with the solution on their own. Only when they were given hints tor specifically told that the general’s story could help them solve the problem did more than 50% of participants produce the multiple routes solution.
Interestingly, in one condition Gick and Holyoak(5) gave participants a diagram (either with or without the analogy) meant to illustrate the multiple routes solution (p. 18):
When the diagram was presented alone, without a hint that it might aid in solving the radiation problem, only 7% of participants produced the multiple routes solution. So the diagram was no help whatsoever. In fact, when participants received the general’s story and the diagram, they did worse than if they’d just been given the story (without a hint, that is).
Why am I telling you all of this? Because in Thomas and Lleras’ study, participants who made eye movements that suggested the multiple routes solution (if you don’t know what I’m talking about, go read Steve’s post, ya lazy bum) spontaneously produced the multiple routes solution about 50% of the time after 19 eye tracking trials. Fifty percent! When I read that, my first thought was (pardon my French), “Well fuck me!” How the hell did they get participants to solve it 50% of the time without a hint? Short of presenting multiple different and explicit analogs, no one gets that kind of solution rate without a hint, and Thomas and Lleras gave them no hints or explicit analogs whatsoever. Just eye movements.
Thomas and Lleras argue that their finding suggests an internal perceptual simulation facilitated by the eye movements. What makes their finding and this explanation even more surprising, though, is that an explicit perceptual clue — Gick and Holyoak’s diagram — had absolutely no impact on the production of spontaneous solutions. I mean, maybe if they’d been given it 19 times (the number of eye-tracking trials needed to get participants to 50%), they might have figured it out, but we’ll never know (who’s going to run that study? not I). For now, it seems that the argument is that internal perceptual simulations (whatever the hell those are) are more powerful than external perceptual clues. Weird.
So for now, color me skeptical about the theoretical explanation. It seems to me that after you get what amounts to 19 analogies, perceptual or not, explicit or implicit, you’ve been so beaten over the head with the solution that if you don’t get it, you’re not trying very hard. Sure, participants reported they didn’t see the connection between the task, and I’m willing to believe that consciously, they weren’t aware of that. But as recent research has shown(6), analogical mappings are often conducted automatically and implicitly. And if you give them 19 shots at it, how can they not be?
The real test of a perceptual symbols/embodied cognition explanation of problem solving would, I think, look like this. You’d run everyone in an eye-tracker, using any of the various conditions in which people have been shown to solve the radiation problem with the multiple routes solution at relatively high rates (e.g., multiple analogies), with and without hints, as well as in a control condition in which they have to solve it spontaneously. Put a picture of the tumor surrounded by healthy tissue around it on the screen, and monitor their eye movements. If people are using perceptual simulations facilitated by eye movements to solve the problem, then participants who solve the problem (in any condition), should make eye movements consistent with the multiple routes solution on their own (and this would mean more than just looking at the skin, as in the Grant and Spivey study mentioned in the abstract above — that data is pretty much irrelevant to the question at hand).
1Thomas, L.E., & Lleras, A. (2007). Moving eyes and moving thought: On the spatial compatibility between eye movements and cognition. Psychonomic Bulletin & Review, 14, 663-668.
2Duncker, K. A. (1926). A qualitative (experimental and theoretical) study of productive thinking (solving of comprehensible problems). Journal of Genetic Psychology, 33, 642-708.
3Gick, M. L., & Holyoak, K. J. (1980). Analogical problem solving. Cognitive Psychology, 12, 306-355.
4Duncker, K. (1945). On problem solving. Psychological Monographs, 58(5, Whole No. 270).
5Gick, M.L., & Holyoak, K.J. (1983). Schea induction and analogical transfer. Cognitive Psychology, 15, 1-38.
6Day, S.B., Gentner, D. (2007). Nonintentional analogical inference in text comprehension. Memory & Cognition, 35(1), 39-49.