One of the ways we navigate a world full of novel situations and problems is by using metaphors. When facing a new situation or problem, we take a leap of faith that things we don’t know are like things we do know. We search through our memory and find a situation that is “similar” to the one at hand. We use that previous experience as a metaphor for the current one. If it’s a good metaphor, it’s a roadmap through the unknown.
An implication of this is that having more metaphors and more diverse metaphors is a powerful asset for thinking. All else equal, having more metaphors increases the chances one of them will be a good fit for your current problem. In this post, I’ll present some arguments that suggests this is the case. The next post adds some nuance: our ability to navigate our personal library of metaphors matters as much (or more) as its size.
Three Cheers for Metaphors
I’m unaware of any study that directly compares innovation and the number of metaphors (drop me a line if you do). But there are a few lines of evidence that strike me as at least consistent with the theory.
1. Metaphors to Solve Problems
The closest thing we have to a direct test of the theory are psychology experiments.
- Give some subjects a metaphor well suited to solving a problem.
- Don’t give it to a control.
- See if the metaphor-equipped group is better at solving the problem.
Gink and Holyoak (1980) is an early example of the type. The authors asked study participants to solve the following problem. A patient has a stomach tumor that must be destroyed. No surgery is permitted, but a beam of radiation can destroy the tumor without operating. The problem is that any beam strong enough to kill the tumor is also strong enough to kill the tissue it must penetrate to reach the tumor. Any beam weak enough to leave the healthy tissue unharmed is also too weak to destroy the tumor. What should the doctor do?
While you ponder that, let me tell you another story. Totally unrelated, I swear. Once upon a time there was a general who wanted to capture a city. His army was large enough for the task, and there were many roads to the city. Alas, each road was mined. Any force large enough to take the city would detonate the mines as it moved down the road. A smaller force could move down the road without detonating the mines, but would be too small to take the city. What to do?
Fortunately, the general came up with a solution. He divided his army into many smaller divisions, and sent each down a separate road. Each division was too small to detonate the mines, and so they all converged on the city at the same time, and captured it.
Wow, what a neat story.
Now, have you figured out the tumor problem?
The trick is to use many weak beams of radiation, each pointing to the tumor from different directions. They should all intersect at the tumor’s location but nowhere else. Their combined energy will destroy only the tumor, and not the healthy tissue that must be penetrated.Figure 1. Converging armies of radiation
The preceding is basically the experiment that Gink and Holyoak perform. They give people the tumor problem. Only 2 in 30 people were able to solve it on their own. Then they tell them the story of the general. This story’s solution is a tailor-made analogy for the tumor problem (converging weak forces), and 14 of 35 people were able to solve the tumor problem if they got the general story. An additional 12 people came up with the solution after given a hint to use the story to figure out the tumor problem.
A meta-analysis of 57 similar experiments obtains similar results. The intervention reliably has a small-to-medium sized effect. Giving people a solution wrapped up in a metaphor helps them find the solution. A bit.
2. Metaphors and Forecasting
Do these lab results carry over into real world settings? Forecasting forms a set of problems that are not contrived but do have definite “correct” answers. Phil Tetlock has been asking people to make political and economic forecasts for decades, and tracking the results. Drawing on a very old dichotomy, Tetlock classifies his forecasters as either “foxes” or “hedgehogs.” The idea is that “the fox knows many things and the hedgehog knows one big thing.” Tetlock consistently finds that foxes are better forecasters than hedgehogs.
Now, this isn’t really a direct test of the hypothesis. Tetlock isn’t “counting metaphors” for his forecasters. He classifies his thinkers as foxes or hedgehogs based on a series of questions about cognitive thinking style. These include agreement with statements such as “even after making up my mind, I am always eager to consider a different opinion” and “I prefer interacting with people whose opinions are very different from my own.” In general, Tetlock uses language like “hedgehogs view all situations through the same lens” and “foxes aggregate information, sometimes contradictory information, from many different sources.”
However, there is evidence that foxes make use of more and different analogies. Tetlock notes “foxes were more disposed than hedgehogs to invoke multiple analogies for the same case (Tetlock, p. 92).” And it seems to help them navigate novel situations.
3. Metaphors and the Individual
There are also some observational studies consistent with the idea that more metaphors make us smarter.
- Highly creative people (which we can use as a proxy for innovation) tend to be open to new experiences and curious (Sawyer, p 64). These are two channels through which people may acquire additional concepts that can be used as metaphors. People who have lived abroad
- Multicultural individuals show more creativity. Living in a different culture is, of course, a rich source of new metaphors.
- Scientific “geniuses” tend to have broad interests (Simonton, p. 112): they have more diverse hobbies (painting, art collecting, drawing, poetry, photography, crafts, music) and are voracious readers, including extensive reading outside their main discipline. Again, this is hardly a direct measure of the size of their metaphor libraries. But broad interests would tend to foster a larger and more diverse set of potentially useful metaphors.
Of course, alternative and additional explanatory factors are also possible. But these threads are at least consistent with the story that having access to more metaphors facilitates innovation.
4. Metaphors over Time
It’s not hard to establish that the set of metaphors has grown over time. In their book on metaphor, Hofstadter and Sander compile an illustrative list of concepts unavailable to most generations of humanity. Each of these is available as a metaphor to people alive today, but not to people living, say 100 years ago. Here are 25 examples from their list of over 100 (p. 129):
- chemical bond
- six degrees of separation
- uploading and downloading
- video game
- data mining
- instant replay
- black hole
- heart transplant
- space station
- bungee jumping
- stock market crash
- wind chill factor
- greenhouse effect
If these concepts are a better metaphor for some novel situations, then denizons of the modern world have a leg-up on their ancestors. They are equipped with a bigger toolbox for handling novelty. This could be one factor explaining the Flynn effect, whereby the IQ scores on standardized tests rise in each generation.
Additionally, there are many scientific theories whose discovery depended on metaphors that were not always available. The proliferation of clocks in Europe may have made Europeans amenable to thinking of the universe as a machine following strict natural laws, instead of the whims of spirits (Wootton link). Neils Bohr used the heliocentric model of the solar system as a metaphor for the atom – a metaphor that would have been basically unavailable before Copernicus. And Einstein used principles derived from Newton’s classical physics to guide his hunt for the theories of special and general relativity. Again, the evidence is at least consistent with more metaphors being an asset to thinking.
5. Metaphors across Geography
More controversially, some have speculated that similar channels explain the correlation between economic prosperity and test performance (IQ, standardized math and others). GDP per capita is positively correlated with the average performance of a nation on standardized tests. A lot of people argue that this is because human capital/intelligence/IQ (whatever you want to call it) leads to economic prosperity (more innovation, better policies, more cooperation, more patience, etc.). But the causal arrow could just as well point in the opposite direction. Countries with more economic prosperity tend to have more complex economies (link to Hidalgo), more literacy, and greater access to digital information. All three of these channels may well expose the typical citizen to a more diverse set of concepts and processes. And these concepts and processes will then be available as metaphors. This bigger library of metaphors could then be a reason people in these countries do better on standardized tests.
Finally, just as there is some evidence multicultural individuals are more creative, countries with populations from lots of different places tend to have more patent intensity and economic prosperity. Again, this is hardly a direct test, but we can imagine people from different countries bring different sets of metaphors with them. A country with people from many different countries might have a more diverse set of metaphors, which could partially account for their higher performance in innovation.
A Virtuous Circle?
Item #1 above provides the most direct evidence that access to metaphors facilitates problem solving. The remaining items all show that more diverse people, information, interests, and concepts tend to lean in the same direction as various metrics for innovation. Correlation isn’t causation, but it’s possible the set of available metaphors is a causal link between the two. If that’s the case, then as society gets more metaphors it gets better at innovating. Maybe we are living in a virtuous cycle where innovation leads to social complexity and social complexity leads to a wider set of metaphors and access to a wider set of metaphors leads to innovation!
I think there is some truth in that story, but also that it’s only part of the story. Maybe a small part. For items #2-#5 above, the evidence is pretty indirect. We don’t know if people really do expand their set of metaphors via the hypothesized channels, and we don’t know if they use those metaphors to innovate. Lots of other things are going on, and we don’t know how much those other factors matter. We also can’t be sure this isn’t a spurious correlation wherein “smart” people have diverse interests, but these don’t inform their ability to innovate.
Item #1 provides the most direct evidence that metaphors are causally related to innovation. However, even when we give people a perfect metaphor right before we test them, the effect is not large. And if we wait a day to test them, performance declines. It appears that there is a lot more to innovation than simply having access to the right metaphor.
Staying in the “metaphor” or having a library of metaphors, a major problem might be our ability to search the library. Which metaphor is the right one for a given problem? This is a problem we turn to in the next post…