How Pinball Helps Explain Ways We Think and Learn

An excerpt from “A Mind for Numbers.”

The following is excerpted from A Mind for Numbers, by Barbara Oakley. 

Focused Versus Diffuse Thinking
Since the very beginning of the 21st century, neuroscientists have been making profound advances in understanding the two different types of networks that the brain switches between—highly attentive states and more relaxed default mode networks.[i] We’ll call the thinking processes related to these networks the focused mode and diffuse mode, respectively—these modes are highly important for learning.[ii] It seems you frequently switch back and forth between these two modes in your day-to-day activities. You’re in either one mode or the other—not consciously in both at the same time. The diffuse mode does seem to be able to work quietly in the background on something you are not actively focusing on.[iii]  Sometimes you may also flicker for a rapid moment to diffuse mode thinking.

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Focused-mode thinking is essential for studying math and science. It involves a direct approach to solving problems using rational, sequential, analytical approaches. The focused mode is associated with the concentrating abilities of the brain’s prefrontal cortex, located right behind your forehead.[iv] Turn your attention to something and bam—the focused mode is on, like the tight, penetrating beam of a flashlight.

The prefrontal cortex is the area right behind the forehead.

Diffuse-mode thinking is also essential for learning math and science. It is what allows us to suddenly gain a new insight on a problem we’ve been struggling with, and is associated with “big picture” perspectives. Diffuse-mode thinking is what happens when you relax your attention and just let your mind wander. This relaxation can allow different areas of the brain to hook up and return valuable insights. Unlike the focused mode, the diffuse mode is not affiliated with any one area of the brain—you can think of it as being “diffused” throughout the brain.[v] Diffuse-mode insights often flow out of preliminary thinking that’s been done in the focused mode. (The diffuse mode must have clay to make bricks!)

Learning involves a complex flickering of neural processing among different areas of the brain, as well as back and forth between hemispheres.[vi] So this means that thinking and learning is more complicated than simply switching between the focused and diffuse modes. But fortunately, we don’t need to go deeper into the physical mechanisms. We’re going to take a different approach.

The Focused Mode – A Tight Pinball Machine

To understand focused and diffuse mental processes, we’re going to play some pinball. (Metaphors are powerful tools for learning in math and science.) In the old game of pinball, you pull back on a spring-loaded plunger and it whacks a ball, which ends up bouncing randomly around the circular rubber bumpers.

This happy zombie is playing neural pinball.

Take a look at the following illustration. When you focus your attention on a problem, your mind pulls back the mental plunger and releases a thought. Boom—that thought takes off, bumping around like the pinball in the head on the left. This is the focused mode of thinking.

In the game “pinball,” a ball, which represents a thought, shoots up from the springloaded plunger to bounce randomly against rows of rubber bumpers. These two pinball machines represent focused (left) and diffuse (right) ways of thinking. The focused approach relates to intense concentration on a specific problem or concept. But while in focused mode, sometimes you inadvertently find yourself focusing intently and trying to solve a problem using erroneous thoughts that are in a different place in the brain from the “solution” thoughts you need to actually need to solve the problem. As an example of this, note the upper “thought” that your pinball first bounces around in on the left-hand image. It is very far away and completely unconnected from the lower pattern of thought in the same brain. You can see how part of the upper thought seems to have an underlying broad path. This is because you’ve thought something similar to that thought before. The lower thought is a new thought—it doesn’t have that underlying broad pattern. The diffuse approach on the right often involves a big-picture perspective. This thinking mode is useful when you are learning something new. As you can see, the diffuse mode doesn’t allow you to focus tightly and intently to solve a specific problem—but it can allow you to get closer to where that solution lies because you’re able to travel much farther before running into another bumper.

Notice how the round bumpers are very close together in the focused mode. In contrast, the diffuse mode on the right has its circular rubber bumpers further apart. (If you want to pursue the metaphor still further, you can think of each bumper as a cluster of neurons.)

The close bumpers of the focused mode mean that you can more easily think a precise thought. Basically, the focused mode is used to concentrate on something that’s already tightly connected in your mind, often because you are familiar and comfortable with the underlying concepts. If you look closely at the upper part of the focused mode thought pattern, you’ll see a wider, “well-trodden” part of the line. That broader path shows how the focused mode thought is following along a route you’ve already practiced or experienced.

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For example, you can use the focused mode to multiply numbers—if you already know how to multiply, that is. If you’re studying a language, you might use the focused mode to become more fluent with the Spanish verb conjugation you learned last week. If you’re a swimmer, you might use the focused mode to analyze your breast stroke as you practice staying low to allow more energy to go into your forward motion.

When you focus on something, what automatically happens is that the consciously attentive prefrontal cortex sends out signals along neural pathways. These signals link different areas of your brain related to what you’re thinking about. This process is a little like an octopus that sends its tentacles to different areas of its surroundings to fiddle with whatever it’s working on. The octopus has only so many tentacles to make connections, just like your working memory has only so many things it can hold at once. (We’ll talk more about the working memory later.)

You often first funnel a problem into your brain by focusing your attention on words—reading the book or looking at your notes from lecture. Your attentional octopus activates your focused mode. As you do your initial focused noodling around with the problem, you are thinking tightly, using the pinball bumpers that are close together to follow along familiar neural pathways. This isn’t a concern if you are trying to figure out something very similar to what you already know. Your thoughts rattle easily through the previously ingrained patterns and quickly settle on a solution. In math and science, however, it often doesn’t take much of a change for a problem to become quite different. Problem solving then grows more difficult.


[i] Andrews-Hanna, 2012; Raichle and Snyder, 2007; Takeuchi, et al., 2011. In a very different line of investigation, Mangan has noted that William James’ description of the fringe includes the following feature “There is an ‘alternation’ of consciousness, such that the fringe briefly but frequently comes to the fore and is dominant over the nucleus of awareness.” (Cook, 2002, 237, Mangan, 1993.)

[ii] Immordino-Yang, et al., 2012.

[iii] Edward de Bono is the grand master of creativity studies, and his vertical and lateral terminology are roughly analogous to my use of the terms focused and diffuse (de Bono, 1970).

Astute readers will notice my mention that the diffuse mode seems to sometimes work in the background while the focused mode is active. However, research findings show that the default mode network seems to go quiet when the focused mode is active. So which is it? My sense as an educator and a learner myself is that some non-focused activities can continue in the background when focused work is taking place, as long as the focused attention is shifted away from the area of interest. In some sense then, my use of the term “diffuse mode” might be thought of as “non-focused mode activities directed towards learning” rather than simply “default mode network.”

[iv] There are also a few tight links to more distant nodes of the brain, as we’ll explore later with the attentional octopus analogy.

[v] The diffuse mode may also involve prefrontal areas, but it probably has more connections overall, and less filtering out of seemingly irrelevant connections.

[vi] Psychologist Norman Cook has proposed that “the first elements in a central dogma for human psychology can be expressed as (1) the flow of information between the right and left hemispheres and (2) between the “dominant” [left hemisphere] and the peripheral effector mechanisms used for verbal communication.” (Cook, 1989) But it should also be noted that hemispheric differences have been used to launch countless spurious over-extrapolations and inane conclusions (Efron, 1990).

Excerpted from A Mind for Numbers: How to Excel at Math and Science (Even if You Flunked Algebra), by Barbara Oakley. Copyright © 2014 by Barbara Oakley. Jeremy P. Tarcher; Penguin Group USA – A Penguin Random House Company.

Meet the Writer

About Barbara Oakley

Barbara Oakley is author of A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra) (Tarcher/Penguin, 2014) and an engineering professor at Oakland University in Rochester, Michigan.

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