Of Maps and Models

The sun was shining and the birds were chirping in the blossoming trees as we walked along the path, trying to find the BBQ. I pushed the stroller around the bend, eyeing the large park map ahead, and glanced at my wife. Her face was set in an expression that told me she was hungry and losing patience. So was I.

We’d been trying to find this BBQ for the past 30 minutes. And now our 4-month old daughter was screaming because she kept inadvertently pulling the pacifier out of her mouth. We approached the map and I helped my daughter find the pacifier while my wife tried to figure out where we were going. Suddenly, despite the tense situation, my inner neuroscientist perked up. I couldn’t help but notice the uncanny similarity between my daughter flailing for her pacifier and our attempts to navigate with the park map.

The look of intense focus my daughter gets whenever she tries to reach for her beloved pacifier testifies to the challenge of controlling her muscles and joints. Such a deceptively simple movement involves reference frame transformations, redundant muscle systems, and nonlinear physiology that all add up to a tough task for a 4-month old. In fact, even though it’s possible for engineers to write complicated equations to calculate how to move an arm, scientists think that such equations would be a pretty poor way for our brains to control movement. After all, 3-year-olds have pretty much mastered reaching. So what’s the alternative? Well, it looks a lot like a map.

Internal models don’t need complicated equations

Instead of equations, scientists hypothesize that our brains might employ a simplified association between our thoughts of moving, or motor commands, and our physical actions, or motor responses. Unlike the homework and tests that we need to learn equations, it is possible to learn this association through observation: simply try out some motor commands and observe the motor response.

Over time, repeatedly trying out motor commands and observing the motor responses results in something scientists refer to as an internal model. This takes the place of complicated equations and can be thought of as an even simpler version of trial and error – good news for a 4-month-old who still hasn’t had her first Fig Newton, much less learned Newton’s laws.

How internal models are like maps

The simple association between motor commands and motor responses works a lot like a park map. Imagine if my wife consulted a blank white page with a red dot that says, “You are here.” The dot is there, but its location is meaningless without a picture on the page. The picture illustrates how the dot corresponds to a location in real life. Put that same red dot on a picture of the park, and suddenly we know where we are in the real world. Not only that, but we can make a plan to get the hungry parents to the burgers at the BBQ.


The picture on a map describes how the red dot on the blank page corresponds to a point in the park. The map makes it possible for the hungry parents to get to the burgers at the BBQ.

The brain learns a similar mapping. Each particular combination of neural activity my daughter can send to her muscles – each motor command – is like a red dot that says “you are here”: without context, the brain has no idea what it means. But over time, her brain will associate each motor command with a particular muscle behavior, giving meaning to each “location” on the “map” of motor commands. This map will allow my daughter to plan the sequence of motor commands that will move her arm towards her pacifier.


Who needs complicated equations? An internal model describes how a motor command maps to a motor response. This association is learned through trial and error and is an alternative to complicated sets of equations and variables. Internal models make it possible to plan a sequence of motor commands that activate muscle groups, generate joint torques, and ultimately save the day by reaching the pacifier. In this simplified example, Neuron A flexes the elbow and Neuron B flexes the shoulder. To reach the pacifier, the brain plans a sequence of motor commands in which Neuron A’s activity decreases and Neuron B’s activity increases.

With a good park map and a good internal model, my wife and I should be able to get to the BBQ and my daughter should be able to reach her pacifier. But sometimes it’s not that easy. Successful navigation, just like successful reaching, requires both an accurate map and following the plan. Without both of these, parents get lost and pacifiers get flung.

There’s more than one way to get lost

No map is accurate

Even if a map is what most people would consider “accurate”, it is actually impossible to accurately project 3D earth onto 2D paper without distortion of some sort. There are many different types of projections that trade off distortions in one of the four basic characteristics of maps – distance, direction, shape, and area. This means that all maps are inaccurate!

Let’s say my wife and I used the map to come up with a plan for getting to the BBQ. Because the map was on a big signpost in the park, we had to leave the map to follow our plan. Soon we came upon an open field, where, according to our plan, we were supposed to walk 100 feet and then turn 90 degrees to the right. If you’ve ever tried to navigate your room in the dark, you know this is hard to do! Even small errors, especially early on, can turn into a big error at the end. These types of errors are in the execution of the plan, or the motor commands.

Alternatively, you might imagine that my wife and I had a paper map which we used to generate a plan. We followed our plan and regularly consulted the map, making sure we followed the plan exactly. But when we got to where the map placed point B, the BBQ was nowhere to be found! This is in fact exactly what happened – it turned out that our map was a few years old and the shelter where the BBQ was got moved around the bend. These types of errors are in the map, or the internal model.

The trouble with creating a plan using an inaccurate map

In both scenarios, we would be left with our tummies rumbling and our patience wearing thin. We’d know something wasn’t right, but how could we know if the error was due to the map or the execution of the plan? We’d be simultaneously trying to assess the accuracy of the map and use it to navigate. Not an ideal situation.

My daughter was going through a similar process. She was trying to learn to reach with her arm, but hadn’t tried out enough motor commands yet to build an accurate internal model. In effect, she was making guesses about motor commands, but she didn’t really know what they would do to her arm or her pacifier. No wonder she kept mis-reaching or, worse, flinging the pacifier across the stroller!

Learning internal models as adults

Personally, I can’t remember the last time I lost control of my arm and inadvertently flung a spoonful of food out of my mouth, so my daughter’s experience might sound foreign to you. But that’s because we, as adults, have an advantage. Over the course of many years, we’ve tried enough motor commands and observed the many motor responses to learn a very accurate internal model of our arms.

Similarly, most maps that we use to navigate are very accurate. If we miss when we reach for something, we can be confident that the error was in the execution of the motor command. And if we get lost, we can be confident that we must have made a wrong turn (sorry guys, can’t blame the map).

Even with this advantage, though, adults still have to learn new internal models when we start attaching things to our bodies, like skis or tennis racquets. These new extensions of our arms and legs change the internal model.

When I first learned to play tennis, I spent some time waving the racquet around, feeling the difference between slicing it through the air and swinging it broadside. At this point I didn’t even think about trying to hit that little green ball. The time spent trying out motor commands and observing the motor responses helped me to learn an internal model. Then, when I tried to hit the ball for the first time and I missed, I knew my motor commands were to blame and I could make a new plan – a process I’ve been working on for years.


Randomly waving her arms and legs is an example of trying out motor commands and observing the motor responses – in addition to being just plain fun! This type of activity helps my daughter learn an internal model that will help her finally take control of how to move her body.

For babies like my daughter, learning an internal model means frequently waving around her arms and legs. The flailing is her trying out motor commands and observing the responses. Soon she will be able to use that internal model to reach her pacifier without my help, and I’ll have two hand free to bite into that delicious BBQ burger.



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