Spatial Reasoning: Turning Shapes in Your Head and What It Predicts

In 1971, two psychologists showed volunteers pairs of three-dimensional figures and asked whether they were the same object, one of them turned, or mirror images of each other. What stood out was not that people could do it but how long it took: response time grew almost in direct proportion to the angle of rotation. It was as if the brain were physically turning the object, at a more or less steady speed.

What spatial reasoning is

It is the ability to imagine, move, and transform objects in your mind: rotating them, folding them, seeing them from another angle, or working out how they fit together. You use it when loading luggage into a trunk, reading a map, assembling a bookcase from a booklet of pure drawings, or deciding whether the couch will clear the doorway.

Psychologists usually split it into several skills. The best studied are mental rotation, which means turning an object in your head, visualization, which means imagining how a shape changes when it is folded or cut, and orientation, which is locating yourself relative to a surrounding space. They do not necessarily come as a set: someone can be superb at rotating shapes and still get lost the moment they leave their own neighborhood.

The Shepard and Metzler experiment

The 1971 study was by Roger Shepard and Jacqueline Metzler. They used figures built from joined cubes and published the result in the journal Science. It was one of the first solid demonstrations that we can manipulate mental images and that the process can be timed with a stopwatch, something that until then had seemed more a matter for philosophers than for the lab. The task has been a staple of cognitive psychology ever since.

What it is good for in real life

One of the most cited lines of research comes from Jonathan Wai, David Lubinski, and Camilla Benbow, who in 2009 analyzed long-term follow-up data on thousands of students. They found that spatial ability in adolescence independently predicted who went on to study and work in science, technology, engineering, and math, even after accounting for verbal and math skills. Traditional schooling tests this kind of talent very little, which is why some researchers call it a "hidden" talent.

There are also signs that the brain adapts to such demands. A study by Eleanor Maguire and colleagues in 2000 found that London taxi drivers, who memorize an enormous street network, had on average a larger posterior hippocampus than other people.

Differences between men and women

On average, meta-analyses of mental rotation show a moderate male advantage, but with enormous overlap: the difference between any two individuals is far larger than the difference between the group averages. The gap also shifts with the task, the culture, and prior experience, and it can narrow with practice. On its own it cannot tell you what any particular person can do.

How to train it

This is one of the few corners of cognition where the answer is fairly encouraging. A meta-analysis by David Uttal and colleagues, published in 2013, concluded that spatial training improves performance noticeably, and that the effects can last and carry over to similar tasks. Some ways to practice:

• Build puzzles, blocks, or models without peeking at the finished picture.
• Play action or 3D building video games, which have shown gains in some studies.
• Draw objects from different angles or sketch them from memory.
• Work through rotation and paper-folding tests.

How it shows up on an IQ test

On intelligence tests it usually appears as figure matrices, block puzzles, or folding and rotation exercises. A typical item: you see one figure and four options, and must pick the one that is the same figure turned. A practical tip is not to rotate the whole thing at once. Lock onto a distinctive feature, such as a corner or an isolated cube, and follow it while you imagine the turn. People who do it that way make fewer errors than those who try to picture the entire figure.

It neither defines you nor limits you: it is one more piece of the cognitive puzzle. If you want to see how you do rotating shapes and completing patterns, our free test includes questions of this kind, and you can try the distinctive-feature trick while you are at it.