Seeing in space

Three jobs, one dimension

Spatial is one of the seven dimensions on your profile. It carries 11% of your overall score, and it is built from three facets. Each facet is a different job your spatial system does, and each has its own games.

Mental rotation

Imagining an object turning, then judging whether it matches another view of the same object. It is the most studied spatial skill of all. In the app it is measured by ShapeDance.

Navigation

Planning and following a route through a space, keeping track of where you are and where the exits lie. In the app it is measured by Pathfinder, where you turn track tiles until a route connects, and Penguin Escape, where you steer through a course that scrolls towards you.

Spatial construction

Building or rebuilding a pattern from its parts: seeing where each piece belongs in the whole. In the app it is measured by Puzzle Reconstruction, whose lesson lives on the Memory shelf because it also depends on holding the pattern in mind.

The facets are related but not identical. Someone can be quick at turning shapes and still get lost in a new campus, and the reverse is common too. That is why the dimension draws on several tasks rather than one.

The experiment that made rotation visible

In 1971 Roger Shepard and Jacqueline Metzler showed eight adults pairs of line drawings of block figures, 1,600 pairs per person. On half the pairs the second figure was the first one turned. On the other half it was the mirror image of the first, turned. The question each time was simple: same or different?

The result was strikingly tidy. For the pairs that matched, the time to answer rose in a straight line with the angle between the two figures. It took about one second when the figures were already aligned and between four and six seconds, depending on the person, when they were 180° apart. The slope worked out at roughly 60° of turning per second. Turning the object in depth took no longer than turning it flat on the page. Participants answered correctly 96.8% of the time, so the delay was not guessing; it was work.

The straight line is the important part. If people recognised shapes by some instant feature check, angle would not matter. A time cost that grows steadily with angle suggests something like a continuous turning process, as if the mind rotated an image through each intermediate position. The mismatched pairs took longer still, averaging 3.8 seconds, and participants later said they turned one end into place and then noticed the other end did not line up.

Lynn Cooper and Roger Shepard extended the idea in 1975 with drawings of hands. Deciding whether a picture showed a left or a right hand took longer the further it was from a natural pose, over 400 ms longer for fingers pointing down. Their account is that you move a mental ‘phantom’ of your own hand into the pictured position and compare. Next time you judge a rotated hand, watch yourself do it.

Try the same experiment on yourself. The drill below shows a shape and a second shape that is either the same one turned or its mirror image turned. It records how long you take at each angle, so you can see whether your own times climb as the angle grows.

Practice drillSign in to try it

Why mirror images are the real test

A mirror image can look almost identical to the original, but no amount of turning on the page will make them line up. Chemists call such objects chiral, from the Greek for hand. Every good rotation test uses mirror images as its lures, because they cannot be rejected by a quick glance at the parts: they have exactly the same parts, joined the same way, in the opposite handedness. The only way to tell is to turn one onto the other and see whether it fits.

That is why ShapeDance fills its field with mirrored copies of the reference. If you pick a mirror, you matched on appearance rather than rotating, and the game reports that separately as mirror confusion.

Visualisation, orientation and navigation

A century of testing has not produced one agreed map of spatial abilities, but some distinctions hold up well.

• Spatial visualisation is imagining a transformation of an object: rotating it, folding it, cutting it. The Uttal et al. review notes that agreement is strongest for this factor.
• Spatial orientation, or perspective taking, is imagining how a scene looks from somewhere else: ‘if I stood at the door, would the window be on my left?’ Mary Hegarty and David Waller showed that this is dissociable from mental rotation even though the two are quite highly correlated. One moves the object; the other moves you.
• Navigation is large-scale: learning an environment you move through and cannot see all at once, from a building to a city.

Uttal and colleagues, following Newcombe and Shipley, also sort spatial tasks along two axes: intrinsic (the shape of one object) versus extrinsic (where objects are relative to each other), and static versus dynamic (whether something moves or transforms). Mental rotation is intrinsic and dynamic. Reading where a café is on a map is extrinsic and static. Steering the penguin through a moving course is extrinsic and dynamic.

Two frames of reference

When you describe a location you choose a frame, usually without noticing.

An egocentric frame is centred on you: ahead, behind, left, right. It changes every time you turn. An allocentric frame is anchored to the world: north of the station, next to the library. It stays put. Roberta Klatzky set out the distinction in a widely cited analysis. Good navigators translate between them fluently; they can look at a map and know which way to turn, and they can walk a route and then point to where they started.

Knowledge of a new place also tends to build in layers. Siegel and White proposed a sequence from landmarks (isolated places you recognise), to routes (chains of turns between them), to survey knowledge (a map-like layout that lets you invent shortcuts).

People differ a great deal in how far they get. When Toru Ishikawa and Daniel Montello drove 24 students along routes through an unfamiliar neighbourhood once a week for ten weeks, some improved steadily, but most either had accurate map-like knowledge from the first session or never developed it at all.

There is also a quieter system underneath. Path integration is keeping track of your position from your own movement alone: how far you have gone and how much you have turned. Many animals, including humans, can head back to a starting point this way without landmarks. It is part of what lets you walk out of a room with the lights off and still find the door.

What the brain is doing

The 2014 Nobel Prize in Physiology or Medicine went to John O'Keefe, May-Britt Moser and Edvard Moser for discovering the brain's positioning system. In 1971 O'Keefe found place cells in the hippocampus of rats: neurons that fire when the animal is at one particular spot in a room. In 2005 the Mosers found grid cells in the nearby entorhinal cortex, which fire in a regular lattice as the animal moves and act like a coordinate system.

Experience shapes this system. Eleanor Maguire and colleagues scanned licensed London taxi drivers and found their posterior hippocampi were larger than those of people who did not drive taxis, and the difference grew with years in the job. It is one of the clearest signs that navigation practice leaves a physical trace in the adult brain.

Where you already use it

• Everyday. Loading a car boot, assembling flat-pack furniture from a diagram, reversing into a parking space, finding your seat in a stadium from the section map.
• Engineering and design. Reading orthographic drawings, imagining a part from three views, laying out a circuit board, predicting how a mechanism moves.
• Software and data. Picturing a tree or graph structure, arranging a dashboard, following a system architecture diagram.
• Medicine. Surgery on a spatially complex structure, and reading scans slice by slice. A small study of 37 surgical residents found that those with higher mental rotation scores did better on a spatially complex procedure.

The next lesson looks at how much this ability predicts in study and at work, and where the evidence is weaker than people assume.

What to remember

• Spatial has three facets in the app: mental rotation (ShapeDance), navigation (Pathfinder, Penguin Escape) and spatial construction (Puzzle Reconstruction).
• Shepard and Metzler found that the time to match two figures rises in a straight line with the angle between them, at roughly 60° per second.
• Mirror images are the real test of rotation because they have the same parts in the opposite handedness.
• Turning an object (visualisation) and imagining yourself somewhere else (orientation) are related but separable skills.
• Egocentric frames move with you; allocentric frames stay fixed to the world.

Sources

1. Shepard, R. N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171(3972), 701–703. doi.org/10.1126/science.171.3972.701
2. Cooper, L. A., & Shepard, R. N. (1975). Mental transformations in the identification of left and right hands. Journal of Experimental Psychology: Human Perception and Performance, 104(1), 48–56. PubMed 1141835
3. Vandenberg, S. G., & Kuse, A. R. (1978). Mental rotations, a group test of three-dimensional spatial visualization. Perceptual and Motor Skills, 47(2), 599–604. doi.org/10.2466/pms.1978.47.2.599
4. Uttal, D. H., et al. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 139(2), 352–402. PDF
5. Hegarty, M., & Waller, D. (2004). A dissociation between mental rotation and perspective-taking spatial abilities. Intelligence, 32(2), 175–191. doi.org/10.1016/j.intell.2003.12.001
6. Klatzky, R. L. (1998). Allocentric and egocentric spatial representations: Definitions, distinctions, and interconnections. In Spatial Cognition (pp. 1–17). Springer. doi.org/10.1007/3-540-69342-4_1
7. Siegel, A. W., & White, S. H. (1975). The development of spatial representations of large-scale environments. Advances in Child Development and Behavior, 10, 9–55. doi.org/10.1016/S0065-2407(08)60007-5
8. Ishikawa, T., & Montello, D. R. (2006). Spatial knowledge acquisition from direct experience in the environment. Cognitive Psychology, 52(2), 93–129. doi.org/10.1016/j.cogpsych.2005.08.003
9. Etienne, A. S., & Jeffery, K. J. (2004). Path integration in mammals. Hippocampus, 14(2), 180–192. doi.org/10.1002/hipo.10173
10. The Nobel Assembly at Karolinska Institutet (2014). Press release: The Nobel Prize in Physiology or Medicine 2014. nobelprize.org
11. Maguire, E. A., et al. (2000). Navigation-related structural change in the hippocampi of taxi drivers. PNAS, 97(8), 4398–4403. doi.org/10.1073/pnas.070039597
12. Wanzel, K. R., Hamstra, S. J., Anastakis, D. J., Matsumoto, E. D., & Cusimano, M. D. (2002). Effect of visual-spatial ability on learning of spatially-complex surgical skills. The Lancet, 359(9302), 230–231. doi.org/10.1016/S0140-6736(02)07441-X