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As easy as 1D, 2D, 3D

Observations in everyday life are commonly collected and described in one or two dimensions. Furthermore, these observations typically use the observer as the point of reference (that is, an egocentric reference); the most famous resultant fallacy of which is the Ptolemaic system or geocentric model. It is therefore no surprise that geologists struggle with incorporating multiple dimensions and perspectives.

Spatial thinking is an invaluable tool in the geologist’s arsenal. Our understanding of earth processes has been greatly improved by our ability to collect and connect spatially disparate datasets. For example, the classification of crystalline systems (the fourteen 3D Bravais lattices) helped us understand crystal structure. Marie Tharp’s topographic map of the Atlantic Ocean floor, drawn from thousands of sonar measurements and published in 1957, identified the Mid-Atlantic Ridge and propelled the theories of plate tectonics. And finally the demonstration by Richard Dixon Oldham that the arrival times of P-waves, S-waves, and surface waves from earthquakes could be explained by a dense planetary core (Oldham 1906), thereby paving the way for modern seismology.

Perhaps our everyday applications of spatial reasoning will not be quite as groundbreaking, but they are essential to both pure and applied geology. And the subjects that benefit from improved spatial reasoning are as equally wide- ranging as those examples. For example, our understanding of deformation patterns is enhanced by our ability to conduct balanced cross-section restoration. Structural field measurements and stereographic projections allow us to create cross-sections of the subsurface, but spatial reasoning impacts how accurately we can bring together these 3D data and present everything in a 2D form. Finally, even relatively simple tasks, such as locating a position on a topographic map from landscape observations, require us to have strong spatial reasoning skills (How far away is the river from the wall? What approximate elevation above the valley bottom am I?). It is therefore essential for a geologist to develop their spatial reasoning skills. But how?

Contrary to common assumption, advanced spatial reasoning ability is not a natural, innate aptitude. It can be taught and practised. For example, numerous studies have shown that response time decreases when attempting to conduct mental rotation after training (e.g. Kaushall and Parsons 1981; Kail and Park 1990). Whilst there is debate as to whether training improves the ability or simply allows the subject to retrieve previous mental rotations from memory (Heil et al. 1998), the result is nonetheless an improvement in spatial reasoning.

The most obvious way in which spatial reasoning is honed in geology is through eldmapping. Not only does the participant learn how to translate the 3D terrain around them to a position on a 2D topographic map, as discussed above, but they must use spatial parameters such as perspective and more complex spatial reasoning to create subsurface cross-sections. In the UK at least, this is a part of undergraduate geology courses in which students either sink or swim.

The sinkers needn’t be disheartened by their apparent inability to think spatially. It is something that can, and must, be practised. Spatial thinking is essential, but it is a skill that can be improved. The web is home to numerous teaching and training techniques: for example, look up And give this puzzle a go: which of the cubes on the right can be created by folding the net shown on the left? 


Note: This chapter was written by Nicholas Holgate, Aruna Mannie, and Chris Jackson.


Heil, M, F Rösler, M Link, and J Bajric (1998). What is improved if a mental rotation task is repeated — the efficiency of memory access, or the speed of a transformation routine? Psychological Research-psychologische Forschung 61 (2), 99–106.

Kail, R and Y-S Park (1990). Impact of practice on speed of mental rotation. Journal of Experimental Child Psychology 49 (2), 227–244.

Kaushall, P and L M Parsons (1981). Optical information and practice in the discrimination of 3D mirror-reflected objects. Perception 10 (5), 545–562.

Oldham, R D (1906). The Constitution of the Interior of the Earth, as Revealed by Earthquakes. Quarterly Journal of the Geological Society 62, 456–475. 

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