Mental Rotation

My visuospatial reasoning skills have proven essential to my learning of anatomy. As I perform a dissection, I’m constantly recalling, scrutinizing, and manipulating mental images.

For example, I’ll think something along the lines of:

I’m currently viewing a cadaver from the anterior side. I know that, on the posterior side, the circumflex scapular artery emerges from the triangular space, between the teres major and minor muscles and medial to the long head of the triceps brachii. Here, I see the subscapular artery, which divides into thoracodorsal and the circumflex scapular. I know that the proximal branch must be the circumflex scapular, since I see it diving deep between the teres muscles, into what, on the posterior side, will become the triangular space.

And so on.

I quickly found that I was not alone in citing the benefits of visuospatial reasoning to medicine (1).

ColonoscopySo, I started to wonder: can visuospatial ability be quantified? Can it be improved?

In 1971, Shepard and Metzler (2) set out to quantify visuospatial ability.

Stanford

Their paper, published in Science, established a standard protocol for measurement of visuospatial ability that lasts through this day.

In their mental rotation task, subjects decide whether or not two 2D representations of 3D objects actually correspond to the same 3D object. Try it yourself! For each image below, determine whether or not the two objects shown are identical. If you want to be extra competitive, time yourself and post your time in the comments. Meanwhile, I’ll post the answers in the comments.

Slide4 Slide6 Slide8 Slide10 Slide12 Slide14

In 1978, Vandenberg and Kuse (3) assigned the mental rotation task to men and women. They noted considerable sex differences.

MenWomanMen performed significantly better on the test. The sex disparity in mental rotation, and, more generally, in visuospatial reasoning, remains one of the most marked and reproducible sex differences studied in psychology.

Just last year, researchers in The Netherlands (4) published a fascinating paper which not only corroborated Vandenburg and Kuse’s result, but further explained it–and complicated it.

CAIS2

They studied individuals with Complete Androgen Insensitivity Syndrome (CAIS). These individuals are genetically male–they have sex chromosomes X and Y–but they lack the androgen receptor. Thus, androgens, including testosterone, have no effect on their bodies. The result is that they develop an entirely female phenotype, with female secondary sex charactaristics, female external genitalia, and so on. And, it turns out, their brains are phenotypically-female as well. Van Hemmen and Veltman (4) found that individuals with CAIS achieved female-like scores on the mental rotation task.

These findings indicate that the sex chromosomes act on the brain indirectly, via hormones, instead of directly. This suggests that mental rotation ability might be something we can control and modify. We know that the brain can be changed. Now we should figure out how we might go about changing it.

Cohen (5) sought out to find where exactly mental rotation is processed in the brain. Using fMRI technology, he found that Brodmann’s area 7 was particularly active during mental rotation.CohenBrodman’s area 7, part of the posterior parietal lobe, is bordered by the occipital lobe, below, and the primary somatosensory cortex, above. The former processes sight, and the latter processes touch. So, Brodmann’s 7 might be thought of as the part of the brain that coordinates the act of reaching out and touching something. This fits my experience: when I solve mental rotation problems, I tend to visualize the process of actually, physically, rotating the objects. I rotate one object until it “clicks” with the other, or fails to. Given Brodmann 7’s role in visuo-motor coordination and object manipulation, it’s not surprising that Cohen saw it light up when subjects performed mental rotation.

Theoretically, we should be able to improve our ability to mentally rotate by training Brodmann’s area 7. And research shows that this is the case.

Practice

This is encouraging. Mental rotation is learnable. Also encouraging is the fact that we can improve our ability to mentally-rotate with activities beyond mental rotation: video games seem to help too (7). And, in fact, they narrow the gap between the sexes.

Video GamesIt appears from these results that, regardless of their mental rotation floor, men and women likely have the same ceiling.

Video games can improve ability at mental rotation. So can activities as diverse as athletics and music (8).

Music

Of course, we would hardly take up music just to get better at mental rotation. The question becomes: does this relationship work in reverse? That is, can we improve at sports, music, navigation, and so on, by practicing at mental rotation?

We all know that practice at Activity A improves performance at Activity A. The important question is whether or not practice at Activity A also improves performance at Activities B, C and D. Brain games like lumosity claim to “Train your memory and attention”–enhancing performance, not just at lumosity, but in general. I’m skeptical.

But it seems like, if there were ever a simple task of which practice would produce widespread benefits, that task would be mental rotation. The sources cited above seem to think so. (1) and (7) claim that visuospatial reasoning is useful for medicine and navigation, driving, assembly or math, respectively. It would then follow that better visuospatial reasoning means better performance in these arenas.

So, should we start doing mental rotation problems every day? Well, maybe. But a better solution might exist. I’ve suggested that visuospatial activity enhances mental rotation, and that mental rotation enhances visuospatial activity. What’s most likely, though, is not that each is responsible for the other, but rather that each is simply reflective of a raw, visuospatial ability–a Brodmann’s 7 factor, if you will. The important part isn’t to practice mental rotation in particular; it’s to train Brodmann’s area 7, by any means–especially by means outside of mental rotation.

We can take an analogy from inside mental rotation. Upon further analysis, maybe not all participants in the mental rotation test actually utilize Brodmann 7. That’s because, according to (9), not all participants use the same strategy. Geiser, et al, distinguish between “rotators” and “nonrotators”. The former use visuospatial technique: “this, turned that way, matches that.” Nonrotators, on the other hand, use a linear, or analytic technique. “Two blocks, then three to the right, then three more upwards.”

Slide2

Interestingly, in Geiser’s study, nonrotators tended to score worse. Moreover, the historically-established sex difference was confirmed in this study, and females were over-represented among nonrotators.

What’s the message here? If one wishes to improve at visuospatial tasks, he or she should strive to be a rotator. Brodmann’s 7 occupies quite a bit of real-estate, and that space shouldn’t go unused.

It seems that females often choose analytic over spatial reasoning by default. But just a few minutes of video games might turn them into rotators (7). On that note, perhaps males, ad initium, are just as likely to choose analytic reasoning. But, due to cultural influences, they are exposed more to video games and video-game-like stimuli than are their female counterparts. So, by the time they take the mental rotation test, they have drifted further towards becoming rotators.

The important part is that the drift towards rotatorship is possible. And we should all strive to make that transition, simply because rotation works.

You might not find the time to practice the mental rotation task (while being sure to rotate and not analyze). But you could consider driving with the help of a map instead of a list of directions. Walk from your bed to the kitchen in the dark. Exercise using body weight, not gym machines. Activities that utilize visuospatial reasoning might well yield improvement at all other activities that utilize visuospatial reasoning. I know that, before my next anatomy test, I’ll be studying from my atlas, not from my textbook.

Resources:

  1. Luursema, Jan-Maarten et al. “Visuo-Spatial Ability in Colonoscopy Simulator Training.” Advances in Health Sciences Education 15.5 (2010): 685–694. PMC. Web. 4 Feb. 2015.
  2. Shepard, R., & Metzler, J. (1971). Mental Rotation Of Three-Dimensional Objects. Science,171(3972), 701-703.
  3. Vandenberg, S., & Kuse, A. (1978). Mental Rotations, A Group Test Of Three-Dimensional Spatial Visualization. Perceptual And Motor Skills, 599-604.
  4. Van Hemmen, J. (2014). Neural Activation During Mental Rotation in Complete Androgen Insensitivity Syndrome: The Influence of Sex Hormones and Sex Chromosomes. Cerebral Cortex.
  5. Cohen, M. “Changes in Cortical Activities During Mental Rotation: A mapping study using functional magnetic resonance imaging” 1996 February 12, 2006
  6. Kail, Robert, and Young-Shin Park. “Impact of Practice on Speed of Mental Rotation.” Journal of Experimental Child Psychology (1990): 227-44. Print.
  7. University Of Toronto. “Playing Video Games Reduces Sex Differences In Spatial Skills.” ScienceDaily. ScienceDaily, 26 October 2007. <www.sciencedaily.com/releases/2007/10/071024145626.htm>.
  8. Pietsch, S., & Jansen, P. (2012). Different mental rotation performance in students of music, sport and education. Learning And Individual Differences,22(1), 159-163.
  9. Geiser, Christian, Wolfgang Lehmann, and Michael Eid. “Separating “Rotators” From “Nonrotators” in the Mental Rotations Test: A Multigroup Latent Class Analysis.”Multivariate Behavioral Research (2006): 261-93. Print.
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2 comments on “Mental Rotation

  1. Josh says:

    Answers:
    1. Same image
    2. Different (mirror images)
    3. Same image
    4. Different (entirely-different images)
    5. Different (mirror images)
    6. Same image

  2. Ben says:

    Your article has the air of somebody who is on the right side of a boundary, and who tries, with insufficient tact, to ingratiate those on the wrong side. These situations are delicate, and one must approach them with some cautions in mind.

    You must earn the trust of those on the other side. You must convince them that you respect them, and that you will never deride their disadvantages.

    You must fully understand, and sympathize with, their circumstances. This involves understanding the causes of their deficits, including, of course, causes over with they do, or do not, have control. It involves understanding their own role, or lack of it, in producing, grasping, and responding to these deficits. It involves, most of all, understanding them.

    You must not offer advice when it’s unsolicited. To do so is to decide, for them, that theirs is a situation which needs to be remedied. Perhaps it’s not, or perhaps they do not feel it to be. In any case, to make this decision for them can be an unwelcome intrusion. Perhaps, they’ve never felt burdened by this “problem” which you’ve so intrepidly decided to set out and fix.

    You must also avoid, or be careful when, trying to produce attractive explanations for the existence of discrepancies which you’ve, perhaps inappropriately, assumed to be a cause for worry. If those to whom your explanations are directed find themselves disputing your account of a purported mitigating factor, they could be left feeling that your “expert” remarks have served only to more effectively point out their flaws.

    Though we — you and I — have identical DNA, and were raised in similar environments, it appears that I have inferior spatial skills, and, when I first attempted the rotation exercises, I was a non-rotator. (I’ve since tried again, and yes, rotating does work better.)

    I was overcome by the conviction that your article did not meet these criteria.

    With that said, I’ll offer a few comments about the subject matter.

    Those who’d really like to pummel Brodmann’s area 7 should take up elementary knot theory. Knot theory concerns twisted strands in three-dimensional space, where two “knots” are considered to be “equivalent” to one another if they differ only by the result of a continuous deformation. The initiation into this subject typically demands scrutinizing endless schematic diagrams of knots, and trying to determine whether the members of various pairs are equivalent (and how). (Note that this resembles the outline of the mental rotation task.)

    In Moscow, I took a course in knot theory under the legendary Alexei Sossinsky. It was a struggle, and it demanded the exertion of my spatial skills to an unprecedented degree. I’ve attached a few images of my notes from that class:



    Many claim that the role of spatial skills in mathematics is more broad. Quoting various abstracts, “A synergistic relation exists between mathematical ability and spatial visualization”, “For at least 30 years researchers have believed that spatial skills contribute in an important way to the learning of mathematics and to sex-related differences that are found in mathematics performance”, “a relationship has been found between spatial abilities and mathematics test scores”; the list goes on.

    The explanations for this purported association are quite interesting: in Why do spatial abilities predict mathematical performance?, Tosto, et. al. note that “Spatial skills have also been shown to rely on neuronal networks partially shared with mathematics,” and that, cognitively, “we think about numbers as organized in space along a mental ‘number line'”, “Mathematical relations may be mentally spatially represented,” and “representation and decoding of complex mathematical ideas may rely on spatial ability.”

    There’s a huge amount of information in this latter article, and I’d suggest your read it. For one, the statistical claims in the “discussion section” seem meaning-laden, though they’re difficult for me to understand (statistics is not part of my course of study).

    The strange point, though, is the case of me. I’ve mentioned my apparently poor spatial skills. Yet I would not consider myself a weak mathematical thinker. I’ll venture to recall — sacrificing modesty for the sake of the point I’m trying to make — that I absolutely excelled at mathematics from an extremely young age, and, largely, I continue to do so. Do I understand mathematics spatially?

    Somewhat. I typically understand mathematical ideas — even, and especially, complex ones — by constructing mental “pseudo-visual” representations of objects and the interactions between them. These representations are visual, but only in a highly vague sense, and, while they can be quite elaborate, they are — and this why the association these researchers purport to describe startles me — beholden to a different standard of accuracy than are the representations used in mental rotations.

    What makes a mathematical mental representation good? It must be efficient, demanding minimal cognitive overhead (per “unit of mathematical complexity”) and it must effectively “absorb” and “dispense” mathematical information. It must be parsimonious and reliable. When I consult it, I should be able to extract conclusions, and these should be correct ones.

    But these representations need not be visually accurate in any sense of the (latter) word. They need not describe real, physical objects, and they need not be subjected to rotations and transformations. They must be parsimonious and reliable. That’s it. These representations are highly abstract. They’re hybrids of the visual and the logical.

    It seems to me that the two skills are different.

    I’m reminded of an article, The Mind’s Eye, written by Oliver Sacks in The New Yorker in 2003. Sacks describes the varying experiences of those who become blind. One man lost “the very idea of seeing, so that concepts like ‘here’ and ‘there’, and a sense of objects having visible characteristics, lost meaning for him.” Another, on the other hand, “motivated by the horror of ’empty darkness’,” began to produce extremely accurate visual images, and “took pains to check the accuracy of his images.” A third, finally, was somewhere in between, and above altogether. She had “an artistic imagination”, and synesthesia, and her mental images were surreal, bursting with bright colors and pulsating shapes. My mathematical imagery, to put things perhaps overly generously, falls closest to this third case. It’s not quite accurate, and it doesn’t need to be.

    Unfortunately, it’s also quite vague; light, ethereal, and almost non-existent. I like that math does not require me to be spatially accurate — compare this to the pedantic demands of those mental rotations — but rather permits me to construct my own visual world.

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