Your hand is not a perceptual ruler

Visual perception has a problem; it doesn't come with a ruler. 

Visual information is angular, and the main consequence of this is that the apparent size of something varies with how far away it is. This means you can't tell how big something actually is without more information. For example, the Sun and the Moon are radically different actual sizes, but because of the huge difference in how far away they are, they are almost exactly the same angular size; this is why solar eclipses work. (Iain Banks suggested in 'Transition' that solar eclipses on Earth would be a great time to look for aliens among us, because it's a staggering coincidence that they work out and they would make for great tourism :) 

This lack of absolute size information is a problem because we need to know how big things actually are in order to interact with them. When I reach to grasp my coffee cup, I need to open my hand up enough so that I don't hit it and knock it over. Now, I can actually do this; as my reach unfolds over time, my hand opens to a maximum aperture that's wide enough to go round the object I'm reaching for (e.g. Mon-Williams & Bingham, 2011). The system therefore does have access to some additional information it can use to convert the angular size to a metric size; this process is called calibration and people who study calibration are interested in what that extra information is.

The ecological approach to calibration (see anything on the topic by Geoff Bingham) doesn't treat this as a process of 'detect angular size, detect distance, combine and scale', of course. Calibration uses some information to tune up the perception of other information so that the latter is detected in the calibrated unit. The unit chosen will be task specific because calibration needs information and tasks only offer information about themselves. A commonly discussed unit (used for scaling the perception of long distances) is eye height, because there is information in the optic array for it and it provides a fairly functional ruler for measuring distances out beyond reach space. 

Linkenauger et al (2014) take a slightly different approach. They suggest that what the system needs is something it carries with it and that remains constant (not just constantly specified, as with eye height). They present some evidence that the dominant hand is perceived to be a fairly constant length when magnified, and suggest that this length is stored and used by the system to calibrate size perception in reach space. There are, let's say, a few problems with this paper. 


The experiments
Experiment 1 asked 15 people to verbally report how magnified their hand and foot and the experimenter's hand and foot were when placed under 18% magnification. (For reference, an 18% magnification adds about 3.2cm length and 1.7cm width to my hand). They were allowed to put the limb in and out of magnification to come up with an answer. 

Figure 1. Results of Experiment 1. Note that hand is being judged as magnified and that magnification is over estimated, but less so than the other limbs

The authors ran a one-way ANOVA with 4 levels, found a main effect, and ran some post-hocs to show that the main effect meant people overestimated the magnification of their foot and the experimenter's hand and foot by the same amount, but that the reported magnification of the dominant hand was less (closer to the actual value). People judge their dominant hand to be less magnified.

(This is, of course, the wrong analysis; this is a 2x2 design and should have been analysed as such. Eyeballing the graph suggests that if they had done this, the predicted interaction would not have been significant.)

Experiment 2 asked 10 people to view their magnified dominant hand and foot and changed the measure to a matching task. People told the experimenter to adjust a tape measure until it matched the magnified length or width of the limb. The authors computed a ratio of estimated magnified area (length * width) to actual unmagnified area and found the hand was judged as unmagnified (see Figure 2).

Figure 2. Results of Experiment 2. Note that now the hand is judged to not be magnified at all

Experiment 3 had 14 participants adjust the size of an aperture until they thought their magnified hand or foot could fit through. They again computed a ratio, this time of estimated required aperture size over actual required aperture size (see Figure 3).

Figure 3. Results of Experiment 3, where the hand magnification is there and overestimated again, just less than the foot. What is up with this?

Experiment 4 had 16 people judge the magnification of their dominant hand vs a familiar object (a pen). The hand was judged as less magnified than the pen.

Figure 4. Results of Experiment 4. The judged hand magnification is finally about 18% here.

Experiment 5 finally got round to running the obvious control condition of having people judge their non-dominant hand as well. This time running under 50% magnification, people judged the length of 8 measures (see Figure 5). They found that the average area of the hand was less magnified for the dominant hand (although the ratio was still greater than 1) and there was some variation in how this played out for the various parts of the hands.

Figure 4. Results of Experiment 5. Note the small magnification ratios for most values, despite the 50% (!) magnification. Neither hand is judged even close to the correct magnification

The authors conclude

The stability of perceived hand size suggests that the hand is a natural perceptual metric that is used to scale nearby graspable objects. Moreover, its perceived constancy promotes its reliability as a perceptual metric, and it is an ecologically relevant metric given its regular use in interacting with  objects in the world. Previous work showed that eye-height constancy is used to scale velocity. These experiments are the first to show that there is also a strong tendency toward perceived hand-size constancy and that the hand may therefore be used as a meaningful, ecologically relevant, and reliable metric for scaling object size.

pg 7

Analysis
1. Hand size is not constant in these data
Hand size was almost never judged to be constant. For this to work as a ruler, the hand would have to be perceived as magnified by 18% (or 50% in Experiment 5) throughout. This only happened once, which I'm guessing is luck. The real question here is why are all the other objects consistently judged as overmagnified? Regardless, being a bit less overestimated is not enough to make hand length a useful ruler.

2. This task is not measuring calibration
The authors want to find out if the hand can be used as a ruler to scale perception. They then ask the wrong question, namely 'is hand length perceived as constant?'. The point of calibration is that it affects your ability to do something else; you don't use the calibration information for anything other than setting up your measurement of the world. The correct question would be, if I magnify the hand does this alter my prehension behaviour in a consistent manner? Only Experiment 3 did anything similar.

3 Calibration doesn't actually want a constant value
The authors draw an analogy between their idea and eye height scaling, but all this does is show how confused they are about what calibration is about:

The perception of one’s own velocity requires that optic flow be scaled to one’s altitude, and the perceptual system determines altitude by using a fixed standing eye height. When eye height is changed, this heuristic breaks down because the perceptual system assumes that eye height has not changed (Lee, 1980). Thus, most individuals feel that they are moving slower than they actually are when traveling in an airplane and that they are traveling faster than they actually are when sitting in a sports car that is low to the ground. Presumably, humans evolved in an environment where eye height was usually a stable unit, because the feet were typically on the ground.

pg 2

The perceptual system does not assume a constant eye height. What it actually does is continuously monitor eye height when specified in the optic array and use that perceived value to scale perception. The reasons why you misperceive your speed in the examples has to do with lack of information about eye height and other relevant scaling, not to mention the temporary errors that occur while you are re-calibrating.

The reason why the system does not assume a stable eye height is that eye height is not stable. Even primitive humans had mastered 'sitting down' technology, and just walking varies eye height a little. Hand length is more stable, although of course it does change over development so presumably has to be regularly perceived and reset anyway. Assuming a constant value is a terrible strategy for calibration, which is why it's actually always based on information about the current state of things.

Summary
These experiments do not actually support the use of the hand as a constant ruler for perceptual calibration. Calibration is an information-based process, and does not 'assume' set values as a heuristic. Even if it did, these data suggest using the perceived size of the hand would be an error because the degree of judged magnification was all over the place, relative to the actual magnification. Just because the dominant hand was a little less magnified than the other limbs and objects doesn't actually mean much of anything at all. 

References
Linkenauger, S. A., Geuss, M. N., Stefanucci, J. K., Leyrer, M., Richardson, B. H., Proffitt, D. R.,, Bulthoff, H. H., & Mohler, B. J. (2014). Evidence for Hand-Size Constancy The Dominant Hand as a Natural Perceptual Metric. Psychological Science, published online 24th Sept 2014 DOI: 10.1177/0956797614548875 Download ($$)

Mon-Williams, M. & Bingham, G.P. (2011). Discovering affordances that determine the spatial structure of reach-to-grasp movements. Experimental Brain Research, 211(1), 145-160. Download