Friday, 9 November 2012

How do we perceive which objects afford throwing the farthest?

Previous work has established that people with throwing experience can perceive the affordance of 'throwability'. If you let these people heft objects with a range of sizes and weights, they will confidently select the one they think they can throw the farthest, and they tend to be correct. It's a very natural task, one you have probably done yourself on a beach or lakeside looking for stones to throw into the water. 

This is only the first, and relatively easy step in any ecological task analysis. Once you've identified an affordance property and established that people are sensitive to it, you need to identify the information supporting this perception. For throwing, this has not been done, and while the paper I'm reviewing here doesn't solve the problem, it does rule out a highly likely contender for the source of the information that has implications for a lot of other research.

Previous research (Zhu & Bingham, 2011) had identified that the objects people select to throw all feel equally heavy, regardless of size. This suggests that people are using the felt heaviness of the objects to judge throwability. 'Felt heaviness' is a function of both size and weight, and produces the size-weight illusion where larger objects must be heavier to feel equally heavy. Zhu & Bingham (2011) gave people balls of different size and weight and, for each size, had people judge which weight they could throw the farthest. They then used one of these objects as the comparison object, and asked people to find which larger ball felt equally heavy from the other size sets. People chose the ball within each set that they had also judged to be maximally throwable. Across sizes, balls that afford maximum distance throwing feel like they are equally heavy; the size weight illusion is not an illusion, it's about throwing.

So how do we perceive heaviness? It's not simply weight, size matters; so the question really is, what property of the object are we perceiving when we judge heaviness? The best suggestion in the literature comes from research on dynamic touch, which suggests that the proprioceptive perception of heaviness is not about the object property 'weight', it's about the object property rotational inertia. There is a wealth of evidence that judgments of heaviness vary with this property, which is the resistance the object offers to being moved in a rotational movement (say, flexing your arm at your elbow; see Amazeen & Turvey, 1996).

So we now have a couple of pieces; can we tie them together? People seem to be using felt heaviness to judge which objects they prefer to throw. Felt heaviness seems to be about the rotational inertia of the object. Zhu, Shockley, Riley, Tolston & Bingham (2012) therefore tested the hypothesis that the key property of the object driving the perception of the affordance for throwing is rotational inertia.

The authors had competent throwers hold balls in their hands that varied in size, weight and rotational inertia. The latter is manipulated by varying the way the mass of the ball is distributed; shifting more of the mass off centre away from the axis of rotation increases the rotational inertia (i.e. makes it harder to rotate). People then hefted the objects by moving their wrists up and down while holding the ball.

After hefting a range of weights and inertias within a given size, people judged which object they thought afforded throwing to a maximum distance. Then, people went through the size sets again. This time, they looked for a ball that felt equally heavy to a comparison object, which, unknown to them, happened to be the ball for that size they had previously judged to be maximally throwable.

The question was this: what objects did they pick, and what properties did these objects all have in common - size, weight, or inertia?

Figure 1. Judgments sorted by object size and weight

Zhu et al looked at the data two ways. The first (Figure 1) was to sort the data by size and weight. There are three basic results. First, people chose the same objects for both the heaviness and throwability task, replicating the previous result. Second, people chose a heavier object for the larger size. Third, which objects people picked in either task were not affected by changes in rotational inertia (contradicting Amazeen & Turvey, 1996 and the work following on from that paper).

Figure 2. Judgments sorted by size and rotational inertia
Figure 2 shows the rotational inertias of the selected objects. Remember, these objects were judged as equally heavy and all affording throws to a maximum distance. However, the rotational inertias varied, and varied differently for the differently sized objects.

The overall pattern of results is that 1) perceived heaviness is the basis of the judgments of throwability but 2) rotational inertia is not the basis of perceived heaviness or throwability. Without knowing the property being perceived, we can't (yet) begin to identify the information about that property. The hunt continues!

Failure to replicate Amazeen & Turvey (1996)

The fact that rotational inertia is not the property underpinning perception of throwability is surprising, but that's how things go. What's more interesting is that rotational inertia, for the first time, was not the property underpinning perception of heaviness. Why did this otherwise robust result not replicate here? 

The main difference is in the objects used. Previous work typically has people wielding long, weighted rods over varying inertia. The resulting inertias (and variation in inertias) are quite large. In contrast, hefting these spheres, all graspable in a hand, produces a small range of smaller inertias. Geoff has suggested to me that the most likely explanation is that the inertias of these spheres is below threshold (although no one has ever done any psychophysics on dynamic touch to establish what the thresholds for rotational inertia are).

The consequence of this result is that because of this threshold issue, rotational inertia can't be the property people are perceiving in this task, and, contrary to previous claims, it can't be the property that explains all perception of heaviness.


People can heft objects and perceive the affordance property throwability. Until we know the relevant object property, however, we can't identify the candidate information variables that property produces and empirically establish which variable people use as information to perceive this affordance. We know that people perceive the affordance in terms of felt heaviness, and that people can select the specific felt heaviness that corresponds to an object that affords throwing to a maximum distance. However, we do not yet know what property of spherical objects determines felt heaviness, and this study rules out the obvious contender, rotational inertia. It's back to the drawing board for throwing, to identify the next candidate relation between size and weight that people are perceiving.

ResearchBlogging.orgAmazeen, E. L., & Turvey, M. T. (1996). Weight perception and the haptic size–weight illusion are functions of the inertia tensor. Journal of Experimental Psychology: Human Perception and Performance, 22(1), 213.

Zhu, Q., & Bingham, G. P. (2011). Human readiness to throw: the size–weight illusion is not an illusion when picking the best objects to throw. Evolution and human behavior, 32(4), 288-293. Download  My blog post

Zhu, Q., Shockley, K., Riley, M., Tolston, M., & Bingham, G. (2012). Felt heaviness is used to perceive the affordance for throwing but rotational inertia does not affect either Experimental Brain Research DOI: 10.1007/s00221-012-3301-7


  1. Nice!
    Now that this topic is apparently up for grabs again, it might be a nice thing to try to tackle with a group. It would take a range of researchers with a combination of psychophysics, experimentation, etc. Where to start?

    Also, do you think it likely that different variables are used with differently shaped objects (the threshold issue aside)?

    I suspect this is a problem that will eventually require a more topological approach (i.e., math without all the baggage of algebra and euclidean geometry). Alas, few in psychology seem to think that is a promising direction.... and the only topologist I know who is deeply interested in such things is in phased retirement.

    1. Also, do you think it likely that different variables are used with differently shaped objects (the threshold issue aside)?
      Geoff's hunch is that threshold, not shape, is the issue. Shape just happens to be the thing that makes the inertia big enough to detect (spheres no, big pendulums yes). If the information for the rotational inertia of an object is below threshold (as it seems to be here) then yes, people will be using different variables because they will need access to a different property.

      No one's done the psychophysics, though, and no one seems to want to.

      What, precisely do you mean by a topological approach? Topology is only one of many geometries, and which one is most appropriate is an empirical matter (e.g the work showing visual perception of reach space is affine).

    2. Lee (Rudolph) argues that we need some pretty barren topological systems. For many of psychology's questions, at least, he thinks that many of the assumptions of our mathematical models are questionable. I can find a few articles, and extract a few passages from our grant proposals if you want. He also just came out with a book, but it is quite expensive: Qualitative Mathematics for the Social Sciences

  2. I wonder if this sort of task could be better formalized in terms of selecting the squash racquet you could hit the ball hardest with? There weight and torque interact with one another in a more useful way (whereas for throwing a stone you are presumably trying to minimize the torques, or the torques are made pretty simply by the spherical stone)

    1. There is research showing that the inertia governs the perception of things like the sweet spot in a racquet, etc. So yes, if you're interested in tasks for which the rotational inertia matter, study a task with an extended object. The point here is that rotational inertia doesn't matter for all hefting and wielding tasks; if it's below threshold, people can't and therefore don't use it, and it's an open question what they're doing.

    2. Also, we're interested in throwing. You can't study swinging a racquet to study throwing, especially in light of the result that inertia isn't doing cutting it in throwing. You'd draw the wrong conclusions!

      And note that it is the case that people can perceive the relevant affordances for a spherical object, even though they don't use the rotational inertia. So we hace something to explain within throwing, and moving to the wrong task won't help.

  3. Easy tiger!

    The paper is about weight perception, not throwing, right? The interest for me comes from weight perception. It seems pretty clear that when we perceive weight, our percept is made at least partially from our perceiving the 'rightness' of something for a particular task. Whereas for stone throwing, the variations in the moment of inertia wouldn't be something you'd obviously search for when selecting the best stone (all you care about is it's mass, size relative to your hand, and to a smaller degree air resistance). But for a racquet weights and torques interact in ways that make different objects seem more or less useful. Why do some prefer 190g head light racquest whereas others prefer 150g head heavy ones? Why is actual performance different? Presumably these combinations can result in the same physical force being applied at the moment of impact, but performance itself as far as the player was concerned would suffer if they weren't using their preferred configuration. What's the variable they are selecting when they feel racquets? And does this combination of variables act as an effective metaphor for many other perceptual experiences?

    1. This paper is about the perception of the throwing affordance, which other evidence has shown is based in perceived heaviness. Heaviness is some function of size and weight, and the question is, what function? How are these combined into a single perceived physical property? The usual suspect is rotational inertia, but it doesn't work here.

      As I said, rotational inertia clearly matters for things like racquets; the variation in inertia is above threshold and functionally related to the performance of the racquet.

      This isn't about metaphors; perceived heaviness doesn't provide the basis for a metaphor where you say 'this feels *like* it's throwable'. It's the thing that makes you perceive *that* it's throwable.

  4. So you think perceived heaviness entirely is perceived throwability? That's a huge claim based on one (arguably 2) papers, and discounts an entire literature (e.g., how perceived heaviness fluctuates as a function of grip to load force ratio, and how it varies with expected heaviness). Throwability, of course, could factor into it when the eventual task is asking people to throw (or pick up in a way that affords throwing). But the authors of the throwing paper could just have easily asked the subject to pick up the object that 'feels most satisfying to lift' or that you could 'kill someone with most efficiently as a club' or any number of other things. and found the same results. But when asking people to precision grip, lift, and hold you still experience the same (albeit watered down) size weight illusion.

    This hunt for the one single parameter to explain pyschological phenomena is such a vast, unhelpful, dead end. There have to be many things feeding into this percept. The challenge is figuring out how they integrate/interact with one another, rather than finding something out and discounting everything that has been researched in the past on the topic. That's what they have to do in the hard sciences.

    1. So you think perceived heaviness entirely is perceived throwability?
      No! I think that perceived throwability is about perceived heaviness. Perceived heaviness is underpinned by the inertia tensor in rods, etc, but not in spheres, so rotational inertia is not responsible for the perceived heaviness that underpins the perception of throwability. The question remains, what is responsible?

      This hunt for the one single parameter to explain pyschological phenomena is such a vast, unhelpful, dead end.
      The goal is to identify the physical variable responsible for the perceived quantity. We know that for perceived heaviness of rods, that parameter is rotational inertia - so no one is discounting anything from the previous literature. Geoff and Arthur make the point in the paper that these data simply show that rotational inertia is not the physical variable responsible for perceived heaviness in general, as has been assumed.

      There have to be many things feeding into this percept.

      Plus surely it's an empirical question, and if the physics of the task present you with a single variable (eg the rotational inertia) that works, why look for more?

    2. Gavin, Andrew,
      The "hunt for the one single parameter to explain psychological phenomena" is a bit of a problem as it is currently understood. Gavin is right that it "is such a vast, unhelpful, dead end", so long as you allow Andrew's caveat of (paraphrasing) "except when it works."

      One problem is the very limited range of math the Connecticut School has been using to define so-called "single parameters." Any integrative interaction of variables, no matter how complex, can always be represented by a single letter in a math equation... the math cares not about what you do or don't find complex.

      Thus, the desire to get to a single letter is silly. We must mean something deeper, but I am not convinced anyone is clear on what that deeper thing is. We seem to know it when we see it, and we often substitute the judgement of others for our own judgement (e.g., whether someone in physics has given it a letter yet), but we will eventually need a more explicit criterion.

      This is not a trivial task, but the whole field seems to take it for granted at the moment.


      P.S. Note that "specification" does not get us out of the mess.

    3. This isn't about a hunt for a single letter. It is always an empirical question what information people are using; so you need to do what I describe here: analyse the task dynamics and the information it creates. the goal is not 'reduce it all to a single variable'; the goal is 'find the right variable that explains the behaviour'. Which variables are options are a function of the task dynamic, not the maths.

    4. This comment has been removed by the author.

    5. Well, yeah...
      But you are still talking in the singular. It is quite possible that people use a variety of variables, in complex ways, that vary with fine details of the task dynamics as well as several other factors external to the task itself. This can all be captured mathematically, but I suspect many ecological psychologist would find such a solution aesthetically displeasing. I was primarily trying to point out that there is a need to critically examine and better understand that aesthetic.


      Rereading my post, I realized that the beginning should have been more forceful:

      Gavin is right that it "is such a vast, unhelpful, dead end", so long as you allow Andrew's caveat of (paraphrasing), "Except when it works, then it is fucking brilliant."

    6. It is quite possible that people use a variety of variables, in complex ways, that vary with fine details of the task dynamics as well as several other factors external to the task itself.
      First, starting with the task dynamic constrains the number of possible sources of information for that task. Each one of those can only tell you about certain things, so it is not necessarily correct to just say 'well there's probably lots of things'.

      Second, factors external to the task dynamic can't affect performance in a task,by definition. If they are, then they should be in your description of the task dynamic because they are clearly part of the task.

      This hand wavy talk sounds too much like the old 'is it nature/is it nurture/oh it's both' crap that gets peddled in intro psychology (can you tell I've been grading undergrad developmental essays lately? :) The middle ground is not always where the action is, and the whole point of the task dynamic approach is to get specific about where the action might possibly be happening.

    7. Look... man... just because I haven't filled in details doesn't mean I'm being hand wavy :- (

      First, there are lots of tasks people suck at... and part of the reason they suck is that they are using non-specifying variables. Also, some of the time when performance is difficult to model, it is because people are switching around their variables on a fairly regular basis. In well trained tasks where people have very high accuracy, I assume you will have fewer of these problems... but those are special cases. I took that to be a big part of Gavin's point.

      Second, as a developmental psychobiologist in my spare time, let me assure you that there are lots of variables that affect performance that would never be on a task-dynamics list: Amount of sleep, blood-sugar level, circulating hormones levels (with things like time of day or time of month often used as a proxy), etc. There will be many tasks in which people use one strategy to solve a task when blood sugar is normal and another one when blood sugar is tanked. I've done a lot of martial arts work, and have seen many people turn from precision machines to crude thumping devices over the course of a long practice.

      As I understand your approach to task dynamics (and I could be wrong): Nothing about the task dynamics changed in the above example, but the people shifted from being in law-like relations with one set of variables to being in law-like relations with another set of variables. The mathematical representation of their behavior would thus have a phase-transition, and that transition would be dependent upon a physiological variable that is not itself part of the task dynamics.

      As for the rest... I am still willfully avoiding my History of Psych essays. I can put them off for another 24 hours or so.... In the meantime I grade simpler things that don't rile me as much :- )

    8. First, there are lots of tasks people suck at...
      Such as? There's a lot of this going around - claims about things we do or don't do without any specifics. What exactly do you have in mind?

      here will be many tasks in which people use one strategy to solve a task when blood sugar is normal and another one when blood sugar is tanked.
      Nothing about the task dynamics changed in the above example, but the people shifted from being in law-like relations with one set of variables to being in law-like relations with another set of variables.

      The task dynamic doesn't include an account of the dynamics of the organism (this is another part of the story and one I admit is very understudied - it's on my list to work on though). So a full account will include the 'task dynamics' of the actor; the effectivities (in the way the task dynamics of the environment are the affordances).

      So again; these things must be part of the complete story, by definition, because as you note, they matter. So

      The mathematical representation of their behavior would thus have a phase-transition, and that transition would be dependent upon a physiological variable that is not itself part of the task dynamics.
      You cannot have a phase transition caused by a variable that isn't part of the dynamic undergoing the transition. This is against the rules.

      Do you see what I'm getting at? The goal is to build a complete dynamical description of the affordances and the effectivities and how these relate to one another via information. If something matters, then it has to be in these dynamics somewhere, otherwise it won't be able to exert and influence on our explanations.

    9. Second part (how to do the models): Yeah, that makes sense. I guess I intuitively think of the larger model, rather than the two pieces. Maybe I don't understand how variables are cleanly divided between the task-dynamic and the effectivity side. Of course, the fact that I don't find the divide appealing doesn't help... but at least I now understand what you are trying to do. Gracias.

      First part (give examples of things people suck at): The UConn crowd asks me this mockingly at conferences on a pretty regular basis, and I am always at a bit of a loss. Everything I see people do they seem (as a group) fairly mediocre at. If I sit in the hallway of a mall, or school, or observe people at their jobs, there are continuous minor errors in their behavior. They mistime getting to a door before it closes, they spill their drinks, they slip, etc. If you sit in the food court of a large U.S. mall for a week, I assure you someone will literally miss their seat while trying to sit down. || When I used to do animal behavior, and spent hundreds of hours watching animals for each study, the animals screwed up all sorts of minor things on a regular basis. The Lemurs, for example, would misjudge a jump distance, fail to grip something strongly enough, bump their heads while trying to go under things, etc. || Then, on top of that, I have extensive martial arts experience, and have seen people struggle for years to execute moves that - from a task-dynamics perspective - are quite simple. First, some people have tremendous difficultly performing the movements (usually they are failing to constrain the movement sufficiently, or their behavior is a function of the wrong opponent-relative variables). Even after the movements are "mastered" in the abstract, many people still have tremendous difficulty executing them precisely, in real time, against an active opponent. Of course, the affordances are right there! The correct thing to do is fully specified in all the ways you could dream, and the dynamics are often ridiculously simple (especially in Aikido), and yet some people take a long, long time to learn them.

      Thus, I am simultaneously: 1) Amazed at how accurate most behavior is. 2) Surprised when people don't think errors are rampant.

      Is there something about your request for examples I just don't understand? Or do you really not see people screwing things up as often as I do? I have students who suck at doing arithmetic with a calculator (no joke), surely it would be unsurprising to learn that they suck at all sorts of perception-action tasks too?

  5. In my own simple thinking, the heavy the object is, the harder for it to throw as you will exert more effort to gather force as compared to lighter ones.

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    1. Not quite. Imagine throwing a golf ball vs a ping pong ball; similar sizes, different weights, and the heavier golf ball will travel further. Each size object has an optimal weight and vice versa; both size and weight matter.