Regularities of the Physical World and the Absence of their Internalization

Howard (1978) presented apparent motion sequences of photographs depicting horizontal and oblique water-levels and asked subjects to report whether the sequence represented a natural or an unnatural event. Using an animated version of task did not improve performance (Howard, 1978; McAfee and Proffitt, 1991). The would-be internalization of horizontality did not come to the fore when pouring events with impossible water-levels were shown by virtue of tilting the camera when the scenes were videotaped. Thus, a variety of methods used to assess the explicit and implicit knowledge of the horizontality invariant produced the same results: the regularity that liquid surfaces at rest remain invariably horizontal with respect to the ground cannot be taken to be internalized by our visual system.

If the horizontality of liquids has been internalized in a more ephemeral manner, visual experience may be required before the internalized regularity manifests itself in behavioral data. Thus, one might argue that with sufficient experience the "illusion" should disappear. However, the opposite is the case. Experienced waitresses and bartenders reveal stronger biases than the average population, they accept water levels as natural that deviate even more from horizontality (Hecht & Proffitt, 1995; but see Vasta, Rosenberg, Knott & Gaze, 1997).

In conclusion, two examples of physical regularities have failed to influence perceptual judgments. The empirical data have thereby failed to fulfill a precondition for the possible internalization of theses regularities. Percepts were vastly different from the defaults that hold in the environment with few exceptions. Knowledge about gravity per se is not used to scale absolute size and distance of objects. However, the general negative relationship between retinal velocity and distance of a moving object could still be called internalized. A much stronger case against the internalization hypothesis is represented by the water-level literature. The regularity that liquid surfaces remain invariably horizontal when at rest is as consistent as the diurnal cycles, it has no exceptions. Nonetheless, a substantial proportion of observers misjudge water-levels indicating that they have by no means internalized this particular regularity.

Thus, the failure to exploit these rather concrete regularities is incompatible with the literal reading of Shepard's hypothesis. However, neither free-fall nor the water-level task have a geometric solution that differs from the laws of classical mechanics. Thus, if one excludes these examples from the domain of internalization theory, the latter may not be threatened. Such an exclusion might be put forth on grounds of insufficient underspecification of the percept in the case of gravity to scale objects and on the importance of cognitive factors in the water-level case. This would rescue the literal interpretation but seriously reduce the scope of the hypothesis.

Let us now look at the abstraction reading of internalization. Given the negative results that were obtained when testing the comparatively simple regularities of gravity and horizontality, we search for evidence of internalization in situations where the percept is severely under-specified but not arbitrary. Such cases are very hard to find. Dreaming and imagining - although suggested by Shepard (1984) - appear to lack specification altogether and in addition to that are very hard to measure. Apparent motion seems to be the only appropriate case that could provide evidence for internalization of abstracted regularities.

For moving extended objects, Shepard (1984, 1994) claims that the perceived trajectory of an object's motion is determined by the geometrically simple geodesics. The model is based on the idea that a group of single rotations (SO[3]) can define the space of all possible 3-D orientation differences (Foster, 1975; Carlton & Shepard, 1990). Within this space, Chasles' theorem describes the simplest single rotation as follows: for any object displacement and orientation change, there exists one axis in space about which the object can be rotated, such that its initial position will be mapped into its final position. This helical motion in 3-D reduces to a single rotation (without concomitant translation) in the 2-D case.

Recently, Shepard (1994) accommodated all deviating results in the apparent motion domain into his theory by claiming that we do not necessarily perceive motion in accordance with kinematic geometry whenever the percept is under-specified, as in apparent motion or imagery. Rather, he makes the weaker claim that kinematic geometry is "more deeply internalized than physics (p. 7)". This claim is too weak to be the basis for any predictions. If we take another intuitive physics example, what would Shepard predict for the following case? Imagine a marble that is rolled through a C-shaped tube, which is positioned horizontally on a table top. What will its movement path look like after it exits the tube? If the observer has internalized an approximation to Newtonian mechanics, she should imagine the marble to continue its path in a straight line perpendicular to the tube's opening (Figure 3, case A). If on the other hand, curved geodesics are internalized, a curvilinear path might be preferred (Figure 3, case B). Empirically, many subjects erroneously think that the marble should continue to curve, presumably because it has acquired a curvilinear impetus (McCloskey, Caramazza, & Green, 1980). However, observers who make erroneous predictions prefer the correct straight path when confronted with visual animations of a variety of straight and curved trajectories (Kaiser, Proffitt & Anderson, 1985; Kaiser, Proffitt, Whelan & Hecht, 1992). Thus, only with less visual support are curved paths preferred. Have curved trajectories beyond Chasles' theorem been internalized, or does internalization fail here because it can predict all interesting outcomes?

The above examples show that the internalization hypothesis is in trouble. Taken together, those candidates of the internalization hypothesis that are amenable to empirical testing call for a revision of this concept. The literal interpretation of internalization is faced with heavy counterevidence. The more likely abstraction interpretation suffers from two very different problems that have to do with in principle limits to its empirical verification. The first problem concerns the resolution or generality of the internalized rules, and the second concerns the need for a criterion that determines when internalization has occurred.

If we say that an organism has internalized a particular regularity or rule, such as the periodicity of the circadian rhythm, we could refer to a very coarse level of resolution: some vague expectancy of day following night. On the other hand, we could mean that the organism has an internal clock and knows down to the minute when the sun will rise. The higher the level of resolution, the easier an empirical test. The level of resolution that we apply to the internalization hypothesis determines to what extent it is amenable to empirical testing.

Kubovy (in this issue, p. xx 5) claim that the internalization hypothesis "has no obvious empirical content and cannot be tested experimentally". This is only true in its broadest reading. In support of Shepard, I not only hold that there are other readings that can be tested experimentally, I also claim that the more fine-grained the operationalization of his hypothesis, the easier it is to refute. For example, the hypothesis that we have internalized the rule that water surfaces at rest are always horizontal is a strong case that allows distinct predictions: we should resolve ambiguous perceptual situations in this context with errors toward a preference for horizontal orientation. On the other hand, the hypothesis that we have internalized some abstraction of this regularity would not necessarily put us in a position to use a few empirical observations of non-horizontal solutions as evidence against the internalization hypothesis. It may not be falsifiable at all if we cannot think of any behavior that could contradict the claim (see Popper, 1935).

In Figure 4 I have tried to depict the relationship between postulated internalizations and hypothesis testing. The resolution of a given internalization hypothesis tends to correlate highly with its amenability to empirical testing. Highly resolved statements that claim generality are easy to falsify and therefore desirable, as for instance the hypothesis that "all perceived apparent motion trajectories follow geodesic paths". Unfortunately, Shepard's internalization hypothesis is most appealing where it is least resolved. It may in fact be so appealing because it is immune to empirical testing. Also the notion of kinematic geometry and some Gestalt laws are at the brink of immunity as long as they are not supplemented with precise predictions, as for instance the Gestalt law of proximity ("objects in close spatial proximity tend to be perceptually grouped together"). Thus, when discussing "the" internalization hypothesis, we always have to add at what level of resolution we are making our argument. The above distinction of a literal and an abstract interpretation was an attempt to do so.

The criterion problem refers to the content of the internalized knowledge. What type of knowledge can in principle be internalized? To answer this question, we need to narrow the concept of internalization. In its ill-resolved form, internalization can accommodate such diverse approaches as indirect and direct theories of visual perception. According to the former without further assumptions, the visual system could not arrive at unique interpretations of the necessarily ambiguous retinal stimulus (von Helmholtz, 1894; Rock, 1983). Visual perception has to solve ill-posed problems that have no unique solution (Poggio, 1990). Assumptions that transform ill-posed problems into well-posed ones are typically not arbitrary, and the percepts they create are not qualified by a question mark (as in the case of a Necker cube, whose percept can change momentarily), but are usually stable and distinct. In other words, the decoding of the stimulus information requires methods of induction (Braunstein, 1994) and additional assumptions about the world, which the visual system has - in some broad sense - internalized (Shepard, 1984). If this is the case, perceptual problems should not only be solved by the visual system, they should be solved in a manner consistent with laws that govern the physical world. Direct theories of perception (Gibson, 1979) would phrase the same basic story rather differently. The makeup of the visual system, as developed through evolution, prepares it to pick up information relevant for proper action. In a sense, internalization is implicit here.

To sharpen the criterion for internalization, a minimal requirement seems to be that the organism must have had a chance to fail to internalize the knowledge in question. Truly universal a prioris of perception would thus not be candidates for internalization. Take, for example, the law of non-contradiction: if an object could at the same time exist and not exist, neither object recognition nor epistemology could work. Proponents of evolutionary epistemology argue that our evolutionary world knowledge has no choice but to work with these necessary constraints. This entails that they are also reflected in perceptual processes (Wächtershäuser, 1987). This does not only hold for laws of logic, but also for basic structural symmetries between the world and perception that may not be coincidental. Campbell (1987) for instance, points out the striking coincidence that almost all objects that reflect or absorb light also block our locomotion and, likewise, all objects that are permeable to light do not obstruct our locomotion. We can see and walk through air, to a lesser degree through water, and not at all through solid objects. This corresponds to the two fundamental constituents of the terrestrial environment, which Gibson (1979) construed to be media and surfaces (of substances). Their existence is too basic to be called internalized in any meaningful fashion. Likewise the optics of the lens, the location of our eye-balls, etc. impose constraints onto the visual system that need to be considered to understand vision, but do not qualify as examples of internalization.

Internalization also does not need to be an explicit or declarative knowledge structure. It can non-trivially be achieved by virtue of the makeup of the system. This has been conceptualized by direct perceptionists with the use of an analogy. The visual system acts like a smart device (Runeson, 1977), as does for instance a speedometer. A speedometer does not measure time or distance, thus has no knowledge about speed, yet nonetheless "measures" speed by means of an induction current caused by the revolutions of the wheel and translated into the position of the speedometer needle. Taking advantage of induction is, in a manner of speaking, evidence for the fact that some principles of physics have been internalized by the speedometer. Likewise, the visual system can be said to have internalized some world knowledge if its behavior is smart.

In sum, to fulfill the criterion of internalization, a regularity has to be non-trivial and must have a chance to be ignored. Only these cases are subject to empirical testing. A second requirement, not explicitly imposed by Shepard, is best described in Aristotle's classification of causes. If the regularity reflects knowledge of efficient causes in the environment (causa efficiens) it can be internalized. If instead the regularity reflects other knowledge, such as action goals (causa finalis), it cannot be internalized. Thus, to support the internalization hypothesis, we have to witness the use of rules that are finely resolved and that reflect world knowledge. Since there are many counter-examples at the high resolution end, and a good deal of arbitrariness at the low resolution end, is the internalization hypothesis valuable at all?

The answer to this question can still be positive if, besides empirical evidence, we have another method to assess the fruitfulness of the internalization hypothesis. I posit that we do. A thought experiment that supposes an opposite principle may be able to generate important insights and help us decide if we want to retain the internalization idea. I suggest externalization as the opposite principle. If this opposite principle leads to predictions that are clearly erroneous, we are likely to be on the right track with internalization. If, on the other hand, we apply the cumulative empirical evidence for internalization to the externalization hypothesis and it fares as well or better, then there is something wrong with internalization.

Principles guiding our perception in cases where the percept is under-specified may be a projection of our own body dynamics onto the perceived reality. In other words, externalized aspects of the motor system rather than internalized aspects of the physical world outside ourselves may provide defaults for our perceptions. This would require a logic opposite from that of internalization. The logic behind the idea of internalization is that some laws governing the universe have been generalized and incorporated into the visual system. An externalization logic, in contrast, would not focus on the receptive visual system but on the active motor system. Considering that the visual system has evolved to guide action and not to give us nice pictures of the world, this appears equally plausible. In a way, the visual system might have "internalized" features of its own motor system. Evidence for this route could be derived from the many instances of ideomotor-action, which demonstrate a very close link between the two systems (see e. g. Prinz, 1987). The motor system, in turn, has of course evolved under the constraints that act in its terrestrial environment and therefore exhibits many features that fall under the realm of classical mechanics. The important difference lies in the fact that the motor system is action-oriented and generates its own forces. If default interpretations performed by the visual system are mediated by the action-oriented motor system, a very different set of laws might smarten the visual system. These laws are not abstracted versions of Newton's motion laws but rather abstracted versions of force-producing body mechanics.

Thus, let us consider how the visual system turns ill-posed questions into well-posed ones: it derives its default solutions from implicit knowledge of the motor system that it serves rather than from abstract universal laws that have observable consequences. This process might best be referred to as an externalization of body mechanics. An example to illustrate and empirically support this idea is reported below. It concerns the understanding of ballistic trajectories of projectiles, which can be traced from Aristotle to our times.

Not only our explicit intuitive knowledge about the dynamics of moving objects (Shanon, 1976) but also our perceptual knowledge about these events is often erroneous, albeit to a lesser extent (Kaiser, Proffitt, Whelan, & Hecht, 1992). For example, explicit knowledge about trajectories of falling objects is seriously flawed. Similar to the above-mentioned belief that a marble rolled through a C-shaped tube preserves its curvilinear impetus, many people believe that objects dropped from a moving carrier fall straight down, as if they lose their horizontal velocity component (McCloskey, Washburn, & Felch, 1983). Correspondingly, adult subjects do not favor the correct parabolic trajectory over other paths.

Hecht and Bertamini (in press) presented drawings of various possible and impossible trajectories of a baseball thrown over a large distance. Subjects favored a sine wave path over the parabolic trajectory, and generally all paths of some continuous curvature were judged to be fairly natural. The canonical trajectory shape was neither preferred nor singled out as special. This lack of perceptual understanding, if not evidence for kinematic geometry, might explain why beliefs about the shape of ballistic trajectories were rather warped from Aristotle's times through the middle ages. It was not until the early 17th century that Galileo suggested the correct parabolic shape (Wunderlich, 1977) that ensues when neglecting air resistance.

In 1572, Paulus Puchner devised an interesting analysis of ballistic trajectories to instruct canoneers of the Saxonian artillery, as visible in Figure 5. Puchner was the weaponry expert at the court of the Saxon elector August. Puchner based his state-of-the-art prediction of cannon ball trajectories and distances on the Aristotelian notion of a three-step flight path (Wunderlich, 1977): a straight ascension phase followed by a curved arc phase, and a straight vertical drop. This three-step trajectory is not easily compatible with medieval impetus theory, because the circular phase of the flight path cannot be explained by air resistance diminishing the original impetus but only by gravity (or something else) continuously acting on the cannonball. The last straight-down phase was probably an empirical observation that cannonballs tended to drop from almost straight above.

Notwithstanding these conceptual errors, observers have some visual knowledge about the correct parabolic trajectory and even better productive knowledge, as Krist and colleagues (Krist, Fieberg & Wilkening, 1993; Krist, Loskill & Schwarz, 1996) have demonstrated. Their moving observers had to hit a stationary target on the ground by dropping an object. Given this facility, adult observers could easily have "internalized" the fact that cannon balls or rocks reach their maximal velocity when they exit the gun barrel or the pitcher's hand. The horizontal velocity component decreases as a function of drag and its change typically remains small in comparison to the deceleration of the vertical velocity component. The latter first decreases to 0, then the ball gains vertical acceleration on the downward part of its trajectory.

Surprisingly, many subjects believe that a ball will continue to accelerate after it has left the pitcher's hand. This belief is mirrored in perceptual judgments when impossible accelerating ball throws were presented in computer animation (Hecht & Bertamini, in press). Figure 6 depicts a trajectory that was judged to be rather natural. The cross indicates the point on the trajectory where observers believed the ball to possess maximal velocity. While these conceptual and perceptual data are grossly incompatible with any law of classical mechanics, including medieval impetus theory, they accurately describe the movement of the pitcher's arm. The latter does accelerate the ball and this accelerating movement might be projected onto the further movement of the projectile. These findings suggest that observers judge the throwing action as a whole and fail to parse the motor action from the mechanical event, or in other words, that the body mechanics of throwing have been externalized and projected onto the inanimate projectile.

A different interpretation may consist in the failure to conceive of the ball as an inanimate object. Obviously, as soon as the ball is no longer a projectile but has its own means of propulsion, an indefinite number of acceleration and deceleration patterns are compatible with the laws of physics. This interpretation is, however, rather unlikely given the evidence that even preschoolers are able to distinguish animate from inanimate objects (Massey & Gelman, 1988). The dynamic motion context together with the mature age of the observers used in the above examples suggest that the ball was taken to be an inanimate object in these situations (see Kaiser, Proffitt, Whelan, & Hecht, 1992; Gelman, Durgin, & Kaufman, 1995).

Even if the notion of externalized body dynamics appears to be rather speculative at this point, the misconceptions as well as the perceptual judgments reflect, in some sense, a continuation of a completed motor action (the acceleration of the arm) and an anticipation of a future motor action (deceleration of the arm and catch of the ball). This piece of evidence, at the least, demonstrates that there are potential competitors for the concept of internalization. If internalization is understood as a principle of abstraction that is prevalent in situations of underspecified perception, it must be legitimate to extend it to the realm of intuitive physics where perception and cognition overlap. In the above example, observers do not behave as if they have internalized regularities about projectile motion. An externalization account fits the data much better. Thus, our final attempt to provide support for internalization by comparing it to its opposite has failed. It even looks as if the notion of externalization has to be taken seriously in its own right.

I have tried to put the notion of internalization to a test while factoring in as many interpretations of the concept as possible. I have argued that internalization, interpreted in a narrow sense, is false. At the same time, broader interpretations run the risk of making the concept immune to any attempts to test it empirically. The middle ground is what deserves discussion. I have scrutinized this middle ground by recurring to examples from intuitive physics for two reasons. First, they are true to Shepard's spirit of looking for the relation of perception to the laws of physics. Second, they could logically have been internalized. I found mostly problems and counterexamples. Observers do not behave as if they make use of knowledge about gravitational acceleration, or the law of horizontal liquid surfaces. Neither do geometric geodesics prescribe our perceptual solutions in more than a few specialized cases. Internal knowledge about world regularities seems to be specific and task dependent, not universal.

Shepard's concept can be understood as the phylogenetic complement to James' notion of habit. A habit (James, 1890) is a law that the organism has acquired during its lifetime and it thus has a clear ontogenetic touch. Habits necessarily disqualify as internalized because they are acquired and can be changed. At the abstract level of analysis this appears to be acceptable. At the level of concrete examples, however, the distinction between habit and internalized rule is very hard to make. Take the case of a simple reaching movement. In a force field that is not typical for the gravitational field on earth, as for instance when being spun on a centrifuge, observers do not take the unexpected forces into account. Their reaches are perturbed. However, after a few more reaches they have adapted to the unusual forces acting on their arms (Lackner & Dizio, 1998). Does it make a difference in this case whether we say that the observer has formed a new habit or that she has quickly overcome the internalized regularity? Or has the normal gravitational force field (1 g) only been internalized when people fail to adapt to the new environment? Maybe resistance to adaptation can be used as measure for internalization. By spelling out the differences between habits and internalized regularities in such exemplar cases, the latter concept might be sharpened.

Two aspects of the visual system, that are well captured by habit seem to render Shepard's approach cumbersome. First, the visual system is flexible. As in the water-level task, observers may change their behavior dramatically with experience. Experienced waitresses and bartenders produced larger deviations from horizontality than naive participants. Does that mean that internalized regularities can be modified on the spot? If this were the case, it would be almost impossible to differentiate between habits and internalization.

Second, Shepard's model excludes the natural environment as the major player in shaping the percept. The examples that I have discussed here attempted to focus on natural viewing situations. They failed to support his model. A system of bounded rationality (Simon, 1969, 1990) such as the visual system may confine its solution space not by resorting exclusively to internal laws but rather by including environmental satisficing constraints that come to the fore depending on the environment and the situation in which the actor finds herself. This position could easily be extended to include the body dynamics of the actor as additional constraints.

5.2. Can the concept of internalization be salvaged?

Shepard's concept can deal in four ways with the failure to find evidence for regularities such as gravity and horizontality. First, all those potential invariants that did not pass empirical testing could be explicitly excluded from the theory. This would narrow the concept of internalization to a small set of applications.

Second, only certain regularities could be predetermined to qualify for internalization. This solution is also unacceptable. Thus far, Shepard has not provided any rules to decide when a regularity needs to have been internalized. As long as these are missing the notion of internalized constraints does not have the status of a theory. It cannot be falsified. Shepard's statement could be formulated as "some regularities of the physical world have been internalized and act as constraints on perception and imagery". This is an existence statement which can only be disproved if we fail to find a single supporting case. Unfortunately, existence statements by themselves do not allow any predictions about other cases.

Third, another unacceptable salvage attempt would be to push the degree of abstraction of the concept even further. In some abstract sense, it cannot be wrong to claim that we have phylogenetically internalized some regularities of the physical world. "When formalized at a sufficient level of abstraction, mental principles . . . might be found . . . perhaps attaining the kind of universality, invariance, and formal elegance . . . previously accorded only to the laws of physics and mathematics" (Shepard, 1994, p. 2-3). This venue of hyper-abstraction leads to immunity and removes internalization from the empirical discourse.

Finally, the only acceptable solution I see is to make the concept of internalization more powerful by adding specific hypotheses that rule out alternative explanations, such as ontogenetic learning of the circadian rhythm. Given the structure of Shepard's argument, such hypotheses should be derived from evolutionary theory. They might add some of the required resolution to the debate. It remains to be seen whether such salvage attempts are going to be worth the effort.

As an alternative to the exhaustion of salvage attempts, other competing concepts to internalization need to be taken seriously. I have assessed whether support for internalization could be derived from the failure of its opposite: the notion that we have not internalized world knowledge but externalized volitional and motor aspects of our own organisms. This opposite - externalization - fared quite well and merits further exploration.

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I wish to thank the Forschungsgruppe "Perception and Evolution" at the ZiF for raising the topic of internalization. I am indebted to William Epstein, Jessica-Gienow Hecht, Mary Kaiser, Michael Kubovy, Donald Hoffman, John Pittenger, Dennis Proffitt, Robert Schwartz, and four anonymous reviewers for valuable comments and suggestions.