The experiments I have presented show that people are cognitively sensitive to two kinds of mechanical information, the mechanical magnitude in single object motion and the dynamic discontinuities in mechanical events. Thus, we can conclude that, cognitively, specific dynamic properties in the mechanical world are part of our mental representations. In this final chapter, discussions of greater depth and theories at a higher level of generality about the dynamic representations of the cognitive system will be given in order to more fully explain our earlier experimental results.
6.1 Newtonian Force F --- Medium for Haptic Perception of Dynamic Information
One question which can be naturally raised from the results of these experiments is how the mass information of an object is possible for the human cognitive system to conceive in the first place. For example, how can a lead ball be represented distinctively differently from a ping-pong ball, or vice versa, when nothing else (i.e., none of the visual and verbal information) was cognitively distinguishable between the two conditions (i.e, the LB condition and the PP condition) in Experiment 1 and Experiment 2?
Because mass, as defined in physics, can not be directly described as spatiotemporal information, thus, be perceived purely visually, we have to believe that people's conception of mass has been formed through means other than visual perception. We have to believe that people's ability to visually perceive dynamic information, such as the relative mass in a collision event, through the kinematic information of the event is possible because the cognitive system makes use of what has already been in the cognitive system, namely, representations of the dynamic information and the kinematic information as well as the relationships between these two types of information. In addition, these representations could not have been the result of Human Evolution in the visual perception alone, because the visual system only takes in spatiotemporal information which, though being closely related to the dynamic information in the physical world, is not dynamic information in the pure sense of the word. Thus, in the perception of dynamic information through the visual system, dynamic content has to be provided by the cognitive system in relation to the purely visual information.
A full discussion on the relationship between dynamic representation and visual perception is certainly quite beyond the scope of what I can handle. In the following, I will only try to answer the question relating to the experimental results I have obtained: how is it possible that people can have a concept of mass when the information of mass that comes from the environment can not even be described by space and time and, thus, perceived purely visually?
It is haptic perception which, I believe, is ultimately responsible for the formation of dynamic concepts within the cognitive system because it allows the cognitive system directly tap into the dynamic content of the physical world. Many researchers in psychology believe that the haptic perception is as important as visual perception. Some call it the 'other sense', others use phrases like 'feeling is believing' or 'the reality that we have lost touch with' to emphasize its importance.
Essentially, touch experiences are triggered by some mechanical pressure or disturbances to the skin through physical contacts with the environment. What are responsible for taking-in these mechanical disturbances in the form of neuronal signals are the so-called mechanoreceptors, which are receptors sensitive to mechanical pressures and deformation of the skin (Johansson and Vallo, 1983; Sherrick and Cholewiak, 1986). According to Johansson and Vallo, the smooth part of the skin on our body contains four different types of mechanoreceptors and there are about of 17,000 in total. Together, these receptors record any changes on the surface of our body. For example, squeezing an object with your fingers would inform you how firm the object is, because the skin of fingers compresses more in the case of a firm object than a soft one. This degree of compression is picked up by the mechanoreceptors and eventually sent to the brain as mechanical information for decoding.
Tactile information from the skin's touch receptors has to be coordinated and processed together with another kind of information, called kinesthesis. Kinesthesis, whose receptors are in muscles, tendons, and joints, informs us about the movements and positions of our limbs and our body. Thus, kinesthesis is like a coordinate system in which touch information of various kinds is integrated. Together, tactile and kinesthetic information form the so-called haptic information, which is believed to be as important as visual information.
Recently, Roland and Mortension developed an energy model for haptic perception (Roland and Mortension, 1987) based on research of the human somatosensory system. In their model, haptic information and the external information about object shape are linked together by the total amount of energy spent in the perception of the shape of an object.
With little modification, this model can be directly applied to the tactile perception of mass. As in Roland and Mortension, in which the amount of energy used in the perception of a geometrical shape can be expressed as an integral of a stimulus function in space and time, the perception of mass can be similarly expressed by an integral of a function of Newtonian force in space and time.
For example, suppose, F(s,t) is the Newtonian force function that describes the mechanical process when the haptic system is maneuvering an object with mass m. In this process, F(s,t) changes in both of its magnitude and direction, i.e., they themselves are functions of time and space. Furthermore, these changes can be quantitatively described by the second law of Newton with respect to the mechanical properties of the object. That is, F(s,t), in the haptic perception of object mass m, equals the product of the mass m and the acceleration a(s,t.) of the object, i.e.,
F(s,t)=ma(s,t).................(5)
Note, since the mass of an object always remains the same, i.e., m is a constant in Equation (5), integrating the function
F(s,t)dtds=ma(s,t)dtds=m a(s,t)dtds=E.................(6)
gives us the energy E spent during the entire haptic movement in maneuvering the object (see in Chapter 2 for the relationship between the Newtonian force and energy). In Equation (6), we can see that the amount of energy spent in the haptic perception of mass is directly proportional to the mass of the object. Because it takes more energy to handle a heavy object than a light one, this equation shows how a difference in mass is related to the difference in energy, which is perceivable as in the energy model of Roland and Mortension. (for a more detailed discussion about how the haptic system functions as a communication system, please see (Roland and Mortension,1987) and (Gibson, 1966).
Hence, as in physics, where gravity (a Newtonian force) is the ultimate medium for the measurement of mass (F. Bueche, 1988), it is only through the medium of Newtonian force and by means of the haptic system can the cognitive system actually tap into the dynamic information of mass, or in other words, can the information of mass be made directly available to the perceiver by means of Equation (6).
Notice, unlike purely visual perception where information can be solely specified in space and time, mass m in fact specifies the dynamic information in Equations (5) and (6) for the haptic perception in addition to the purely spatiotemporal information. This indispensable role of mass in the specification of dynamic information can be easily seen in Equation (5), where the variable a(s,t) can be seen as containing all the spatiotemporal information in the Newtonian force function F(s,t); In other words, without mass m in it, this equation would be a purely spatiotemporal description, i.e., the observable information for the visual perception, of this mechanical event, since a(s,t) contains all the variations of the event in space and time. Therefore, the presence of mass m in Equation (5) in fact provides the dynamic content to the spatiotemporal movement described by a(s,t).
Mathematically, in both Equations (5) and (6), the spatiotemporal information can be seen as being weighted by mass m to be transformed into mechanical information; or put it differently, m specifies the dynamic magnitude or strength of the Newtonian force and energy function by weighting the spatiotemporal information a(s,t,) and a(s,t)dtds. The difference between these two cases is that the weighting in ma(s,t,) is instantaneous and in space and time, whereas the weighting in ma(s,t)dtds weights the entire spatiotemporal information all at once, thus requiring 'memories' of the information in space and time. In either case, the important role of mass in the specification of dynamic information by weighting the spatiotemporal information is quite clear.
Thus, the mechanical information as characterized by the Newtonian force, F(s,t), is a mechanical function of space and time. Physically, though the functional variations of F(s,t) in space and time can be sufficiently described as kinematic or spatiotemporal information, the specification of the dynamic magnitude or strength of F(s,t), however, requires the dynamic information of mass. Dynamic perception through the haptic system therefore involves both the spatiotemporal information, a(s,t) and a(s,t)dtds, and the dynamic information, m. Interestingly, the Newtonian force function, F(s,t), wraps both types of information into itself, connects the dynamic properties of the physical world to the biological system capable of perceiving, and provides the haptic sense of this system the information with mechanical content.
Newtonian force, like light which is the medium for the visual perception of spatiotemporal or form information through the visual system, is therefore the medium for the perception of dynamic information through the haptic system. Further, like light which is invisible to the visual system itself, the Newtonian force is also inaccessible by the cognitive system.
An important feature of haptic perception of dynamic information through the Newtonian force medium is that dynamic information can only be perceived through contact. (I define contact as different from impact. Generally, I will use 'impact' to describe interactions between two mechanical objects and 'contact' to describe the interactions between a perceiver and a mechanical object). It is only in contact and through contact that the Newtonian force acts as an information carrier and informs the cognitive system about the dynamic properties of the world. This means that the medium for haptic dynamic perception is fundamentally different from the medium for visual perception. Although both can be regarded as information media, the Newtonian force informs only in contact. In other words, it is a dynamic medium, as opposed to the static medium of light for visual perception.
Therefore, the dynamic information and the spatiotemporal information, carried by two different information media, the dynamic and the static, and processed by two different information processing units, the haptic system and the visual system, form within the cognitive system two distinct types of cognitive representations in term of information content, the dynamic and the spatiotemporal. Though only a simplified model of perception, this view is quite consistent to a recently proposed theory that mechanical information and spatiotemporal information are processed in two different cognitive modules, ToBy and the visual system (A. Leslie, 1994). This view further finds support in recent neurological research and consistency with the modern Theory of Evolution. Patients with severe damage to their visual cortex and with no ability to generate visual images were found to still have knowledge about the tactile properties of objects (Damasio, 1994). Evolutionarily, vision is regarded as a more efficient sense able to process distal (form) information, but nonetheless has developed from the more primitive sense of touch (DelBruck, 1986; Humphrey, 1992), which explains why, without the haptic system, purely visual perception itself can not account for the formations of dynamic representations.
One distinction has to be made here. The haptic perception of dynamic information, which requires contact and the dynamic medium, is quite different from the conception of dynamic information, which requires dynamic representations. At present, we are only concerned about the haptic perception of dynamic information. And, I have suggested that it is impossible for dynamic representations to come into existence without the haptic perception of the dynamic qualities of the world, either in the sense of Evolution or Empiricism. The relationship between perception and conception has been a hotly-debated topic among philosophers and psychologists. With respect to the relationship dynamic perception and conception, the reader may find some recent discussions in (Freyd, 1987; Spelke, 1992; Yates, 1985; Yates, 1988). In particular, the idea of enactment of Yates may be quite helpful.
Finally, in haptic perception of dynamic information, the third law of Newton, which states 'for every force F, there is another force -F, equal in magnitude but opposite in direction', can help us further analyze a mechanical contact in the case of haptic perception of dynamic information in term of the information content that is available for the cognitive system to perceive. In contact, following this law, for every force function F(s,t), there will be another force function -F(s,t). Therefore, in the case of haptic perception of dynamic information, if one force is acting on the world, the other would be acting on the perceiver; if one force informs the perceiver about the world, the other would inform the perceiver about the perceiver's own action. Together, the lawfully necessary connection (under the third law of Newton) between these forces allow them to unfailingly carry information about the dynamic relationships between the world and the perceiver. The earlier discussion about the perception of mass, referring to Equations (5) and (6), is a specific example to show how the Newtonian force medium carries the mass information of an object, whereas purely spatiotemporal information does not. This simple fact may have great implications for the dynamic representations and causal concepts in the human cognitive system. It is quite likely that it underlies some of the important causal principles in the cognitive system. (See (Bullock, Gelman, and Baillargeon, 1982) for a discussion of causal principles.)
Before going to the next section, one more comment needs to be made. The separability between the spatiotemporal and the dynamic information, as shown in Equations (5) and (6), is in fact the foundation for Runeson's KSD Principle and the reason why most of the research on motion perception can focus exclusively on the spatiotemporal information. However, as can be seen in Equation (5), m determines the dynamic magnitude or strength of F(s,t) by weighting a(s,t). This means, a(s,t) alone is not enough for the specification of F(s,t), because infinitely many different a(s,t)'s can specify the same F(s,t) by the specification of infinitely many different m's; And, one single a(s,t) can specify infinitely many F(s,t)'s by also the specification of infinitely many m's. But, the specification of m is the specification of dynamic information. Therefore, a sufficient representation of the force information is possible only by specification of both the spatiotemporal information and the dynamic information. This conclusion does not conflict the classical example (Runeson, 1977) shown in Equation (4), because only relative mass is specified kinematically in this example, which in itself suggests that a complete specification of dynamic information by means of spatiotemporal information alone is not possible. Similarly, the well-known experiment in (Todd and Warren, 1982) is also about visual perception of relative mass in a collision event. In the case of specifying relative mass in a collision event, a key piece of information is in fact left unspecified --- the dynamic magnitude of either objects involved in the event.
6.2 SUBSTANTIAL FORCE --- The Primitive of Dynamic Representations
In spite of the fact that it is Newtonian force which enables the haptic system to pick up the dynamic information and the cognitive system to directly perceive the dynamic properties of the world, it is not Newtonian force, however, which can be naturally represented by the cognitive system (otherwise, why would we need Newton?).
The Newtonian concept of force is a scientific discovery characterized by its accuracy in describing Newtonian force in the mechanical world with Newtonian laws around this concept, which however are formulated not by the concept of Newtonian force itself but completely through mass-space-time relationships. The discovery of these mechanical laws is the result of scientific exploration by many generations. The objectivity of such a concept has grown out of several conceptual revolutions in history. In comparison, people's natural conception of force is highly subjective, diverse, and inaccurate. It is mainly the result of human evolution and life experiences. Therefore, it is quite a useless endeavor to try to figure out why people do not naturally have Newtonian concepts. Instead, it is important that, in the study of dynamic representations in psychology, this distinction be made at the very beginning.
Then, what is the most basic dynamic concept or the cognitive primitive of dynamic representations which the cognitive system can be aware of? Based on recent research on infants (Baillargeon, R., 1986; Leslie, A., 1993; Spelke, E., et. al, 1992) and the discussion in the last section, I now propose such a cognitive primitive, SUBSTANTIAL FORCE, which lies at the roots of all dynamic representations.
As I have argued, the cognitive system can not be aware of Newtonian force as the visual system can not see light in space. However, like the visual system sees object-form through light, the cognitive system can be aware of one root dynamic representation (primitive) through haptic perception --- SOLIDNESS/RESISTANCE, which is the most primitive dynamic representation, i.e., of the lowest level of dynamic information. In other words, SOLIDNESS/RESISTANCE is the smallest dynamic unit which the cognitive system can 'see' in the information medium of Newtonian force conveyed by the haptic system or conceive in its information storage. (Caution: solidness, the way I use it here, is different from 'being solid'. I define solidness as a representational dimension, along which the solidity of objects in different degrees can be cognitively 'expressed'). Following the discussion in the last section, since dynamic information can only be 'seen' by means of physical contact, through which Newtonian force as the perceptual medium informs the cognitive system about the dynamic properties of the world, the perceiver, and the interactive relationship between them, a primitive of this sort has to be a twofold representation in term of its semantic content, i.e., being SOLID as well as RESISTIVE.
Such a conclusion can be derived directly from the nature of the Newtonian force function F(s,t). As already mentioned, the third law of Newton commands the coexistence of the active force and the reactive force and, as a result, necessitates the bi-directionality and simultaneity of any dynamic information exchange between the perceiver and the dynamic world. In other words, it unconditionally requires that all information carried by F(s,t) in the process of dynamic perception appear or disappear in the exact location in space and at the exact moment in time, exist and change exactly simultaneously in information content, yet always polarizes around the dynamic world and the perceiver. Because the dynamic information can be expressed by the Newtonian force function in both time and space, the minimum amount of dynamic information can then be explicitly reached by reducing the scales of both space s and time t in the force function F(s,t) to a single location in space and a single moment in time, for example, s0 and t0. Then, F(s0,t0) carries the minimum amount of dynamic information. Taking in this information in F(s0,t0), the cognitive system can extract therefore minimally two pieces of information, SOLIDNESS about the dynamic world and RESISTANCE about the perceiver with respect to that dynamic world. Hence, the dynamic representational primitive, SOLIDNESS/RESISTANCE.
Therefore, from an information processing point of view, the proposal of SOLIDNESS/RESISTANCE as a cognitive primitive is a direct result of Newtonian force as the information medium for haptic perception of dynamic properties of the world through physical contact and the use of third law of Newtonian physics. This primitive of dynamic representation is, on one hand, 'pointing' to part of the mechanical world with a dynamic 'description' (SOLIDNESS), and, on the other hand, 'pointing' from it with another dynamic 'description' (RESISTIVE). Thus, SOLIDNESS is the cognitive system's object-ive description of the mechanical world and RESISTIVE is the cognitive system's subjective (or agentive) description of the mechanical world. This dualistic primitive, which represents both the dynamic world and the perceiver as a mechanical agent at the most basic dynamic level as the objective and the subjective, can not further be divided itself semantically into smaller pieces in the cognitive system.
In order to adequately capture the rudimentary and dualistic character of such a dynamic representational primitive, the term SUBSTANTIAL FORCE is adopted for this primitive concept. Here, the word substantial is intentionally chosen to emphasize the substantive nature of solidness in the primitive; and force is used to represent and generalize resistance in the primitive.
As a cognitive primitive, SUBSTANTIAL FORCE can be regarded as a pure and smallest dynamic component in an object concept and the representation of a local feature of the object. When SUBSTANTIAL FORCE is applied to the object level, the concept of mass replaces the concept of substantial force. In other words, the concept MASS is the SUBSTANTIAL FORCE of an object. The relationship between SUBSTANTIAL FORCE and the concept of mass is by no means trivial and, to save space, will be treated in detail elsewhere. Here, I will only point out that what distinguish between these two concepts lie in the notion of mechanical boundary and the kinematic properties of an object. However, like SUBSTANTIAL FORCE, MASS is also bi-directional and dualistic in semantic content, but, taking a different and more complex form. The SOLIDNESS in MASS is no longer local, i.e., it no longer corresponds to a local feature in an object, but describing the substantive feature with respect to the whole object. Similarly, RESISTANCE in MASS, which is conceptually inherent in the concept MASS, is also referring to the resistance of the whole object. Therefore, the SUBSTANTIAL FORCE of an object, i.e., the concept of mass, is no longer a primitive representation, because it is based upon another more primitive representation, namely, SUBSTANTIAL FORCE. Note, the same can not be said about SUBSTANTIAL FORCE.
In the experiments presented earlier, we have dealt with mechanical events that are all above the object level, i.e., in conceiving an object in these events, the cognitive system not only represents the substantial force or mass of the object, but also other mechanical information, such as mass in motion and mass under the influence of Newtonian force, etc.. In order to adequately discuss these different kinds of mechanical information and the representations of them by the cognitive system, I now give a more precise account of the notion of mechanical state.