Size Information: Analog or Discrete? A. Introduction One of the fundamental intuitions about visual mental images is that they retain their distinctively visual (or quasi-visual) quality because they are the bearers of information initially gained through visual perception. Visual experience allows us to categorize objects in the world according to shape, color, location, and size. We can retain information about these properties of common objects for long periods of time. We can recall, for example, the shape, color and size of individual books, cars, tables, rooms, coins, and so forth. Frequently, we can compare our present visual perceptions to those we can recall by means of mental images. We can judge is the present object we see is smaller, larger, a different shade of red, or a different shape than some other object we have encountered. From a pre- analytical perspective, it seems obvious then, that mental images are induced through visual experience and that mental images in long term memory are responsible for our retaining, shape, color, location and size information. We have no reason to suppose, again from a pre-analytical perspective, that we ought to think information initially gained through visual input is transformed into some other form of information during storage and then transformed back again into "visual" information in the form of a mental image. A scientific perspective will raise some questions about this view. The notion of using visual images to answer questions about the properties of objects is a topic in the general field of semantic memory -- that part of long term memory in which the meaning of terms (physical object nouns in particular) are stored. A fundamental question about this form of memory is whether or not there are actually images stored in memory that contain some of the fundamental information about objects. In what sense ought we to say that we store and retrieve images? One of the forms of information we store and retrieve with relative ease is information about the size of physical objects. In what sense are mental images involved in this process? Psychologists have found a fundamental similarity between the perceptual judgments of the relative size of physical objects and size judgments based on memory. In the case of perception, the closer in size objects are, the longer it takes to reach a judgment as to relative sizes. We have no hesitation, for example, in judging whether a dime or a quarter is larger, but it is sometimes difficult to judge which of two apples is larger. Judgments based on memory are similar in that when subjects are asked to make judgments of object sizes from memory, more time is required if the actual sizes of the objects involved are nearly equal. The general inverse relation between closeness in size and time to reach a judgment regarding size is known as the size discrepancy effect. This effect suggests a general parallelism between the way in which perceptions are compared and the way in which mental representations of non-present objects are retrieved and compared. Despite this is rather convenient and promising discovery, there is probably no other topic within the literature on mental images that is as confusing and question-begging as the topic of the mental images and size information. Almost one hundred pages of densely-reasoned text is devoted to size information experiments in Kosslyn's 1980 book. One of the first appeals Kosslyn makes to the notion that mental images are not epiphenomenal is based on the retrieval of size information. For the purpose of developing his overall theory Kosslyn's analysis of the experimental evidence is extremely important. Yet, the experiments and the reasoning behind them remain, in my view, too complicated and too remote from common sense to serve as useful examples. In this section, therefore, we depart to a certain extent from our previous method. Rather than experimental details, the focus will be on theoretical models and conceptual problems for size information theory. As in the other facets of the debate, the principal issue on the topic of size information is stored in a form that is analog or discrete. The use of the term "analog" in the context of the literature on size information deserves special note, because it is used in several senses. Among the meanings that have currency are the following: (1) admitting of extremely fine (or perhaps infinite) degrees of variation in size information; (2) having spatial properties, such as being larger or smaller (as in a "large" or a "small" mental image of a mouse); and (3) being non- reducible or convertible in mode (that is, operating as distinctively "visual" as opposed to "verbal" information). While there are no substantially new notions introduced here, it is useful to bear in mind that the terms "analog" and "imagistic" seem to be used interchangeably with greater frequency when it comes to the topic of size information. This section is more broader in scope and more speculative previous sections. I undertake two tasks in this section. The first is a negative critique. I suggest that the various models of size information storage and retrieval, whether imagist or propositional, are merely attempts to make theory conform to phenomenology. These models lack predictive value and can be made to conform to virtually any data. I also indicate, in the final subsection, that the behaviorist methodology inherited by cognitive science does not do justice to the conceptual nuances of psychological testing procedures, particularly in the case of size information experiments. An enumeration of the many problems faced by the these accounts, is sufficient, in my view, to warrant the conclusion that any further pursuit of them is unlikely to yield a coherent account of our cognitive abilities to store and use size information. The second task is speculative, but attempts a positive account of size information storage and retrieval. Aside form its possible explanatory function, the account serves as an exercise demonstrating the need for a more faithful and consistent phenomenological and scientific vocabulary in cognitive science. The proposed account argues, on conceptual grounds, that size information is indeed automatically stored by computational processes of the visual system, but that the information is not stored in a form that is can be called an image. I suggest that since the appearance of mental images bearing size information in consciousness is computationally unnecessary, the mental images involved in retrieving this information probably derive image evolutionary constraints. The critique of the theory and methods of cognitive science presented in this section, as well as the positive account suggested, work together to provide the impetus toward developing an alternate view about the nature of mental images. B. Paivio's Model Moyer (1973, as reported in Paivio, 1975) conducted experiments demonstrating showing the size discrepancy effect using memories of the sizes of common animals. Subjects were given the names of two common animals and asked to judge which was larger. Their response times were tabulated. The time delays as a function of size difference were similar to those usually found for perceptual judgments. Paivio has used size discrepancy data to argue in favor of the analog nature of the internal representations storing size information. In summarizing Moyer's results, Paivio hypothesized that subjects compare animal names by making an "internal psychophysical judgment" after first converting the names to analog representations that preserve animal size" (Paivio, 1975, p. 635). The idea that mental representations derived from vision should be characterized as "analog" follows Shepard and Cooper. Paivio reasoned that the analog nature of visual size information also supported his own dual code theory since it retained the idea that long term visual memory knowledge is isomorphic in form with visual experience. Paivio argued that propositionalist schemes could not account for the continuous nature of sizes we are capable of recognizing and recalling for two reasons. First, in order to match our capabilities using discrete categories, the number of physical size categories included would have to be huge, corresponding to the innumerable fine degrees of perceptual discriminations we can make among physical objects. Second, propositionalist schemes can explain the size discrepancy effect only by creating elaborate procedures and complicated data structures that intervene in the decision process causing the appropriate delay. The way in which an appropriate propositionalist scheme must be elaborated in order to account for empirical data deserves some further examination. This will illustrate some of the difficulties faced in making models conform to data. A typical propositionalist theory posits conceptual nodes linking nouns with properties, categories and other information. These semantic memory models generally propose that noun terms are given their meaning in virtue of their interconnections with other terms in a set of structured relations that define categories and properties. The term "lion" for example, could be linked to terms "animal" as a superordinate category and to "mane" as a property. This type of theory proposes that if the question "Is a lion and animal?" is posed, the answer is generated by means of utilizing the links established by the system. The meaning or sense of terms like "animal" is derived from the superordinate and subordinate categories it is linked to, e.g., "living thing" and "mammal." The structure of this network would also define the time to identify if certain properties were associated with a term. It is supposed that if only one link separates "lion" and "mane" this will take less time to check than if one asks about lion and "living thing," since these terms are separated by two links. One of the immediate and pervasive problems with this sort of model is the discrepancy it creates between the logical considerations of such structures and certain empirical findings. Most notably, the standard logic of efficient hierarchical structures would dictate that general properties would be remotely located from noun terms. This is not borne out by the evidence of timed experiments, which show that general information is very quickly retrieved (e.g. "Is a lion an animal?" generally gets a faster response than "Does a lion have a long tail?"). An example using size information will illustrate this problem in greater detail. Response times to questions about the relative sizes of duck versus goose are slower than questions about the relative sizes of iceberg versus ant. Since this is the case, the size information for duck and goose (Figure 2-XXa) would have to be stored further from the noun than in the network encoding various information about iceberg and ant (Figure 2- XXb). The descriptivist model must be of this sort if it is to explain the data. Yet, the two structures differ radically in logical organization, and there is absolutely no a priori or theoretical reason to suppose some common objects would have size information encoded "further" away from the object name than others. This problem for a descriptivist nodal network model convinced Paivio that these schemes are simply post hoc inventions made to match the empirical data. Paivio concluded descriptivist models of this sort lack a consistent rationale or predictive power and can not be used for science. duck goose | | quack honk | | bird bird | | medium size medium large size Figure 2-XXa. Conceptual Node Arrangement for Duck/Goose. A nodal hierarchical arrangement of properties showing size information as remote or difficult to retrieve. iceberg ant | | very large very small | | white black | | natural object insect Figure 2-XXb. Conceptual Node Arrangement for Iceberg/Ant. A nodal hierarchical arrangement of properties showing size information as near or easy to retrieve. These theoretical arguments are powerful, but Paivio also wanted empirical verification of an imagist alternative model. It was possible that Moyer's results were anomalous. Since he tested only for animal sizes, it remained a possibility that the size discrepancy effect for animal sizes was the result of the structure of a special network of information for animal sizes. Paivio therefore decided to test across several categories of common objects. He used a list of 174 common items, ranging from salt grains to icebergs, and asked subjects to rate their comparative sizes on a scale of 1 to 9. From this list of commonly-accepted size differences, he generated a scale of relative sizes for use in further experiments. Paivio noted that the subjective reports obtained in the process of compiling the list showed subjects thought that imagery, rather than verbal strategies, were the most useful in making the size comparisons. Paivio's list of normative sizes has been used and referenced as a source of subjective size estimation data in psychology in many studies since Paivio first compiled it (1975). Paivio's first experiment arranged the names of objects in pairs presented on file cards. The objects pairs included those that reflected small, difficult to judge differences in size (in a ratio of 1:1.17), to pairs that reflected large, obvious difference in size (in a ratio of 1:7). To test the variation across categories, object pair names from different categories were tested against pairs from the same categories. Subjects were presented with the names of two objects and asked to decide which was larger in real life. The results are shown in Figure 2-XX. The similar straight lines generated for the several categories tested indicates that the time delay function is constant across categories. This implies that size information is stored and accessed in the same manner for all types of common objects. Figure 2-XX. Mean reaction time for size comparison of animal- animal (AA), object-object (OO), and animal-object (AO) pairs as a function of scaled ratio size difference. (From Paivio in Pick, 1978, p. 44) Paivio placed a great deal of stock in this finding: "This finding in itself suggests that the comparisons are based on analogue representations containing rather precise relative size information" (Paivio in Pick, 1978, p. 44). Paivio also made a very strong claim in support of one side of the imagery debate. He claimed that at least as far as size information was concerned, the discrete or single code theory was refuted by his experiments (Paivio in Pick, 1978, p. 50). Although he had both theoretical and experimental support for his model, Paivio also needed to account for a phenomenological fact: that in some cases of size judgments based on memory information, subjects report no imagery experiences. Paivio covers this fact with the following explanation. These representations apparently are manifested sometimes as consciously experienced visual images, as in the case of subjects who provided the normative size judgments...but it is conceivable that the analog information can also be functional in a task without any conscious experience of imagery. This suggestion simply acknowledges a necessary logical distinction between a functional cognitive system and its behavioral manifestations. In this case the hypothetical imagery system is assumed to have various functional properties that are not necessarily dependent on conscious imagery, although the latter is obviously a salient expression of the activity of the underlying system. ...The important point here is that consciousness is not viewed as a necessary defining attribute of the imagistic representations presumably involved in size comparisons and other tasks, although it often provides supplementary evidence that such a process is functionally activated. (Paivio, 1975, p.646). Paivio's explanation shares an important assumption with Kosslyn's theory. Conscious imagery experiences may be similar in form to the underlying mechanisms accounting for them, but the actual, functional properties of the underlying system are the properties in question for the psychologist and these properties can be revealed without our conscious experiences being examined. Paivio describes the underlying representations as "imagistic." In his theory, this means (among other things) representations that are dedicated to visually-derived information, that produce distinctively visual experiences when reactivated from memory (when do they result in conscious experiences) and that retain the analog or fine-grained information of the actual sizes of objects. The purpose of covering Paivio's model will now, I trust, become clear. As in other models derived from contemporary empirical approaches, this model is driven by response times. A theory has been proposed to explain the response times. Let us pose some naive questions. Does this approach really tell us the qualities of images or how they store size information? The "images" doing the job are either conscious, or in some cases, (rather conveniently) not conscious. Yet, according to the theory, the unconscious images are still images, they are still "analog." I what way does this advance our understanding of what we mean by stored "size information"? We already know (without much needed in the way of experiment, one might add) that we can make innumerable fine degrees of differentiation in our memories of the sizes of objects. What is meant by saying that the information is analogue other than that it is very fine grained? How can we distinguish between fine-grained discrete information and analog information? If this is all that is meant by designating this information "analog," how has our knowledge of the nature of images been improved? Concerning the speed of responses, can not one argue that the speed is irrelevant? After all, we know or have some indication through introspection, whether or not images are used in the ordinary (conscious) sense. What we want to know is if the conscious images themselves "contain" this information. How can a supposition that size information is analogue help explain the presence of an image? Might not the same image appear if the information were discrete? The fact that nodal network models don't match the response time requirements, does not eliminate the many other discrete code models that might be considered. Most of all, one can question whether the entire approach illuminates what we normally mean by having a mental image of the size of an object. How, precisely, are such images generated, and how are they given the "size" they appear to have, when we know that it is not the image per se that has any size at all, but the object that it represents? I suggest that these many unanswered questions within the literature on size information are almost sufficient in themselves to warrant a fresh approach to the entire topic. Before we venture in that direction, however, let us examine Kosslyn's model of size information retrieval. C. Kosslyn's Model Kosslyn argues against Paivio's view that size information is encoded always and exclusively in imagistic format. He argues that the best explanation of both introspective and experimental evidence is that size information is encoded in both propositional form and imagistic form. It is worth noting at the outset that Kosslyn's model, while he presents it as a rejection of Paivio's, should really be understood just an extrapolation, since Kosslyn does not fundamentally disagree with Paivio on the issue of the existence and functional significance of images. Kosslyn merely attempts to incorporate propositional features into a pictorialist model of size information storage and retrieval. Kosslyn proposes a "race model" of retrieving size information in which the retrieval process for size information is initiated by simultaneous processes in two forms: one process attempts to retrieve size information through imagistic information; the other, through a search of categorical or propositional information relevant to the object in question. An example, based on Kosslyn's own, will illustrate Kosslyn's reasoning (Kosslyn, 1980, p. 349). a) Which is larger, an elephant or a mouse? b) Which is larger, a toaster or a mouse? c) Which is larger, a mouse or hampster? Kosslyn observes that most people report no imagery occurs in answering the first question. The second and third questions take longer to answer and tend to elicit imagery in many subjects. Kosslyn's model accounts for the ease of answering the first question by supposing that it involves propositional representations. Subjects report that they "just know" an elephant is larger than a mouse, and that questions involving objects obviously belong to separate size categories are ridiculously easy. This can be accounted for if we suppose the animals fit into natural size categories of "large" and "small" respectively. Since the size categories the animals belong to are not the same, the need for additional, more detailed information about the size and/or appearance of the animal is not necessary, so the search for information is terminated, and no imagery is evoked. The second and third questions, by contrast, involves objects that may both belong to the "small" category. In this case, a conclusion can not be reached through accessing the propositional knowledge available, so the imagery process (concurrently operating) continues, resulting in images that can be inspected in order to make a relative size estimation. Kosslyn's alternative theory raises still another question for theories of size information. If the explanations are this variable (conscious and unconscious images, propositional and non-propositional encodings), is there any introspective evidence that a suitably complex theory can not be made to conform to? Although Kosslyn has gone to extraordinary lengths in developing experimental support for his theory, it is, in my view, a theory that has been constructed primarily to cover introspective evidence and is not sufficiently constrained by prior considerations of computational considerations or the realities of vision processing. His theory, ultimately, in my view, is a phenomenological report. If this appraisal is true, it again underscores the need for addressing precisely how we are to understand the role of introspection in contemporary psychology. Needless to say, Kosslyn and others might vigorously be able defend their theory with data and other arguments I have not presented here. C. Discussion: Toward an Alternate View 1. Conceptual Problems There are conceptual problems with the topic of size information, its storage and function as it appears to be understood by contemporary cognitive psychology. Rather than attempt to refute any specific model from cognitive science based on specific empirical data, I propose to examine the concept of size information based on a general knowledge of the visual system. The questions we need to address are (1) How is size information stored? and (2) What do we mean by size? In the discussion that follows I shall adopt some of the language of folk psychology. In shall assume not that folk a psychological account is necessarily the last word on the matters at hand, but that it communicates with sufficient accuracy a relatively common phenomenological and conceptual base. Such expressions as "seen with the mind's eye" are presumed to be understood in ordinary discourse even if the phenomenon itself can not be explained by folk psychology. Part of what I present, it should be noted, will also be in accord with some of the pictorialist assumptions, since I shall assume that certain vision-derived conceptual and phenomenological constraints hold for the imagery experiences of the vast majority of people. I presume that mental images have what we may meaningfully term as subjective size. By this I mean whatever is imagined can be seen in the mind's eye as taking up all of an imaginary field of view or as taking up only a small portion of it. We can imagine a circle as being almost dot or as taking up all of our field of view. Imagine walking toward a large car. At a certain point, the ends of the car may be said to "disappear" from the imagined field of view, and we imagine clearly only some small portion of the car's surface. The same is true of a penny. Imagined as on the sidewalk, it is only a dot, devoid of detail. Imagined very close, the circumference of the penny overflows the imagined field of view, and only the details of Lincoln's head are seen clearly in the mind's eye. In each of these cases, the subjective size of the image is the size that we imagine it to take up in our field of view. Our beliefs about the actual size of an object are independent of the subjective size of a mental image. An imagined arbitrary circle, for example, has no actual size, but it may have any subjective size we choose. With perhaps somewhat more difficulty, we can separate the subjective size of a mental image of an elephant from our belief that an elephant has an actual size in reality. We know that an elephant is a large animal. We know that, if we were to stand next to an elephant, we could only see a portion of it at any one time. If we imagine the elephant as it would appear farther away, the subjective size of the image will be smaller. The subjective size, actual size, and distance relationships are posited or implicit in our understanding of our own mental representation. These relationships need not be maintained as initially posited, however. The image of an elephant and the image of an arbitrary circle are the same in that no specific actual size need be assigned to the imagined object. Assigning a size to the imaged object is an optional act. If we thought that the elephant, of which we presently had a mental image, were a miniature elephant, only one foot high, seen from close up, the subjective size of the image need not change. These considerations lead to a conclusion and also pose a question. The conclusion is that, evidently, our having a mental image of a certain subjective size is a state independent of our belief that the object has any particular size. The phenomenal image does not itself indicate the actual size of the object imagined. The question is: how do we store the information of actual sizes? More pointedly, this question becomes one we have seen repeatedly in the discussion of imagery: what is the purpose of conscious mental images? Evidently, they do not indicate the size of objects. Rather, we posit a size for them. Therefore, the images are useless. 2. Absolute and Relative Size Information In addition to distinguishing between analog and discrete, Kosslyn, Paivio and others have also made use of the distinction between absolute and relative size information. We shall briefly address how these are understood in the literature. One view is that we store the absolute size of objects. In this case, the size of objects is not conceptualized as larger or smaller than some other object, but is given an independent assignment. For example, assume that a subject is familiar with both footballs and basketballs, having had occasion to hold each at arms-length at one time or another. In this case, each object has been held at a uniform distance from the subject's eyes, and each has produced a physical image on the retina. These physical images on the retina differ is size and shape. Because the two images were created under equivalent distances from the object, the sizes of these images are in fact directly proportional to the actual sizes of the objects. Given this circumstance, it is not too much to suppose that our cognitive systems can translate these retinal images into an estimate of true physical object size. What kind of estimate of size? If size information is stored in the absolute form, the estimate is not a verbal one such as "larger than a grapefruit," but must consist of an amodal encoding of the size of the object, allowing this information can be instantly transformed into other modes, such as motor or verbal activity. The subject may hold their hands to indicate the object is "this big," or they may respond to a question by saying "it is about ten inches long." In either case, the capability to indicate the size derives from information that has no intrinsic mode that limits its form of access. This theory comes with a further, and somewhat troublesome, assumption. One must assume there exists the equivalent of "mental inches," that is the basis for this information retrieval. As in Pylyshyn's theory, "mental inches" does not imply that this information is has in fact been translated into an explicit linguistic code. For example, the storage of absolute size information might enable a person to be able to hold their hands apart to indicate the size of a basketball very accurately. Yet this same individual may not be able to state its diameter in commonly-accepted units of measurement. The advantage of assuming that size information is stored in the absolute format in long term memory is that this would automatically allow us to be able to recognize the shapes and sizes of objects at various distances. Processes in the visual/imaginary system perform distance/size compensation calculations so that objects seen at various distances remain experienced by us as constant in size. In this respect, the experience of size constancy is given an explanation similar to color constancy. Both are essentially automatic processes handled by the visual system. The theory of absolute size storage is distinguished in the literature from the view that the size information we store is based on the continuous assessment of the relative sizes of objects. In this case we need not assume that mental inches exist, but only that categories of larger and smaller apply to huge network of objects. It is easy to understand how the relative sizes of objects we see simultaneously could be judged relative to each other and the appropriate information stored. In each instance we would encode the equivalent of "X is larger than Y." The basis for the ability to make size comparisons of objects we have never experienced simultaneously is less obvious. Presumably, this would involve a deduction using previous relative size information (e.g., if A is larger than B and B is larger than C, then A is larger than C). Needless to say, such a system of information storage would become exceeding complicated. Simplicity of explanation and a basis in laws of optics are strong factors in favor of the absolute size theory for the encoding of size information. All of the information we need to know the actual size of objects, as measured in "mental inches" can be gained directly from perception at a specific distance, plus a calculation based on the optical and physiological laws governing retinal images. This calculational ability is probably innate in the brain. We conclude, therefore, that the automatic storage of size information in amodal absolute size format probably needs to be a starting assumption for a theory of size information processing. A comment is warranted on how this applies to Kosslyn's theory. Nothing prevents us from consciously translating absolute size to a verbal assessment of whether one object ought to be considered "large" or "small." We do this all the time, and this would explain why we answer some questions using our linguistically-encoded beliefs, and some (apparently) using an image. But this is not, as I read it, Kosslyn's theory. The question we need to address for a theory is "How do we initiallyencode size information?" Kosslyn seems to assume that we store both analog images and verbal (discrete) codes initially, simultaneously, and unconsciously. He uses this assumption to explain the certain phenomenological facts. Although his theory fits the phenomenological facts, it still does not sufficiently explain the need for conscious mental images -- a topic we address in the next section. 3. The Need for Conscious Mental Images The need for mental images in consciousness during size estimation is not easy to explain. From what we have stated so far, the mere appearance of the image in consciousness at the time of size estimation provides no information relevant to the actual size of the object imagined. Normally, we are, of course aware (or ready to be aware of) the actual size of an object. If we imagine an elephant, we also supply the cognitive context in which the subjective size of our mental image implies an actual elephant of a certain actual size would be a certain distance away. Our imagined elephant has, as it were, a "title": "elephant seen from a safe distance." This implied distance (or size) can be made more explicit simply being more definite in setting the task for the imagination. "Imagine an elephant where the desk is," causes one to access the information about size one already has. A size comparison task, if it evokes images, has a tendency to cause us to automatically posit that the objects are at the same distance and to scale the subjective size of the two images appropriately. The absolute size information is used in the construction of the images, but exists independently of the image. From an abstract information processing standpoint (unencumbered by biological or phenomenological considerations, considering information only as it might be used in some hypothetical machine), it would be possible for the information to be accessed without the image. From an abstract information processing standpoint, there is no logical requirement for images to appear in consciousness during size comparison tasks. The reason for images, then, since they evidently occur, must have something to do factors other than abstract machine- based logic. If it is literally impossible for us to become conscious of size information we retain in memory, except by constructing an image, then the necessity of conscious images is biological, not logical. Evolutionary factors may have forced this particular mode of conscious experience. Perhaps the only way we can recall detailed size information is to dredge up the (logically unnecessary) pictorial information along with the size information. The subjective scaling of the image, that is, the positing of an implied distance for an appropriate subjective size image, is all automatic, brought upon us despite the logical requirements of a specific task, by the contingencies of evolutionary design. This feature of evolutionary design causes us to become conscious of information extraneous to a specific task at hand, but it may also be of advantage in meeting spontaneous needs of the environment. The expectation that one will see an object of a certain size in a dangerous situation may also draw on other information that would prepare us for sensing certain shapes, colors, sounds or smells. Although the above account is very speculative, it is, on the whole I suggest, more satisfactory than the explanatory framework supplied by Paivio's or Kosslyn's models. These theories offer no explanation why images appear in consciousness when they are computationally unnecessary. It remains only to address how timed responses for tasks are to be accounted for in keeping with our own proposed analysis. 4. Reaction Time Evidence and Judgments Timed reactions to stimuli, if they are to mean anything, must be able to isolate a specific variable causing variations in the reaction time. Kosslyn and others have assumed that the term "size" has a univocal meaning and that each object encoded in memory has been given a specific size designation encoding (absolute or relative). These encodings are non-context sensitive, or fixed in nature. According to the models as I understand them, the size encoding is, as it were, atomic or static in nature. Once accessed, the size determination for that object is finished. I propose that the conceptual considerations of the term "size" and introspective evidence demonstrates that reaction time evidence does not provide conclusive evidence for a specific form of size information storage. A basic assumption of contemporary experiments on size estimation via imagery is that response times are due to time to retrieve information, rather than time to consider the meaning of a question. The supposition behind this is that the form of the data itself, the information structures themselves determine the time of the outcome of cognitive processes. In fact, the entire computational theory that Kosslyn seeks to support is very much slanted toward the supposition that we do not think about questions we only respond to them. This raises a special consideration in the analysis of size information retrieval. I contend the question "Which is larger?" is inherently ambiguous. This ambiguity in meaning is a feature Kosslyn and other cognitive psychologists appear to have completely overlooked. This ambiguity introduces a context- sensitive and interpretive element into their results that depends on the meaning of terms and our thinking about them rather than pure response-driven behavior. Some examples, using items from Paivio's list of common items for which the size is generally known by test subjects, will serve to illustrate the problem of conceptual ambiguity in size comparison tasks. 1. Which is larger, an ant or an iceberg? 2. Which is larger, a moose or a refrigerator? 3. Which is larger, a refrigerator or a piano? Most people will have no hesitation giving an answer to question 1, but questions 2 and 3 may cause a delay in responding. I suggest that one cause for delay can be conceptual confusion. What is meant when we are to compare the "size" of a moose and a refrigerator? Are we to judge the approximate size on the basis height alone, height plus length, or perhaps total approximate volume? A moose, facing us, would not be as wide as a refrigerator, but it would be deeper. Should we include antlers or not? Are we to average the sizes of the objects involved based on personal experience? Are we to assume that the piano is an upright? In the absence of specific instructions, there are many possible options the subject might consider before making some assumptions that will enable him to answer the question. Some assumptions considered might include ideas about what the test givers (experimenters) might expect as an answer. For example, a subject might think that his familiarity with stock phrases, such as "big as a moose" was being tested and that he therefore ought to answer in a particular way. Phenomenologically, I suggest that what happens is that suitable images of a moose and a refrigerator are available almost immediately and that the major portion of the delay in answering is caused not in accessing, as if perceptually, which is "really" a larger image, but trying to understand what is meant by the apparent insistence (implied by a yes or no question) that it makes sense to judge one larger than the other. The question requires the subject to provide a rationale for defining "larger" in this context. The rationale in the case of the ant/iceberg question is that there is no interpretation under which an ant is larger than an iceberg. This possibility simply does not exist in the English language, except perhaps in a poetic context. In the moose/refrigerator question, a rationale for the meaning of size must be adopted, e.g., not just area seen face on, but width plus length, or, perhaps, greatest diagonal. If we accept this phenomenologically-based explanation of why some questions about size take longer than others, the entire basis of the experimental data collected by psychologists on the phenomenon of size comparison is thrown into serious doubt. 5. Conclusion It is possible for a theory like Kosslyn's to allow for the conscious, thoughtful, adoption of assumptions in responding to questions of this type, but only at the cost of compromising any attempt to find meaningful results through response times. Suppose subjects consider a series of different ideas about what is meant by "size" as they make various judgments during the experiment. In this case only the average of various response times derived from various strategies will be measured. Suppose that after a few questions, each subject adopts one strategy for answering all the questions, but that subjects vary in their strategies. In this case, again, only the average time employ various strategies is measured. We saw that this was a possibility in the rotation experiments. The result of using a hypostatized average time to explain actual mental phenomena is that one supposes a mechanism that corresponds to no actual cases at all. In order to be able to isolate and measure the phenomenon in question, experimenters must assume that responses are due to the application of a specific strategy, identical in each case, and determined entirely by automatic mechanisms. In Kosslyn's theory, our answers are conditioned by the computational function that is triggered by the question posed to the subject during the experiment. The mechanisms involved in the triggering response to the question are presumed to be automatically delivered to consciousness. By analogy, we might say the answer to the question is "delivered" to consciousness, as a postman delivers a letter. We open the letter, read it, and therefore know the answer to the question. The only variable in this story is that sometimes we have difficulty opening the letter, so some information becomes evident to us at a slower rate. We have seen repeatedly that it is in the interest of experimental psychology to exclude from consideration the idea that an experiment might involve conceptual ambiguity or conformance of the subjects to implicit task demands. I conclude that in the case of size information tests, it has not been sufficiently demonstrated that the instructions are unambiguous. Therefore, reaction time data can not be a significant tool in revealing the nature of the underlying mechanism involved. We are now ready, hopefully, to entertain another possibility about the "kinds" of information encoded to in the brain and available to us. Perhaps the search to verify the existence of "pure" analog or discrete coding information is not a problem of experimental design. It may be that the lack of separation of the two supposedly distinct "kinds" is a feature of the information itself. The examination of the size information models has been instructive in this regard and has prepared us for additional evidence in the same vein.