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					Mental Imagery

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Mental Imagery Defined
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Different interpretations and definitions in many different fields (philosophy, psychology, cognitive science)  much controversy on what this is & if it even exists

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Folk definitions:
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“visualizing”, “seeing in the mind‟s eye”, “having a picture in one‟s head”, “imagining”, etc.

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Broad definition:
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A mental representation of a non-present object or event Quasi- perceptual conscious experience (note: quasi means “having some resemblance”)  experience that resembles perceptual experience, but which occurs in the absence of the appropriate stimuli for the relevant perception
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Philosophical/scientific definitions (Thomas, 2005):
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Historical Overview
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Philosophic period (pre-scientific)
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Important topic in classical philosophy
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Many classical Greek philosophers believed mental imagery to be the foundation of human knowledge and the elements of thought
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Plato uses the metaphor of an inner artist painting pictures in the soul (Philebus 39c) Aristotle states "The soul never thinks without a mental image" (De Anima 431a 15-20). Thomas (of CSU): Aristotle as the first cognitive theorist with mental images holding the central role-- images play something very like the role played by the more generic notion of "mental representation" in modern cognitive science mental images = thought.  Almost universally accepted in the philosophical tradition, even by non-Aristoteleans, up until the 20th century. With certain exceptions (most notably Descartes), the "ideas" that played such a large role in philosophy and cognitive theory from the 17th through the 19th century are direct descendants of Aristotle's mental images (notable philosopher: John Locke, George Berkley & David Hume).

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Also still important topic modern philosophy
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However, like in psychology, philosophical focus in early 20th century shifted to analysis of language and mental imagery not considered as central as once was believed
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Historical Overview
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Measurement period (late 19th century)
Early psychology focused on mentalism following philosophical tradition equated mental imagery to “ideas”  Wundt (late 1870’s)– theoretical system and experimental method for the study of thought (including ideas aka mental images as crucial)  Galton (1880-1907)– conducted quantitative assessments  Having subjects report on their visual images, created a pioneering measure of imagery vividness  James (1890)– wrote/theorized about mental imagery  Külp (1901)– conducted research that challenged Wundt’s assuptions– introspection findings led to "imageless thoughts― results (conscious contents without any sensory or perceptual quality). ("Thinking in words" is plausibly regarded as a form of auditory or vocal-kinaesthetic imagery (Paivio, 1971).)  Titchener (1909)-- counter’s Külp’s findings reworked Wundt’s introspection method, theories= mental content is mental imagery, experiments like having subjects rate ability to visualize an object (apple, sunset, etc.)
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Historical Overview
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Behaviorism (early 20th century)
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Bitter and irresolvable ―imageless thought‖ controversy between Külp and Titchener findings fueled behaviorist movement- introspective methods (the critical methodology of early experimentation on mental imagery) became discredited amongst the majority of experimental psychologists denounced as not valid or scientifically sound Led to the argument of mental imagery as a non-psychological reality not only scientifically study-able but non-existent
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Watson preached iconophobia = skepticism about/ disbelief of mental imagery

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Those still using introspection change focus away from imagery to studying values & motives Leader studying eidetic memory (Jaensch) connected to Nazi Germany Freud
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Regarded visual images as part of his patients neuroses that could be cured with ―rational‖ insights
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Mental imagery research out of favor from 1920‟s- 60‟s (although some was done)

Historical Overview
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Cognitive/Neurocognitive period (1960‟s- present)  Cognitive revolution spurs interest in internal representations, including mental imagery  Some pre-cursors of the 1950‟s/early 60‟s
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Development of Electroencephalography (EEG) Discovery of REM sleep Finding that direct stimulation of certain brain areas results in vivid images (Penfield, 1958) Applied psychology research on sensory deprivation and hallucinogenic drugs (1950 & 60‟s) Growing interest in 1960‟s in application of imagery-based techniques in psychotherapy (“guided imagery”) and psychosomatic medicine
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Historical Overview
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Cognitive/Neurocognitive period (1960‟s- present)
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Interest in imagery research took off in the mid/late 1960‟s
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Major instigator = work on visual mnemonics
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Yates' (1966) historical work The Art of Memory on the significance of imagery mnemonics in Ancient to Renaissance periods Luria‟s case study of S.V. (extraordinary user of method of loci) was translated to English and became well-known Paivio starts major research in mnemonic effects of research in early 60‟s and is know as the established theorist/leader in the field by the end of the decade  Two principle effects established: *Subjects who follow explicit instructions to use imagery-based mnemonics to remember verbal material had better recall * Paivio & others claim findings that imagery plays large implicit role in certain verbal memories (without directions to do visualize) “cat” has high imagery value whereas “truth” has low imagery value Concept of “Mental Representation” established as a vital psychological theory (Influential book of Neisser, 1967)  Led way to influential theorizing/research on imagery & memory in the 70-80s (Shepard, Kosslyn)
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Why the psychological interest in Mental Imagery today?
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Mental Images believed to play major role in memory and occurs in many cognitive tasks  As a LTM code-- as echoes, copies or reconstructions of actual perceptual experience  Involved in anticipating possible future experiences (crucial for survival)  Centrally involved in visio-spatial reasoning  Crucial to inventive and creative thought May help to understand other psychological phenomena:  hallucinations  daydreaming  dreaming May be useful to understanding how to elicit imagery during therapy
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“Some” modern agreement on Mental Imagery
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Mental imagery has an essential role in mental economy (Thomas, 2005)
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Imagery as real/scientifically interesting because it is an explanatory necessity  belief that results of experiments on cognitive functioning cannot be explained without the use of the storage/processing of imagery knowledge representations
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Explanations that rely on mental imagery are known to be true (based on research), therefore mental imagery exists

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Mental imagery has intentionality
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Images are OF something– in the sense of being of, about or directed at something (whether real or unreal) Plays a important role in conscious thought processes Distinguishable from superficially similar but non-intentional perceptual phenomena such as afterimages Although images come to mind unbidden or can‟t “shake” an image– most people, most of the time can voluntarily conjure up/manipulate a mental image (given some familiarity of object/event in question)

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Mental imagery is subject to “volume control”
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Dual Code Theory (Paivio)
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Dual Code Theory (Paivio, 1971)
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LTM

Theory states:  Mind operated on two distinct classes of mental representations (called ―codes‖) mental images and verbal representations  Memory is therefore two independent (but interacting) stores image memory and verbal memory
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CAT

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Word evokes associated image (either spontaneously or through deliberate effort) = 2 separate but linked memory traces put down (one in each store) so increases chance of retaining and recalling that memory Information stored in either or both (truth vs. cat) Copyright © Allyn & Bacon 2005

Dual Code Theory (Paivio)
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Three types of processing:
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(1) representational, the direct activation of verbal or non-verbal representations (2) referential, the activation of the verbal system by the nonverbal system or vice-versa (3) associative processing, the activation of representations within the same verbal or nonverbal system.

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A given task may require any or all of the 3 types of processing

Two different types of representational units: "imagens" for mental images and "logogens" for verbal entities-- described as being similar to "chunks". Logogens are organized in terms of associations and hierarchies while imagens are organized in terms of part-whole relationships.

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Dual Code Theory (Paivio)
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Psychological Support for Dual Code Theory
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This theory explains a lot of empirical psychological evidence, has “stood up” over the decades and is considered one of the most influential theories of the 20th century  Supports broad range of findings beyond original context of verbal learning: memory for pictures & comparisons of size, distance, etc, thinking styles, creative thinking, thinking in reading, writing, science, athletic performance enhancement through visualization. Strongest support from abundant research that has found the Selective Interference Effect:  People are unable to simultaneously do two mental tasks which call for manipulation in the same code (two verbal tasks or 2 visual/spatial tasks at the same time)
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Dual Code Theory (Paivio)
Selective Interference Effect (continued)  Subjects do measurably poorly (slower and/or with more errors) than when doing either task with a task in the other code (a verbal task and a visual/spatial task at the same time)  Findings interpreted as– 2 tasks that use the same code interfere strongly with each other because they call upon the same representation and processing resources (not the case when using different codes– argues that there then are different codes!)

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Neuroscientific Support for Dual Code Theory
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Neurologically damaged patients show that left hemisphere impairment impacts verbal memory; right hemisphere impairment impacts visual information

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Common vs. Dual Code Debate
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Common Codes:
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Before 20th Century (Philosophically/early psychology): single common code =imagery in the form of pictures in the mind
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Picture theory: Argument that imagery is the prime vehicle of thought meaningfulness (semantics) of language as grounded in the mental picture Resemblance Theory: assumed that images represent their objects because they resemble them: an image of a bear, like a photograph of one, looks like a bear
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Captures analogous concrete and spatial information
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Common vs. Dual Code Debate
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By early 1960/70’s: single common code of knowledge = verbal = propositions
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Stance taken by some in 1960-70‟s that the meaningfulness (semantics) of images are grounded in the mental language challenged the concept of mental pictures all together, instead we “pretend” to ourselves to “see” mental things Main argument is that mental pictures cannot have intentionality themselves (Fodor, 1975)– what a image is of is indeterminate unless associated with a linguistic description  An image of a bear represents a bear not because it resembles a bear, but because our minds attach a “mentalese” caption to it saying “BEAR".  Mentalese: an innate, unconscious “language of thought” (Fodor, 1975) or descriptions in the natural language that the imager speaks (Kaufmann, 1980)
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Mentalese, not imagery, is the fundamental form of representation (common code) and the source of intentionality Pylyshyn (1973)-- imagery consists of mentalese also grounds the intentionality of imagery in that of mentalese as the common code.

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More common in the psychological field is to speak of propositional representations (rather than “mentalese”) as the common code
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Common vs. Dual Code Debate
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Although substantially support for Dual Code Theory– has not gained universal acceptance
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Particularly because Dual Code Theory does not match well with models of the mind understood based on computers which is a major force in cognitive psychology

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Also, theory neglects other senses– Flanagan (1984) suggests a Six-Code Theory (rather than dual)– where is the olfactory imagery code?
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Calls into question whether the sight and smell of a rose we imagine is a single, integrated imaginative experience or separate, associated visual and olfactory images Calls into question how connected imagery is to sensory channels & related perception theories
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3 Arguments on the Nature of Mental Imagery
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Picture Theory (Resemblance theory)  Traditional (historical) conception of Mental Imagery  Actual picture-like representations in the head inner pictures  Often related today to analog coding (computer’s 1’s & 0’s) Description Theory/ Conceptual-Propositional Hypothesis  Internal representation is a (verbal) description of the stimulus in the form of propositional coding Functional-Equivalency Hypothesis
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Imagined information is represented and processes in the same ways that perceptual information is represented and processed  Inner representations of any sort that give rise to quasi-perceptual conscious experience  Embodied as brain states where imagery and perception are highly similar
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Analog vs. Propositions Debate (picture vs. description)
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Arose in the 1970‟s and still going today This debate concerns the nature of imagery itself  Main issue: what is the underlying nature of imagery? Often entangled with common vs. dual code debate but that is concerned with the functional role of imagery in the cognitive processes of memory and thought)

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Analog vs. Propositions Debate (picture vs. description)
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That images are not literally pictures:  Form a vivid image of the front of North Hall.  How many windows are there? How many doors?
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Mental image tells us that there are windows and doors on the front of North Hall, it does not tell us how many. Makes mental images seem like propositions
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a propositional representation could tell us that there are windows and doors without telling us how many, but a picture would have to contain information about how many.

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However, if asked about peripheral visual details, usually not stored directly in propositional form but the details can be remembered by visualizing the scene and "re-looking" at it to see the visual details that were not noticed before (as if actually revisiting the scene).  For example, when asked the following questions about the TV show American Idol, most people who have seen the show will answer by visualizing and re-looking:
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Can the performers sing behind the judges? Is Ryan taller than Simon? On the other hand, questions like the following seem more like directly remembering propositions: What kind of shirt does Simon usually wear? Where does Paula sit?
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Analog vs. Propositions Debate (picture vs. description)
Description Argument
Images behave like propositions, so images are a kind of propositional network (using spatial and visual relations like next-to and on-top-of) Description Theory: The view that imagery consists of
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descriptions encoded in a language-like representation format Pylyshyn (1973)-- The underlying representational reality of imagery (and of actual perceptual experience) is not picturelike, but rather a detailed mentalese description of a scene

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Conceptual Propositional Hypothesis
Store interpretations of events (whether visual or verbal) rather than imaginal components Form of storage is as abstract propositions (a descriptive "sentence" of mentalese )about objects and their relationships
Prominent Researchers: Pylyshyn, Bower, Anderson
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Analog vs. Propositions Debate (picture vs. description)
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Psychological evidence for Propositional Code:
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Extracting Parts of Mental Image (Reed, 1974)  decide whether or not a pattern was part of a previous stimulus that they would have to imagine to decide  subjects performed not above chance  Conclusion-- subjects must not be storing the image as a picture, but rather as a description Ambiguous / Reversible Figures (Chambers & Reisberg, 1985)  show picture briefly and ask subjects to form a mental image of it; only enough time to make one interpretation  Subjects were asked to give a second interpretation of the figure  no subjects could do this task  subjects asked to draw the mental image of what they saw  subjects able to make second interpretation only after they reproduced the drawing themselves  Suggests verbal interpretation of mental image  propositional code can dominate over analog code
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Analog vs. Propositions Debate (picture vs. description)
Picture Argument
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Evidence implies that imagery must be a distinct, non-language-like form of representation. Quasi-Pictoral Computational Theory (Kosslyn, 1980):
Based on an analogy with computer graphics. Computer graphics files store information in a compressed, non-pictorial form, but when displayed translated into a mathematical map (bitmap) on the computer monitor screen, that specifies the color at each pixel (tiny dot) on the screen itself. Kosslyn contends visual information may be stored in the brain as compact descriptions, but we experience an image only when this information is used to create a two dimensional map of visual space in a special, functionally defined memory area he calls the "visual buffer” (equates to Visual-Spatial Sketchpad area of Working Memory). The picture in Kosslyn's theory is merely "quasi", because there is no equivalent to the monitor screen to display it.
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What we experience as imagery, and what is available to the cognitive processes that use imagery, is the functional picture, the mathematical map, in the visual buffer.
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Prominent Researchers: Shepard and Metzler, Kosslyn

Analog vs. Propositions Debate (picture vs. description)
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For example, this theory would store the image of a house as a schema containing property propositions like:
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has-a (house, front) has-a (house, roof) has-a (house, windows) has-a (house, entrance) BUT, it would also have coordinate information in an house-image((3, 30), (4,40), ...)
these are polar coordinates which mean go out 3 units and rotate 30 degrees and activate that pixel, then go out 4 units and rotate 40 degrees then activate that pixel, etc.), which would address pixels (picture elements) in an array in the Visual-Spatial Sketchpad. Activating the addressed pixels would then sketch out the image for a house at a very rough or fuzzy level (this is why we can have fuzzy mental images). Then there are linked sub-images for roof, windows, and entrance which have more propositions and image coordinates. As these sub-images are retrieved and added to the sketch in Working Memory, the resolution of the image becomes sharper (we begin to lose the fuzziness). Thus, to turn our perception of a picture into a particular mental image involves breaking up the overall picture into meaningful pieces and noticing properties in the overall image and the sub-images (this is sort of like learning to interpret a painting in an art history course). If different sub-images are chosen, then the picture can yield different mental images -- i.e., different interpretations of the picture. Copyright © Allyn & Bacon 2005

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Analog vs. Propositions Debate (picture vs. description)
Analog Code internal representation is a copy of the external stimulus mental picture Propositional Code internal representation is a description of meaning of the concept verbal description

stored like a bitmap binary code in memory: 0011100 0100010 1000001 0100010 0011000

Stored as propositions in memory: Has a: circle at the top Has a: line comes straight down from bottom of circle Has: 2 lines sticking out in either directions from middle and of straight line

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Analog vs. Propositions Debate (picture vs. description)
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Psychological Evidence for Analog Code:
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Mental Rotation Studies (Shepard & Metzler) Image Scanning Studies (Kosslyn) Image size comparison Studies Neurological Evidence for two types of Imagery Cognitive Maps/ Navigation

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All support that mental images are functionally related to real-world objects
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Second-order isomorphism:  Imagery relationships in memory are the same as relationships between real-world objects  Objects not directly or structurally represented in our brain, but internal relationships work in a very similar way to external relationships

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Psychological Evidence for Analog code
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Mental Rotation
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Imagine a Capital letter T. Rotate it 90 degrees to the right. Put a triangle to the left of the figure, pointing to the right. Rotate the figure 90 degrees to the right. Which of these figures is the correct one?

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Psychological Evidence for Analog code
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Mental Rotation: A series of studies showed coding
could not be propositions because images can be transformed in continuous ways (go through intermediate states like movement in the real world does). Shepard and Metzler (1971) found that when shown a geometric figure and then another one that was either a rotated version of the first or the mirror image of a rotated version. The amount of time it took to judge that it was a rotated version varied linearly with the angle of rotation. This would only happen if the study participants visualized the object moving continuously through the intervening space until it either matched the last figure or didn‟t.

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Psychological Evidence for Analog code
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Image Scanning:
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Kosslyn, Ball & Reiser (1978): did several experiments to determine whether images act as functional representations which have real life spatial characteristics. Subjects were timed on how long it took them to scan a mental map. The results suggested that images do represent metric distance and that this property affects real-time processing of images. This implies that images also have spatial boundaries, and this was also tested, by seeing if subjects could image to the point of overflow. Subjects' reports indicated that there was a high correlation between the size of the imagined object and distance. It was also found that it took longer for subjects to see properties on subjectively smaller images. These results support the claim that our experienced images are spatial entities and their spatial properties have real consequences for some forms of information processing

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Psychological Evidence for Analog code
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Image Size Comparison:
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Moyer (1973) Subjects asked judge size in mental images Asked which is larger, a moose or a roach? Which is larger, a wolf or a lion? Research shows that when subjects have greater difficulty in judging the relative size of two pictures or mental images that are similar in size Kosslyn, 1975  Subjects asked to imagine different sized animals side by side.  A rabbit next to an elephant should be imagined smaller than a rabbit next to a fly.  Subjects asked about some detail of the animal (Does the rabbit have red eyes?)  Research shows subjects respond faster when the imagined animal is large than when it is small
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Psychological Evidence for Analog code
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Two Types of Imagery:
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Research suggests people are sensitive to spatial structure and size in their mental images
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Created interest in distinguishing spatial properties and visual attributes of mental images
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Spatial qualities can be attached to any modality (tactual, auditory) Certain visual experience (color) unique to visual modality

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WM- identified “where” pathway for processing spatial information and “what” pathway for processing object information
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Parietal regions support spatial aspects of imagery
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Activation of parietal during spatial rotation tasks Activation of temporal areas when people imagine object properties/details

Temporal lobes support visual aspects of imagery

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Research with brain damage patients show specific imagery deficits
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Patient with temporal damage– deficits in judging color, size and shapes but not mental rotation, image scanning, letter scanning
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Suggest spatial information can be represented irrespective of modality during imagery in the parietal region but separate temporal imagery system comes into play when processing distinctly visual information
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Synthesis: Mental Models
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Knowledge structures constructed to understand and explain experiences  The structure corresponds to the functional relations among entities as they would exist in the world  A simulation of events in the world, either real or imaginary Proposed are three types of mental representations  Propositional representations which are pieces of information resembling natural language
cat
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under

table

Mental models which are structural analogies of the world (any cat/table, prototype) Mental imagery which are perceptual models from a particular point of view (particular cat, table)

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Johnson-Laird

Are visual images like visual perception?
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Imagine a capital letter N. Connect a diagonal line from the top right corner to the bottom left corner. Now rotate the figure 90 degrees to the right. What do you see? Imagine a capital letter D. Rotate the figure 90 degrees to the left. Now place a capital letter J at the bottom. What do you see?
Finke et al. 1989

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This task illustrates an important function of mental imagery
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the ability to construct new objects in the mind and inspect them The ability to make judgments about imagined objects and come to the same conclusions as if they had been actually seen

Subjects shown figure b, asked to imagine lines so form mental image like figure a, then asked to judge line length– produced classic Ponzo illusion results
(a) (b) Wallace, 1984
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Are visual images like visual perception?
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Functional-Equivalency Hypothesis: Imagined information is represented and processes in the same ways that perceptual information is represented and processed  Strong neuroscientific evidence:
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“similar mechanisms in the visual system are activated when objects or events are imagined as when they are the same objects or events are actively perceived” (Finke, 1989, p. 41)
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Roland & Friberg (1985) rCBF (regional cerebral blood flow) indicated the same areas of the brain are active when we see vs. „image‟ an object – examined 3 tasks: mental arithmetic, memory scanning for auditory stimulus and visualizing– found different brain areas activated for each task and specifically occipital lobe and temporal areas important for visual and memory processing Goldenberg et al. (1990) Using Pet scans, asked participants questions that did/did not require imagery– found activation of occipital, posterior parietal and temporal visual processing areas for questions requiring imagery use (other questions did not activate those areas)
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Are visual images like visual perception?
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Strong neuroscientific evidence for Functional-Equivalency Hypothesis:  Using PET scans, Kosslyn et al. (1993; 1995) showed that when subjects perform visual imagery tasks, the occipital visual cortex is activated, analogous to how it activated when objects are physically present (also interesting to note that this activation is GREATER with imagery tasks than with perception of physical stimulus -- greater effort??)  Kosslyn et al. (1993; 1995) also found that with a mental imagery task in which subjects had to imagine small versus large letters, in the small condition the visual cortex was activated in a more posterior region closer to where the center of the visual field is (topographically) represented in the visual cortex ... makes sense because a small visual image would be more concentrated at the center of one‟s visual field than a larger image  O‟Craven & Kanwisher (2000) – when subjects either viewed or imagined faces and scenes– particular areas for location and faces in temporal area similarly activated
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Are visual images like visual perception?
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From previous studies and many more, several conclusions can be made:  Visual imaginal tasks and vision seem to be situated in similar locations in the brain  Visual imaginal tasks, which require associative knowledge, seem to activate regions of the brain affiliated with memory and vision  Because of their top-down nature, imaginal tasks may require more energy to process than perceptual tasks, which may be initially bottom-up  The use of neurological measures may offer support/ new directions for research in mental imagery
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Cognitive Maps
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Draw NYC

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Cognitive Maps
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Imaginal representation of the external environments  From the early work of Tolman in the 1930‟s on rats in mazes  Mental imagery considered to be crucial to working and moving about in the environment Three types of knowledge
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Landmark knowledge
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Information about particular features based on images and propositios Specific pathways used to get from one location to another
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Route Knowledge
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“Straight until light, turn left, go two blocks, turn right”

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Survey Knowledge
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Global relationships between environmental cues– a spatial image of the environment

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Thorndyke & Hayes-Roth (1982)-- With experience, route-map representations of our environment evolve into survey-map representations Copyright © Allyn & Bacon 2005

Cognitive Maps
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Which city is further west- Los Angeles or Reno? What is the first major country directly south of Detroit, Michigan? Tversky (1981); Tversky & Taylor (1992)
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Distortions of memory for geographic locations occur because people use propositional strategies to remember geographic information Geographic information is structured in memory in terms of abstract generalizations rather than specific images

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Cognitive Maps
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Geocentrism  You are the center of your world Draw a map — get insight on the representation of that knowledge and imagery in the mind. Saarinen (1987)- 4,000 subjects from 49 countries drew maps the majority showing a Eurocentric worldview Subjects did not draw their countries disproportionately larger Prominent countries (US, Russia, England, France, etc.) on most maps Africa generally under-represented Americans did poorly, subjects from Hungary and Russia had the most details

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Cognitive Maps
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Neuroscience:
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Recordings from rats shows hippocampus important for maintaining cognitive maps (implanted electrodes in hippocampus recorded responses in neurons only when rat entered an arm of the maze it had previously entered) Size of hippocampal structures have been related to spatial ability Brain imaging studies show when humans are navigating their environment, there is high hippocampal activation
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Cognitive Maps
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Neuroscience:
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Two different aspects of cognitive maps:
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Egocentric representation
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―you‖ rotate or translate your view

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Allocentric representation (map w/o specific point of view) and object-based spatial transformation
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Metally rotating an object or location (like flipping around a physical map)

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Different locations in the brain activate for each transformation Also, increase in reaction time for object-based spatial transformations rather than egocentric transformations
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Other uses for Imagery
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In addition to storing and retrieving images from memory, images have been shown to be used in a variety of cognitive tasks. For example, imagery is used to represent setting and layout information as part of understanding written and verbal language. Black, Turner, & Bower (1979) found that even when reading a minimal narrative like: John was working in the front yard. Then he went inside.
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people form a rough image that at least lays out the scene spatially and establishes a point of view, because a change in point of view provided by one word like: John was working in the front yard. Then he came inside.

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causes people to take longer to read the sentences and mis-remember them later as having a consistent point of view.

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Franklin & Tversky (1980) reported studies showing people forming complex 3-D images when reading narratives about events like going to an opera house Taylor & Tversky (1992) –subjects were equally fast at judging questions from route descriptions, survey descriptions and actual maps– concluded we can convert verbal descriptions into rich cognitive maps of our environment as effectively as from actual maps

Copyright © Allyn & Bacon 2005

Other uses for Imagery


Schwartz & Black (1996) showed that imagery can be used when reasoning about mechanisms-showed that adults can use animated image simulation to reason about what happens when two gears are rotated with their teeth intermeshed. Hachey (2005) showed that 1-4th graders also use imagery to solve these types of problems! This reasoning yields the same linear function of response times and angles of rotation that we discussed earlier in the mental rotation of single objects.
Copyright © Allyn & Bacon 2005


				
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Maria  Brioso Maria Brioso
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