Second-order isomorphism of internal representations: Shapes of states

Shepard, Roger N.; Chipman, Susan F.

doi:10.1016/0010-0285(70)90002-2

Cited by 545 publications

(249 citation statements)

References 14 publications

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“…In mathematics, descriptions of two systems which differ only by irrelevant elements but leave the relevant well-defined functional structure invariant are called isomorphic [32]. This structural isomorphism is referred to as second-order resemblance [463,464]. In second-order resemblance, the requirement that representing vehicles share physical properties with their represented objects can be relaxed in favor of one in which the functional relations among a system of representing vehicles mirror the functional relations among their objects [465].…”

Section: Integration Of Space-time Of Brain and Mind Through Unified mentioning

confidence: 99%

Natural world physical, brain operational, and mind phenomenal space–time

Fingelkurts

Neves

2010

Physics of Life Reviews

166

233

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Concepts of space and time are widely developed in physics. However, there is a considerable lack of biologically plausible theoretical frameworks that can demonstrate how space and time dimensions are implemented in the activity of the most complex life-system -the brain with a mind. Brain activity is organized both temporally and spatially, thus representing space-time in the brain. Critical analysis of recent research on the space-time organization of the brain's activity pointed to the existence of so-called operational space-time in the brain. This space-time is limited to the execution of brain operations of differing complexity. During each such brain operation a particular short-term spatio-temporal pattern of integrated activity of different brain areas emerges within related operational space-time. At the same time, to have a fully functional human brain one needs to have a subjective mental experience. Current research on the subjective mental experience offers detailed analysis of space-time organization of the mind. According to this research, subjective mental experience (subjective virtual world) has definitive spatial and temporal properties similar to many physical phenomena. Based on systematic review of the propositions and tenets of brain and mind space-time descriptions, our aim in this review essay is to explore the relations between the two. To be precise, we would like to discuss the hypothesis that via the brain operational space-time the mind subjective space-time is connected to otherwise distant physical space-time reality.Key words: spatial, temporal, consciousness, cognition, operation, architectonics, EEG, field, metastability, physics, coordinative dynamics, self-organization, cortex.

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Section: Integration Of Space-time Of Brain and Mind Through Unified mentioning

confidence: 99%

Natural world physical, brain operational, and mind phenomenal space–time

Fingelkurts

Neves

2010

Physics of Life Reviews

166

233

View full text Add to dashboard Cite

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“…A nonarbitrary approach is needed for learning about phonetically relevant optical descriptors. Shepard and Chipman (1970) considered the problem of establishing the isomorphism between physical stimuli and internal (perceptual) representations. They noted that internal representations are unlikely to be structurally isomorphic with stimuli, in the sense that the internal representation of a square is not likely to be square.…”

Section: Physical Signals and Speech Perceptionmentioning

confidence: 99%

“…The same is likely true for visual phonetic perception. Shepard and Chipman (1970) argued for the validity of second-order isomorphism when knowledge about the descriptors of a first-order isomorphism is not available. They also noted that physical properties of a stimulus could be internally represented with different weightings but that the overall similarity of objects has functional significance to organisms.…”

Section: Physical Signals and Speech Perceptionmentioning

confidence: 99%

Similarity structure in visual speech perception and optical phonetic signals

Jiang

Auer

Alwan

et al. 2007

Perception & Psychophysics

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A complete understanding of visual phonetic perception (lipreading) requires linking perceptual effects to physical stimulus properties. However, the talking face is a highly complex stimulus, affording innumerable possible physical measurements. In the search for isomorphism between stimulus properties and phonetic effects, second-order isomorphism was examined between the perceptual similarities of video-recorded perceptually identified speech syllables and the physical similarities among the stimuli. Four talkers produced the stimulus syllables comprising 23 initial consonants followed by one of three vowels. Six normal-hearing participants identified the syllables in a visual-only condition. Perceptual stimulus dissimilarity was quantified using the Euclidean distances between stimuli in perceptual spaces obtained via multidimensional scaling. Physical stimulus dissimilarity was quantified using face points recorded in three dimensions by an optical motion capture system. The variance accounted for in the relationship between the perceptual and the physical dissimilarities was evaluated using both the raw dissimilarities and the weighted dissimilarities. With weighting and the full set of 3-D optical data, the variance accounted for ranged between 46% and 66% across talkers and between 49% and 64% across vowels. The robust second-order relationship between the sparse 3-D point representation of visible speech and the perceptual effects suggests that the 3-D point representation is a viable basis for controlled studies of first-order relationships between visual phonetic perception and physical stimulus attributes.

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“…As Shepard (1975) and Shepard and Chipman (1970) have effectively argued, it is not quite clear what is implied by such a "firstorder" isomorphism. The research strategy that we have adopted here to extend our earlier work (Jonides & Baum, Note I) draws on the concept of a "secondorder" isomorphism.…”

Section: S/lmentioning

confidence: 99%