-- Go to Jeffrey Scott Longstaff home page -- | |||
Longstaff, J. S. (1996). Cognitive structures of kinesthetic space; Reevaluating Rudolf Labans choreutics in the context of spatial cognition and motor control. Ph.D. Thesis. London: City University, Laban Centre. (HTML Edition) |
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INDEX -- CONTENTS -- REFERENCES -- |
Contents |
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I. INTRODUCTION |
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I.10 Brief Historical Review of the Work of Rudolf Laban. |
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.21 Components of Labans Study of Movement. |
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I.30 Summary and Conclusions of the Research. |
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.31 The Realm of Choreutic Study. |
II. KINESTHETIC SPATIAL COGNITION: DEFINITIONS. |
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IIA. Kinesthesia. |
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IIA.10 Variety of Terminology and Working Definitions. |
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.11 Variety of Terms. |
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IIA.20 Types of Kinesthetic Raw Data. |
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.21 Muscular Receptors. |
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IIA.30 Deriving Kinesthetic Perceptions. |
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.31 Sense of Balance and Equilibrium. |
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IIA.40 Conclusions: Kinesthesia. |
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IIB. Kinesthetic Space. |
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IIB.10 Factor Spaces. |
44 |
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.21 Physical Space, Environmental Space, External Space. |
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IIB.30 Perceptual-Motor Spaces. |
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.31 Sensory-Perceptual-Motor Space; Spatial Fields. |
47 |
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IIB.40 Motor Spaces. |
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.41 Motor Space. |
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IIB.50 Mentally Represented Space. |
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.51 Imaginal Space, Conceptual Space, Represented Space. |
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IIB.60 Conclusion: Kinesthetic Space. |
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IIC. Kinesthetic Spatial Cognition. |
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IIC.10 Spatial Cognition versus Verbal Cognition. |
58 59 |
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.31 Spatial Cognition. |
59 65 67 68 69 |
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IIC.40 Conclusions: Kinesthetic Spatial Cognition. |
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IIIA. Systems of Reference. |
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IIIA.10 Egocentric vs Exocentric Reference Systems in Psychology |
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.11 General Distinctions. |
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IIIA.20 Labanotation and Choreutic Reference Systems. |
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.21 Constant Cross of Axes Reference System. |
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IIIA.30 Conclusions: Reference Systems. |
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IIIB. Location Code. |
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IIIB.10 Spatial Positioning Tasks. |
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.11 Location versus Distance Recall. |
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IIIB.20 Mass-spring Model for Motor Control. |
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.21 Mass-spring System. |
96 97 |
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IIIB.30 Trajectory Formation. |
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.31 Path Segments, Curvature Peaks. |
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IIIB.40 Choreutic Peaks and Phases. IIIB.50 Location Code in other Motor Tasks. |
103 |
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.51 Motor Control of Handwriting. |
105 |
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IIIB.60 Coordinative Structures; Muscle Collectives; Kinematic Chains. |
112 |
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.71 Automatic Processing of Location Information. |
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IIIB.80 Conclusions: Location Code. |
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IIIC. Map-like Images of Spatial Knowledge. |
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IIIC.10 Cognitive Maps. |
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.11 Equiavailable, Path Free, Spatial Knowledge. .12 Locations, Landmarks, Reference Points. .13 Hierarchy of Map-like Spaces. |
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IIIC.20 Kinespheric Image as a Map, Grid, Net, Scaffolding, etc. IIIC.30 Cognitive Structures of the Kinespheric Net. |
126 |
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.31 Cartesian Coordinates and Planes. |
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.34a Octahedron and cubic nets. |
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IIIC.40 Conclusions: Map-like Images. |
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IIID. Symmetrical Transformations. |
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IIID.10 Necessity of Symmetrical Transformations. |
136 |
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.21 Body Transfer. |
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IIID.30 Specifying Symmetry Operations in Cognition Research. IIID.40 Explicit Studies of Symmetry in Dance. IIID.50 Symmetry within Choreutics. IIID.60 Proposed Notation Symbols for Symmetrical Transformations. IIID.70 Conclusions: Symmetrical Transformations. |
154 156 159 162 |
IV. REEVALUATING CHOREUTICS. |
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IVA. Prototype / Deflection Hypothesis. |
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IVA.10 Directions and Direction-Symbols. |
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.11 Directional Lines versus Directional Points. |
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IVA.20 Directions as Conceived in Choreutics. |
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.21 Undifferentiated Spherical Conception of Space. |
169 |
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.22a Three Dimensions. |
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.23 Diagonals. |
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.23a Pure diagonal directions. |
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.24 Diameters, Primary Deflections. |
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.24a Primary deflections, Square Cartesian planes. |
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.25 Inclinations, Secondary and Tertiary Deflections. |
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.25a Flat, steep, and suspended inclinations. |
IVA.30 Prototype (Schema) Theory in Psychology. |
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.31 General Statements. |
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.32a Prototypes perceived and recalled fastest. |
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IVA.40 Prototype / Deflection Hypothesis in Choreutics. |
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.41 General Statements. |
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IVA.50 Prototypical Angles and Orientations in Spatial Cognition |
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.51 Prototypes in Language. |
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IVA.60 Prototypes and Deflections in Ballet. |
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.61 Ballet Facing. |
IVA.70 Anatomical Constraints. |
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.71 Choreutic Deflections from Anatomical Constraints. |
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IVA.80 Choreutic Organic Deflections. |
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.81 Deflected Ballet Foot Positions. |
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IVA.90 Ergonomic Shape of the Workspace. IVA.100 Conclusions: Prototype / Deflection Hypothesis. IVA.110 Experiment: Probing for Kinespheric Reference Points. |
219 220 |
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.111 Reference Points. |
IVB. Categories of Kinespheric Form. |
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IVB.10 Introduction. |
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.11 The Need for Kinespheric Categories in Psychology. |
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IVB.20 Kinespheric Poses. |
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.21 Pin-, Wall-, Ball-, and Screw-shaped Poses. |
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IVB.30 Kinespheric Paths |
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.31 Generalised Inwards / Outwards Movement. |
249 |
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.33a Zones and Super-zones of the Limbs. |
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.34 Kinespheric Paths as Topological. .35 Method for Deriving a Taxonomy of Kinespheric Paths. |
261 |
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IVB.40 Conclusions: Categories of Kinespheric Form. |
265 |
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.51 Clustering and Subjective Organisation |
V. SUMMARY AND CONCLUSIONS. |
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Appendix I. |
Research Proposal and Transfer of Registration to Ph.D. |
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Appendix II. |
Kinesthesia. |
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Appendix III. |
Spatial versus Verbal Cognition. |
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Appendix IV. |
Spatial Information Processing. |
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Appendix V. |
Varieties of Spatial Stimuli. |
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Appendix VI. |
Kinesthetic-Motor Mechanism in Spatial Adaptation. |
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Appendix VII. |
Coordinative Structures. |
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Terminology for Cartesian Planes and Dimensions |
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Appendix IX. |
Analysis of Vector Symbols as used in Choreographie. |
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Appendix X. |
Angles between Dimensions and Diameters. |
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Appendix XI |
Range of Articulation at Single Joints. |
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Appendix XII. |
Deflected Ballet. |
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Appendix XIII. |
Reference Points in Kinesthetic Space: Stimuli and Data. |
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Appendix XIV. |
Variability of Practice Hypothesis in Schema Theory. |
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Appendix XV. |
Virtual Forms. |
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Appendix XVI |
Method for Deriving a Taxonomy of Kinespheric Paths. |
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Appendix. XVII. |
Subjective Organisation in Kinesthetic Recall: Raw Data. |
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Reference List. |
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Volume One |
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IIB-1. |
Joint space as a graph of joint angles. |
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IIIA-1. |
Labanotation symbols for reference systems. |
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IIIA-2. |
Labanotation for standard cross of axes with divided front. |
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IIIA-3. |
Labanotation for body cross of axes with divided front. |
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IIIB-1. |
Biceps as a spring supporting the mass of the forearm. |
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IIIB-2. |
Planar positioning apparatus. |
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IIIB-3. |
Deriving a curved path from a polygonal representation. |
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IIIB-4. |
Relative timing of four motors in mechanical handwriting. |
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IIIC-1. |
Tolmans rat maze. |
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IIIC-2. |
Four point path followed with arm movements or walking. |
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IIIC-3. |
Proportions of the human figure (Leonardo Da Vinci). |
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IIIC-4. |
Grid of proportions (Le Corbusier). |
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IIIC-5. |
Pentagonal body pose (Laban). |
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IIIC-6. |
Planar quadrangle network. |
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IIIC-7. |
Tetrahedral network. |
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IIIC-8. |
Octahedral net. |
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IIIC-9. |
Cubic net. |
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IIIC-10. |
Rectangle-shaped Cartesian Planes. |
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IIIC-11. |
Linked corners of Cartesian planes builds an icosahedral net. |
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IIIC-12. |
Higher-order octahedral and lower-order tetrahedral nets. |
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IIID-1. |
Translatory symmetry. |
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IIID-2. |
Reflection symmetry. |
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IIID-3. |
Rotational symmetry. |
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IIID-4. |
Labanotation symbols for reflection symmetries. |
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IIID-5. |
Labanotation symbols for rotational symmetries. |
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IIID-6. |
Proposed symbol for an item. |
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IIID-7. |
Proposed general symbol for symmetry. |
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IIID-8. |
Proposed symbols for symmetry transformations. |
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IIID-9. |
Notation for body transference. |
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IIID-10. |
Notation symbols for specific reflections. |
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IIID-11. |
Notation symbols for specific size scaling. |
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IIID-12. |
Notation symbols for rotational transformations. |
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IIID-13. |
Symmetry notation for en croix.. |
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IIID-14. |
Symmetry notation for transfer from the hand to the leg. |
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IIID-15. |
Symmetry within the A-scale. |
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IVA-1. |
Three levels. |
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IVA-2. |
Shapes of symbols for nine directions in each level. |
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IVA-3. |
Direction symbols. |
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IVA-4. |
Dots as motion between two directional points. |
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IVA-5. |
Vector symbols. |
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IVA-6. |
Free inclination symbols. |
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IVA-7. |
Direction of the progression symbols. |
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IVA-8. |
Notation for . . . approaching a particular point. |
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IVA-9. |
End-points of the dimensional cross form an octahedron. |
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IVA-10. |
End-points of the diagonal cross form a cube. |
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IVA-11. |
Square plane, edge ratio 1:1. |
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IVA-12. |
Rectangular plane, edge ratio ‰1.618:1. |
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IVA-13. |
End-points of primary deflected diameters form a cuboctahedron. |
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IVA-14, |
Cuboctahedron derived by joining the cubic edge mid-points. |
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IVA-15. |
End-points of modified diameters form an icosahedron. |
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IVA-16. |
Personal square for orientation of body facing. |
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IVA-17. |
Dimensional reference lines in ballet theory of design. |
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IVA-18. |
Shape of the normal working area in the horizontal plane. |
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IVA-19. |
Horizontal, frontal, and paramedial kinetospheric cross-sections. |
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IVB-1. |
Higher-order pose configurations. |
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IVB-2. |
Higher-order curved pose . . . |
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IVB-3. |
Feuillets pathways: straight, open, round, waving, and beaten. |
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IVB-4. |
Hierarchical path-form taxonomy (Preston-Dunlop, 1980). |
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IVB-5. |
Hierarchical path-form taxonomy (Eshkol and Wachmann, 1958). |
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IVB-6. |
Seven-link movable chain. |
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IVB-7. |
Overhand knot. |
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IVB-8. |
Three-part knot. |
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IVB-9. |
Icosahedral planar sequence as 9-part plastic knot. |
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IVB-10. |
Dimensional sequence as 6-part knot. |
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IVB-11. |
Forms and orientations of the sixteen kinespheric-items. |
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IVB-12. |
Relationship between . . . intertrial repetitions. |
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Volume One |
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Table IV-1. |
Examples of dimensional notations. |
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Table IV-2. |
Examples of diagonal notations. |
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Table IV-3. |
Modified diameter end-points. |
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Table IV-4. |
Notations of cuboctahedral diameters. |
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Table IV-5. |
Symbols for cuboctahedral and icosahedral diameters. |
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Table IV-6. |
Notations of icosahedral diameters. |
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Table IV-7. |
Secondary deflections (cuboctahedral inclinations). |
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Table IV-8. |
Tertiary deflections, (icosahedral inclinations). |
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Table IV-9. |
Steep deflections of diagonal up-right-forward. |
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Table IV-10. |
Six test-pairs which approached significance. |
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Table IV-11. |
Performance measures. |
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Table IV-12. |
Frequency of occurrence for each of the strongest S-units. |
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Table IV-13. |
Kinespheric item orientation and number of F-unit occurrences. |
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Volume Two |
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APX.V-1. |
Example of Brooks matrix. |
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APX.VI-1. |
Pointing . . . with and without prism-glasses. |
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APX.IX-1. |
Axis scales (Laban, 1926). |
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APX.IX-2. |
Scales combined from primary-directions in four diagonals. |
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APX.IX-3. |
Scales combined from primary-directions in four diagonals. |
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APX.IX-4. |
Scales combined from primary-directions in four diagonals. |
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APX.IX-5. |
Augmented three-rings. |
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APX.IX-6. |
Trial notation, pure dimensions. |
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APX.IX-7. |
Scales assembled from short peripheral directions. |
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APX.IX-8. |
Scales assembled from short peripheral directions. |
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APX.IX-9. |
Vector symbols translated . . . |
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APX.X-1. |
Shapes of Cartesian planes. |
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APX.X-2. |
Constructing the golden rectangle. |
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APX.X-3. |
Golden rectangle plus a second square. |
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APX.X-4. |
Dodecahedral rectangular plane. |
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APX.X-5. |
Exact angles between dimensions and cubic diameters. |
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APX.X-6. |
Exact angles between dimensions and octahedral diameters. |
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APX.X-7. |
Interpenetrating cubic and octahedral planes. |
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APX.X-8. |
Angles between dimensions and dodecahedral diameters. |
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APX.X-9. |
Angles between dimensions and icosahedral diameters. |
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APX.XII-1. |
Passé. |
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APX.XII-2. |
Développé á la quartiéme devant. |
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APX.XII-3. |
Renversé (first half). |
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APX.XV-1. |
Free-body diagram. |
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APX.XV-2. |
Tetrahedral molecular structure of water. |
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APX.XV-3. |
Octahedral arrangement of electron paths in a neon atom. |
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APX.XV-4. |
Circle packing. |
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APX.XV-5. |
Four spheres pack into a tetrahedron. |
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APX.XV-6. |
Exterior perceived tension translated into muscular tension. |
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Volume Two |
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Table A. |
Reversal. | 166 |
Table B. | Direction change. | 166 |
Table C. | Direction change with a reversal | 167 |
Table D. | Three-phasic cycle. | 168 |
Table E. | Four-phasic cycle. | 168 |
Table F. | Hip circumduction. | 168 |
Table G. | One cycle of elbow-centred spiral. | 169 |
Table H. | One cycle of shoulder-centred spiral. | 169 |
Table I. | Elbow and shoulder wave. | 169 |
Table J. | Elbow and shoulder wave variation. | 169 |
Table K. | Hip wave with rotation reversal. | 170 |
Table L. | Multi-joint wave with rotary pronate/supinate reversal. | 170 |
Table M. | Hip figure-8 with rotation reversal. | 170 |
Table N. | Multi-joint figure-8 with rotary pronate/supinate. | 170 |
Table O. | Wrist-forearm figure-8. | 171 |
Table P. | Eight-phase continual-cycle figure-8. | 171 |
Table Q. | Continual-cycle figure-8 merged into four phases. | 172 |
Special thanks to Dr. Valerie Preston-Dunlop for her endless hours of discussion, personal experience and vision of choreutics, and her tireless reading of the rough drafts of this thesis. My participation in her recreation of Labans early German dances and her choreutics classes gave inner depth to this thesis. Without her constant and good humored support this research would never have come to completion.
Also thanks to many others for their inestimable assistance. Thanks to Dr. Linda Pring for discussions about the psychological components of this thesis and help with statistics. Thanks to Peter Bassett for making the special collections and equipment available within the Laban Library. Thanks to Michael Lovitt for navigating me through myriad academic regulations. And thanks to Jean Jarrell and Walli Meier for many supportive personal conversations.
Finally, greatest appreciation is given to Dr. Marion North and her opening of the resources of the Laban Centre for Movement and Dance without which this thesis could never have become a reality.
And deepest affection for Sarah, Gundela, Sigred, Stuart, Chandri, Evamaria, Kim, Jen, Angela, Cathy, and Aubergine.
I grant powers of discretion to the University Librarian to allow this thesis to be copied in whole or in part without further reference to me. This permission covers only single copies made for study purposes, subject to normal conditions of acknowledgement.
The choreutic conception of the spatial aspect of body movements (originated by Rudolf Laban) was reevaluated according to cognitive and motor control research.
Kinesthetic spatial cognition (analogous to visual spatial cognition) was identified as the psychological realm of choreutic knowledge. Kinesthesia was identified as arising from sensory receptors throughout the body. Kinesthetic space was defined as spatial information derived from kinesthesia. Kinesthetic spatial cognition was defined as cognitive processes (eg. mental rehearsal) involving kinesthetic spatial knowledge. This concept of kinesthetic spatial cognition has not been heretofore explicitly developed in cognitive science.
Elements of the choreutic conception were psychologically validated since they are also well identified in cognitive and motor research. These include how spatial information is defined relative to a reference system; kinesthetic spatial knowledge is based on a mental code of elemental locations; higher-order networks of locations are collected into map-like spatial images; and many symmetrical operations can be performed. Close similarities were identified between choreutic polyhedral-shaped cognitive maps of the kinesphere and the trajectory formation model.
A choreutic prototype/deflection hypothesis posits that dimensions and diagonals serve as conceptual prototypes while actual body movement consists of deflections. Similar spatial prototypes were identified in visual spatial cognition, a kinesiological analysis supported the bodily tendency towards deflections, and this concurred with ergonomic measurements of the shape of the workspace. An experiment attempted to identify prototypes in kinesthetic spatial cognition.
Categories of kinesthetic spatial information are distinguished within choreutics and dance. These were reevaluated according to perceptual processes and kinesiology. Choreutic topological forms deflecting across various kinespheric nets are analogous to N. Bernsteins conception of the co-ordinational net of the motor field . . . as oscillating like a cobweb in the wind. An experiment demonstrated that kinesthetic spatial information is organised into cognitive categories and that choreutic material and Labanotation symbols can be advantageously used in experimental research.
The Labanotation* direction symbols are used within this thesis. They refer to spatial directions as listed here. For further details see Hutchinson (1970), Hutchinson-Guest (1983), Knust (1979a; 1979b), Laban (1975b), and Preston-Dunlop (1969). The direction symbols are also discussed in Section IVA of this thesis.
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* Laban originally named this system of movement notation kinetography (Knust, 1948a, p. 28), literally movement-writing. Other systems of dance/movement notation or kinetography have also been developed (for a review see Hutchinson-Guest, 1989). In order to distinguish Labans system it has been referred to as Laban Kinetography (Knust, 1948a, 1948b), kinetography Laban (Preston-Dunlop, 1969), Laban Notation (Laban, 1948, p. 6), or as either kinetography Laban or Labanotation (Hutchinson, 1970; Knust, 1979a; 1979b). There are some differences between European Kinetography-Laban and American Labanotation, but these are not critical to this thesis. The term Labanotation is used here to refer generally to the overall system of body-movement-notation originated by R. Laban and of which the direction symbols are still at the core.