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Longstaff, J. S. (1996). Cognitive structures of kinesthetic space; Reevaluating Rudolf Laban’s choreutics in the context of spatial cognition and motor control. Ph.D. Thesis. London: City University, Laban Centre. (HTML Edition) 

INDEX  CONTENTS  REFERENCES  
Contents 


I.10 Brief Historical Review of the Work of Rudolf Laban. 


.21 Components of Laban’s Study of Movement. 

I.30 Summary and Conclusions of the Research. 


.31 The Realm of Choreutic Study. 
II. KINESTHETIC SPATIAL COGNITION: DEFINITIONS. 







.11 Directional Lines versus Directional Points. 

IVA.20 “Directions” as Conceived in Choreutics. 


.21 Undifferentiated Spherical Conception of Space. 
169 

.22a Three Dimensions. 

.23 Diagonals. 


.23a Pure diagonal directions. 

.24 Diameters, Primary Deflections. 


.24a Primary deflections, Square Cartesian planes. 

.25 Inclinations, Secondary and Tertiary Deflections. 


.25a Flat, steep, and suspended inclinations. 


.31 General Statements. 


.32a Prototypes perceived and recalled fastest. 

IVA.40 Prototype / Deflection Hypothesis in Choreutics. 


.41 General Statements. 

IVA.50 Prototypical Angles and Orientations in Spatial Cognition 


.51 Prototypes in Language. 

IVA.60 Prototypes and Deflections in Ballet. 


.61 Ballet Facing. 


.71 Choreutic Deflections from Anatomical Constraints. 

IVA.80 Choreutic Organic Deflections. 


.81 Deflected Ballet Foot Positions. 

IVA.90 Ergonomic Shape of the Workspace. IVA.100 Conclusions: Prototype / Deflection Hypothesis. IVA.110 Experiment: Probing for Kinespheric Reference Points. 
219 220 

.111 Reference Points. 
IVB. Categories of Kinespheric Form. 




.11 The Need for Kinespheric Categories in Psychology. 

IVB.20 Kinespheric Poses. 


.21 Pin, Wall, Ball, and Screwshaped Poses. 

IVB.30 Kinespheric Paths 


.31 Generalised Inwards / Outwards Movement. 
249 

.33a Zones and Superzones of the Limbs. 

.34 Kinespheric Paths as Topological. .35 Method for Deriving a Taxonomy of Kinespheric Paths. 
261 

IVB.40 Conclusions: Categories of Kinespheric Form. 
265 

.51 Clustering and Subjective Organisation 



Appendix I. 
Research Proposal and Transfer of Registration to Ph.D. 

Kinesthesia. 


Appendix III. 
Spatial versus Verbal Cognition. 

Appendix IV. 
Spatial Information Processing. 

Appendix V. 
Varieties of “Spatial” Stimuli. 

Appendix VI. 
KinestheticMotor Mechanism in Spatial Adaptation. 

Appendix VII. 
Coordinative Structures. 

Terminology for Cartesian Planes and Dimensions 


Appendix IX. 
Analysis of “Vector Symbols” as used in Choreographie. 

Appendix X. 
Angles between Dimensions and Diameters. 

Appendix XI 
Range of Articulation at Single Joints. 

Appendix XII. 
Deflected Ballet. 

Appendix XIII. 
Reference Points in Kinesthetic Space: Stimuli and Data. 

Appendix XIV. 
Variability of Practice Hypothesis in Schema Theory. 

Appendix XV. 
Virtual Forms. 

Appendix XVI 
Method for Deriving a Taxonomy of Kinespheric Paths. 

Appendix. XVII. 
Subjective Organisation in Kinesthetic Recall: Raw Data. 


Volume One 

IIB1. 
“Joint space” as a graph of joint angles. 

IIIA1. 
Labanotation symbols for reference systems. 

IIIA2. 
Labanotation for standard cross of axes with divided front. 

IIIA3. 
Labanotation for body cross of axes with divided front. 

IIIB1. 
Biceps as a spring supporting the mass of the forearm. 

IIIB2. 
Planar positioning apparatus. 

IIIB3. 
Deriving a curved path from a polygonal representation. 

IIIB4. 
Relative timing of four motors in mechanical handwriting. 

IIIC1. 
Tolman’s rat maze. 

IIIC2. 
Four point path followed with arm movements or walking. 

IIIC3. 
Proportions of the human figure (Leonardo Da Vinci). 

IIIC4. 
Grid of proportions (Le Corbusier). 

IIIC5. 
Pentagonal body pose (Laban). 

IIIC6. 
Planar quadrangle network. 

IIIC7. 
Tetrahedral network. 

IIIC8. 
Octahedral net. 

IIIC9. 
Cubic net. 

IIIC10. 
Rectangleshaped Cartesian Planes. 

IIIC11. 
Linked corners of Cartesian planes builds an icosahedral net. 

IIIC12. 
Higherorder octahedral and lowerorder tetrahedral nets. 

IIID1. 
Translatory symmetry. 

IIID2. 
Reflection symmetry. 

IIID3. 
Rotational symmetry. 

IIID4. 
Labanotation symbols for reflection symmetries. 

IIID5. 
Labanotation symbols for rotational symmetries. 

IIID6. 
Proposed symbol for an “item”. 

IIID7. 
Proposed general symbol for symmetry. 

IIID8. 
Proposed symbols for symmetry transformations. 

IIID9. 
Notation for body transference. 

IIID10. 
Notation symbols for specific reflections. 

IIID11. 
Notation symbols for specific size scaling. 

IIID12. 
Notation symbols for rotational transformations. 

IIID13. 
Symmetry notation for en croix.. 

IIID14. 
Symmetry notation for transfer from the hand to the leg. 

IIID15. 
Symmetry within the “Ascale”. 

IVA1. 
Three levels. 

IVA2. 
Shapes of symbols for nine directions in each level. 

IVA3. 
Direction symbols. 

IVA4. 
Dots as motion between two directional points. 

IVA5. 
Vector symbols. 

IVA6. 
Free inclination symbols. 

IVA7. 
Direction of the progression symbols. 

IVA8. 
Notation for . . . approaching a particular point. 

IVA9. 
Endpoints of the dimensional cross form an octahedron. 

IVA10. 
Endpoints of the diagonal cross form a cube. 

IVA11. 
Square plane, edge ratio 1:1. 

IVA12. 
Rectangular plane, edge ratio ‰1.618:1. 

IVA13. 
Endpoints of primary deflected diameters form a cuboctahedron. 

IVA14, 
Cuboctahedron derived by joining the cubic edge midpoints. 

IVA15. 
Endpoints of modified diameters form an icosahedron. 

IVA16. 
“Personal square” for orientation of body facing. 

IVA17. 
Dimensional reference lines in ballet “theory of design”. 

IVA18. 
Shape of the normal working area in the horizontal plane. 

IVA19. 
Horizontal, frontal, and paramedial kinetospheric crosssections. 

IVB1. 
Higherorder pose configurations. 

IVB2. 
Higherorder curved pose . . . 

IVB3. 
Feuillet’s pathways: straight, open, round, waving, and beaten. 

IVB4. 
Hierarchical pathform taxonomy (PrestonDunlop, 1980). 

IVB5. 
Hierarchical pathform taxonomy (Eshkol and Wachmann, 1958). 

IVB6. 
Sevenlink movable chain. 

IVB7. 
Overhand knot. 

IVB8. 
Threepart knot. 

IVB9. 
Icosahedral planar sequence as 9part plastic knot. 

IVB10. 
Dimensional sequence as 6part knot. 

IVB11. 
Forms and orientations of the sixteen kinesphericitems. 

IVB12. 
Relationship between . . . intertrial repetitions. 

Volume One 

Table IV1. 
Examples of dimensional notations. 

Table IV2. 
Examples of diagonal notations. 

Table IV3. 
Modified diameter endpoints. 

Table IV4. 
Notations of cuboctahedral diameters. 

Table IV5. 
Symbols for cuboctahedral and icosahedral diameters. 

Table IV6. 
Notations of icosahedral diameters. 

Table IV7. 
Secondary deflections (cuboctahedral inclinations). 

Table IV8. 
Tertiary deflections, (icosahedral inclinations). 

Table IV9. 
Steep deflections of diagonal uprightforward. 

Table IV10. 
Six testpairs which approached significance. 

Table IV11. 
Performance measures. 

Table IV12. 
Frequency of occurrence for each of the strongest Sunits. 

Table IV13. 
Kinespheric item orientation and number of Funit occurrences. 

Volume Two 

APX.V1. 
Example of Brooks’ matrix. 

APX.VI1. 
Pointing . . . with and without prismglasses. 

APX.IX1. 
Axis scales (Laban, 1926). 

APX.IX2. 
Scales combined from primarydirections in four diagonals. 

APX.IX3. 
Scales combined from primarydirections in four diagonals. 

APX.IX4. 
Scales combined from primarydirections in four diagonals. 

APX.IX5. 
Augmented threerings. 

APX.IX6. 
Trial notation, pure dimensions. 

APX.IX7. 
Scales assembled from short peripheral directions. 

APX.IX8. 
Scales assembled from short peripheral directions. 

APX.IX9. 
Vector symbols translated . . . 

APX.X1. 
Shapes of Cartesian planes. 

APX.X2. 
Constructing the golden rectangle. 

APX.X3. 
Golden rectangle plus a second square. 

APX.X4. 
Dodecahedral rectangular plane. 

APX.X5. 
Exact angles between dimensions and cubic diameters. 

APX.X6. 
Exact angles between dimensions and octahedral diameters. 

APX.X7. 
Interpenetrating cubic and octahedral planes. 

APX.X8. 
Angles between dimensions and dodecahedral diameters. 

APX.X9. 
Angles between dimensions and icosahedral diameters. 

APX.XII1. 
Passé. 

APX.XII2. 
Développé á la quartiéme devant. 

APX.XII3. 
Renversé (first half). 

APX.XV1. 
Freebody diagram. 

APX.XV2. 
Tetrahedral molecular structure of water. 

APX.XV3. 
Octahedral arrangement of electron paths in a neon atom. 

APX.XV4. 
Circle packing. 

APX.XV5. 
Four spheres pack into a tetrahedron. 

APX.XV6. 
Exterior perceived tension translated into muscular tension. 

Volume Two 

Table A. 
Reversal.  166 
Table B.  Direction change.  166 
Table C.  Direction change with a reversal  167 
Table D.  Threephasic cycle.  168 
Table E.  Fourphasic cycle.  168 
Table F.  Hip circumduction.  168 
Table G.  One cycle of elbowcentred spiral.  169 
Table H.  One cycle of shouldercentred 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.  Multijoint wave with “rotary” pronate/supinate reversal.  170 
Table M.  Hip figure8 with rotation reversal.  170 
Table N.  Multijoint figure8 with “rotary” pronate/supinate.  170 
Table O.  Wristforearm figure8.  171 
Table P.  Eightphase continualcycle figure8.  171 
Table Q.  Continualcycle figure8 merged into four phases.  172 
Special thanks to Dr. Valerie PrestonDunlop 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 Laban’s 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; higherorder networks of locations are collected into maplike spatial images; and many symmetrical operations can be performed. Close similarities were identified between choreutic polyhedralshaped 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. Bernstein’s conception of the “coordinational 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), HutchinsonGuest (1983), Knust (1979a; 1979b), Laban (1975b), and PrestonDunlop (1969). The direction symbols are also discussed in Section IVA of this thesis.
____________
* Laban originally named this system of movement notation “kinetography” (Knust, 1948a, p. 28), literally “movementwriting”. Other systems of dance/movement notation or kinetography have also been developed (for a review see HutchinsonGuest, 1989). In order to distinguish Laban’s system it has been referred to as “Laban Kinetography” (Knust, 1948a, 1948b), “kinetography Laban” (PrestonDunlop, 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 KinetographyLaban 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 bodymovementnotation originated by R. Laban and of which the direction symbols are still at the core.