Foundations of Science

, Volume 7, Issue 1–2, pp 49–72 | Cite as

Systems of Logical Systems: Neuroscience and Quantum Logic

  • Gin McCollum


Nervous systems are intricately organized on many levels of analysis.The intricate organization invites the development of mathematicalsystems that reflect its logical structure. Particular logical structures and choices of invariants within those structures narrowthe ranges of perceptions that are possible and sensorimotorcoordination that may be selected. As in quantum logic, choicesaffect outcomes.

Some of the mathematical tools in use in quantum logic havealready also been used in neurobiology, including the mathematicsof ordered structures and a product like a tensor product. Astheoretical neurobiology is developed on its own foundation, wemay expect a rich dialogue between theoretical neurobiology andquantum logic.

neuroscience quantum logic sensorimotor 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aerts, D. and I. Daubechies: 1978, Physical Justification of Using Tensor Products to Describe Physical Systems as One Joint System. Helvetica Physica Acta 51: 661–675.Google Scholar
  2. Bialek, W.: 1987, Physical Limits to Sensation and Perception. Annual Review of Biophysics and Biophysical Chemistry 16: 455–478.Google Scholar
  3. Bloedel, J.R. and J. Courville: 1981, A Review of Cerebellar Afferent Systems. In V.B. Brooks (ed.), Handbook of Physiology.American Physiological Society, Bethesda, Maryland, pp. 735-829.Google Scholar
  4. Borghese, N.A., L. Bianchi and F. Lacquaniti: 1996, Kinematic Determinants of Human Locomotion. Journal of Physiology 494(3): 863–879.Google Scholar
  5. Boring, E., H. Langfeld and H. Weld: 1948, Foundations of Psychology. Jolen Wiley, New York.Google Scholar
  6. Braitenberg, V.: 1973, Texture of Brains. Springer-Verlag, Berlin.Google Scholar
  7. C. J: 1952, Living without a Balancing Mechanism. The New England Journal of Medicine 246(12): 458–460.Google Scholar
  8. Castelfranco, A.M., L.T. Robertson, G. McCollum: 1993, Detail, Proportion, and Foci among Face Receptive Fields of Climbing Fiber Responses in the Cat Cerebellum. Somatosensory and Motor Research 11: 27–46.Google Scholar
  9. Clark, K.: 1959, Leonardo da Vinci revised edition. Viking Penguin, New York.Google Scholar
  10. Collewijn, H.: 1977a, Eye-and Head Movements in Freely Moving Rabbits. Journal of Physiology 266: 471–498.Google Scholar
  11. Collewijn, H.: 1977b, Gaze in Freely Moving Subjects. In R. Baker and A. Berthoz (eds.), Control of Gaze by Brain Stem Neurons, Developments in Neuroscience 1. Elsevier/North-Holland Biomedical Press, pp. 13–22.Google Scholar
  12. Cooper, H.S.F. Jr.: 1976, A House in Space. Holt, Rinehart, and Winston, New York.Google Scholar
  13. de'sperati, C. and P. Viviani: 1997, The Relationship between Curvature and Velocity in Two-Dimensional Smooth Pursuit Eye Movements. Journal of Neuroscience 17(10): 3932–3945.Google Scholar
  14. Foulis, D.J., R.J. Greechie and M.K. Bennett: 1994, Sums and Products of Interval Algebras. International Journal of Theoretical Physics 33(11): 2119–2136.Google Scholar
  15. Fuller, J.H.: 1992, Comparison of Head Movement Strategies among Mammals. In A. Berthoz, W. Graf and P.-P. Vidal (eds.), The Head-Neck Sensory Motor System. Oxford University Press, Oxford, chapter 13.Google Scholar
  16. Goldberg, J.M. and C. Fernández: 1984, The Vestibular System. In J.M. Brookhart, V. B. Mountcastle and I. Darian-Smith (eds.), Handbook of Physiology – The Nervous System III. pp. 977–1022.Google Scholar
  17. Graf, W. and R. Baker: 1983, Adaptive Changes of the Vestibulo-ocular Reflex in Flatfish Are Achieved by Reorganization of Central Nervous Pathways. Science 221: 777–779.Google Scholar
  18. Graf, W., C. de Waele, P-P. Vidal, D.H. Wang and C. Evinger: 1995, The Orientation of the Cervical Vertebral Column in Unrestrained Awake Animals. II. Movement Strategies. Brain, Behavior, and Evolution 45: 209–231.Google Scholar
  19. Graf, W., J.I. Simpson and C.S. Leonard: 1988, Spatial Organization of Visual Messages of the Rabbit's Cerebellar Flocculus. II. Complex and Simple Spike Responses of Purkinje Cells. Journal of Neurophysiology 60: 2091–2121.Google Scholar
  20. Gutfreund, Y., T. Flash, R. Yarom, G. Fiorito, I. Segev and B. Hochner: 1996, Organization of Octopus Arm Movements: A Model System for Studying the Control of Flexible Arms. Journal of Neuroscience 16(22): 7297–7307.Google Scholar
  21. Holly, J.E.: 1997, Three-Dimensional Baselines for Perceived Self-Motion during Acceleration and Deceleration in a Centrifuge. Journal of Vestibular Research 7(1): 45–61.Google Scholar
  22. Holly, J.E. and G. McCollum: 1995, d-Space Problem and Solution Set: Relearning to Walk after a Stroke. International Journal of Theoretical Physics 34: 1601–1607.Google Scholar
  23. Holly, J.E. and G. McCollum: 1998, Timing of Secondary Vestibular Neuron Responses to a Range of Rotational Head Movements. Biological Cybernetics 79: 39–48.Google Scholar
  24. Holly, J.E., G. McCollum and R. Boyle: 1999, Identification of Head Motions by Central Vestibular Neurons Receiving Linear and Angular Input. Biological Cybernetics 81: 177–188.Google Scholar
  25. Llinas, R.R.: 1975, The Cortex of the Cerebellum. Scientific American 232(1): 56–71.Google Scholar
  26. Llinas, R.R.: 2001, I of the Vortex: From Neurons to Self. MIT Press, Cambridge, Massachusetts.Google Scholar
  27. Mathews, C.K.: 1993, The Cell – Bag of Enzymes of Network of Channels? Journal of Bacteriology 175(20): 6377–6381.Google Scholar
  28. McCollum, G.: 1992a, Invariants of the Second Transformation Expressed in Activation Ranges. Brain and Behavioral Sciences 15: 346.Google Scholar
  29. McCollum, G.: 1992b, Rules of Combination that Generate Climbing Fiber Tactile Receptive Fields. Neuroscience 50: 707–725.Google Scholar
  30. McCollum, G.: 1994a, Dissonance: A Nervous System Analogue to Quantum Incompatibility. International Journal of Theoretical Physics 33: 41–52.Google Scholar
  31. McCollum, G.: 1994b, Navigating a Set of Discrete Regions in Body Position Space. Journal of Theoretical Biology 167: 263–271.Google Scholar
  32. McCollum, G.: 1998, Dynamics of Olivary Neurons International Journal of Theoretical Physics 37(10): 2627–2652.Google Scholar
  33. McCollum, G.: 1999a,Mutual Causality and the Generation of Biological Control Systems. International Journal of Theoretical Physics 38(12): 3253–3267.Google Scholar
  34. McCollum, G.: 1999b, Sensory and Motor Interdependence in Postural Adjustments. Journal of Vestibular Research 9: 303–325.Google Scholar
  35. McCollum, G.: 2000, Social Barriers to a Theoretical Neuroscience. Trends in Neurosciences 23(8): 334–336.Google Scholar
  36. McCollum, G. and R. Boyle: 2001, Conditional Transitions in Gaze Dynamics: Role of Vestibular Nuclei in Eye-Only and Eye/Head Gaze Behaviors. Biological Cybernetics 85(6): 423–436.Google Scholar
  37. McCollum, G., C. Holroyd and A.M. Castelfranco: 1995, Forms of Early Walking. Journal of Theoretical Biology 176: 373–390.Google Scholar
  38. McCollum, G. and P.D. Roberts: 2002, Dynamics of Everyday Life: Rigorous Modular Modelling based on Bloch's Dynamical Theorem.Google Scholar
  39. Osborn, C.E. and R.E. Poppele: 1992, Parallel Distributed Network Characteristics of the DSCT. Journal of Neurophysiology 68(4): 1100–1112.Google Scholar
  40. Ovádi, J.: 1991, Physiological Significance of Metabolic Channelling. Journal of Theoretical Biology 152: 1–22, commentaries pp. 23–141.Google Scholar
  41. Paulin, M.G.: 1996, System Identification of Spiking Sensory Neurons Using Realistically Constrained Nonlinear Time Series Models. In I. Gath and G. Inbar (eds.), Advances in Processing and Pattern Analysis of Biological Signals. Plenum Press, New York, pp. 183–194.Google Scholar
  42. Paulin, M.G. and L.F. Hoffman: 1996, Maximum Information-predictingModels of Bullfrog Semicircular Canal Afferent Spike Trains. Society for Neuroscience Abstracts 22: 660.Google Scholar
  43. Ramon y Cajal, S.: 1955, Histologie du Système Nerveux. Instituto Ramon y Cajal, Madrid.Google Scholar
  44. Randall, C.H. and D.J. Foulis: 1983, Properties and Operational Propositions in Quantum Mechanics. Foundations of Physics 13(8): 843–863.Google Scholar
  45. Rinzel, J.: 1987, A Formal Classification of Bursting Mechanisms in Excitable Systems. In E. Teramoto and M. Yamaguti (eds.), Mathematical Topics in Population Biology, Morphogenesis, and Neurosciences, Lecture Notes in Mathematics 71. Springer-Verlag, New York, 267–281.Google Scholar
  46. Rota, G.-C.: 1986, Husserl and the Reform of Logic. In M. Kac, G.-C. Rota and J.T. Schwartz (eds.), Discrete Thoughts: Essays on Mathematics, Science, and Philosophy. Birkhäuser, Boston.Google Scholar
  47. Sacks, O.: 1984, A Leg to Stand On. Summit Books, New York.Google Scholar
  48. Schotland, J.L. andW.Z. Rymer: 1993a,Wipe and Flexion Reflexes of the Frog. I. Kinematics and EMG Patterns. Journal of Neurophysiology 69(5): 1725–1735.Google Scholar
  49. Schotland, J.L. and W.Z. Rymer: 1993b, Wipe and Flexion Reflexes of the Frog. II. Response to Perturbations. Journal of Neurophysiology 69(5): 1736–1748.Google Scholar
  50. Schwartz, E.L.: 1977, Spatial Mapping in the Primate Sensory Projection: Analytic Structure and Relevance to Perception. Biological Cybernetics 25: 181–194.Google Scholar
  51. Simpson, J.I., D.R. Wylie and C.I. De Zeeuw: 1996, On Climbing Fiber Signals and their Consequence(s). Behavioral and Brain Sciences 19: 380–394.Google Scholar
  52. Singer, W. and C.M. Gray: 1995, Visual Feature Integration and the Temporal Extraction Hypothesis. Annual Review of Neuroscience 18: 555–586.Google Scholar
  53. Soechting, J.F. and F. Lacquaniti: 1981, Invariant Characteristics of a Pointing Movement in Man. Journal of Neuroscience 1(7): 710–720.Google Scholar
  54. Soechting, J.F. and C.A. Terzuolo: 1987, Organization of Arm Movements. Motion is Segmented. Neuroscience 23(1): 39–51.Google Scholar
  55. Viviani, P. and C.A. Terzuolo: 1981, The Organization of Movement in Handwriting and Typing. In B. Butterworth (ed.), Language Production: II. Production of Non-Speech Modalities. Academic Press, New York.Google Scholar
  56. von Hofsten, C. and S. Fazel-Zandy: 1984, Development of Visually Guided Hand Coordination in Reaching. Journal of Experimental Child Psychology 38(2): 208–219.Google Scholar
  57. Wertheim, M.: 1995, Pythagoras' Trousers. Random House, New York.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Gin McCollum
    • 1
  1. 1.Neurological Sciences InstituteOregon Health Sciences InstitutePortlandUSA, E-mail

Personalised recommendations