Bruce Schuman
PO Box 23346
Santa Barbara, CA 93121
(805) 966-9515
Synthetic Dimensionality
Synthetic Dimensionality | Forum on Conceptual Structure
Design for a Transcendental Bridge
Linkage of the universal and the particular

Introduction to the Theory of Concepts
General principles of conceptual structure

The Dimensionality of Concept Structure
Similarities and differences in category formation

The Universal Hierarchy of Abstraction
Framework for a mathematical epistemology

Synthetic Dimsionality
The recursive algebra of semantic space

Foundations of this model

Background and history

Synthesizing a Universal Logic from the Interdisciplinary Spectrum

The entire ORIGIN RESEARCH project can be described as a design for "systematic confluence", involving the attempt to synthesize a highly inclusive and integrative theoretical perspective by bringing traditionally independent lines of thinking and academic disciplines into close relationship with one another. The objective in this crossing of traditional categorical boundaries has been to achieve an interdisciplinary cross-fertilization, which endeavors to find in these diverse disciplines common underlying factors, and which attempts to assemble from these factors an integrating and unifying theory defining universal insights, capable of proving useful at the common interface of all intellectual and scientific activities.

The books collected in this bibliography represent a modest attempt at defining the initial boundaries of a kind of scientific spectrum, which, though it is incomplete and must be substantially expanded in a very great number of ways, does provide an initial philosophic and scientific framework for the kind of sophisticated intellectual network which a project of this type must embody.

The listings in this bibliography thus define a broadly diverse array of interrelated subjects, each of which contributes some particular perspective or class of insights pertinent to the general questions with which mathematical epistemology is concerned, and which has been chosen because it seemed to adequately represent some particular domain or class of discussion which was felt to be critical. The project of commenting in detail on exactly how each of these works contributes to this project is a substantial undertaking, but each of these topics merits such a discussion.

Abian, Alexander (1965)
The Theory of Sets and Transfinite Arithmetic, W.B. Saunders, Philadelphia

Agresti, Alan (1984)
Analysis of Ordinal Categorical Data, John Wiley & Sons, New York

Allman, William F. (1989)
Apprentices of Wonder, Inside the Neural Network Revolution, Bantam Books, New York

Anderberg, Michael R. (1973)
Cluster Analysis for Applications, Academic Press, New York

Anderson, John (1983)
The Architecture of Cognition, Harvard University Press, Cambridge, Mass.

_____ (1980)
Cognitive Psychology and Its Implications, W.H. Freeman, San Francisco

_____ (1985)
Cognitive Psychology and Its Implications (Second Edition), W. H. Freeman, San Francisco

Aho, Alfred V., and Ullman, Jeffrey D. (1977)
Principles of Compiler Design, Addison-Wesley, Reading, Mass.

Allen, James (1987)
Natural Language Understanding, Benjamin/Cummings, Menlo Park

Asbhy, W. Ross (1952)
Design for a Brain, John Wiley, New York

Banchoff, Thomas F. (1990)
Beyond the Third Dimension, Geometry, Computer Graphics, and Higher Dimensions, W. H. Freeman, Scientific American Library, New York

Bancilhon, Francois, and Peter Buneman (1990)
Advances in Database Programming Languages, ACM Press, Addison-Wesley, New York

Barnsley, Michael (1988)
Fractals Everywhere, Academic Press, New York

Barnsley, Devaney, Mandelbrot, Peitgen, Saupe, Voss, Fisher, McGuire (1988)
The Science of Fractal Images, Springer-Verlag, New York

Barrett, Edward (1989)
The Society of Text, The MIT Press, Cambridge, Mass.

Bateson, Gregory (1988)
Mind and Nature, A Necessary Unity, Bantam Books, New York

Bateson, Gregory, and Mary Catherine Bateson (1988)
Angels Fear, Towards an Epistemology of the Sacred, Bantam Books, New York

Bell, Eric Temple (1987)
Mathematics: Queen & Servant of Science, Tempus Books, MicroSoft Press, Redmond, Washington

_____ (1965)
Men of Mathematics, The Lives and Achievements of the Great Mathematicians from Zeno and Poincare, Simon and Schuster, New York

Bertalanffy, Ludwig von (1968)
General Systems Theory, George Braziller, New York

Bielawski, Larry, and Robert Lewand (1991)
Intelligent Systems Design, Integrating Expert Systems, Hypermedia, and Database Technologies, John Wiley & Sons, New York

Booch, Grady (1991)
Object Oriented Design with Applications, Benjamin/Cummings, Redwood City, CA

Bohm David, and F. David Peat (1987)
Science, Order, and Creativity, Bantam Books, New York

Brand, Stewart (1987)
The Media Lab, Inventing the Future at MIT, Viking Penguin, Inc. New York

Briggs, John, and F. David Peat (1990)
Turbulent Mirror, an Illustrated Guide to Chaos Theory and the Science of Wholeness, Perennial Library, Harper & Row, New York

Brodie, Michael L., John Mylopoulos and Joachim W. Schmidt, eds. (1984)
On Conceptual Modelling, Perspectives from Artificial Intelligence, Databases, and Programming Languages, Springer-Verlag, New York

Calvin, William H. (1990)
The Cerebral Symphony, Seashore Reflections on the Structure of Consciousness, Bantam Books, New York

Chestnut, Harold (1966)
System Engineering Tools, John Wiley and Sons, New York

Churchland, Paul (1992)
Matter and Consciousness, Bradford Books, MIT Press, Cambridge, Mass

Clarke, Andy (1990)
Microcognition, Philosophy, Cognitive Science and Parallel Distributed Processing, MIT Press, Bradford Books, Cambridge

Clifford, H. T., and W. Stephenson (1975)
An Introduction to Numerical Classification, Academic Press, New York

Cofer, C. N., and Appley, M. H. (1964)
Motivation: Theory and Research, John Wiley, New York

Collins, Allan, and Edward E. Smith (1988)
Readings in Cognitive Science, A Perspective from Psychology and Artificial Intelligence, Morton Kaufmann, San Mateo, CA

Dantzig, Tobias (1954)
Number, The Language of Science, Free Press, Macmillan, New York

Davis, Paul (1988)
The Cosmic Blueprint, New Discoveries in Nature's Creative Ability to Order the Universe, Simon and Schuster, New York

_____ (1983)
God and the New Physics, Touchstone Books, Simon & Schuster, New York

Davis, Philip J., and Hersh, Reuben (1981)
The Mathematical Experience, Birkhauser, Boston

Dertouzos, Michael et al
"Communications, Computers and Networks", special edition of Scientific American Magazine, September, 1991

Everitt, Brian (1974)
Cluster Analysis, John Wiley & Sons, New York

Freeman, Walter
"The Physiology of Perception", Scientific American Magazine, February, 1991

Firesmith, Donald G. (1993)
Object-Oriented Requirements Analysis and Logical Design, John Wiley & Sons, New York

Gardner, Howard (1986)
The Mind's New Science, A History of the Cognitive Revolution, Basic Books, New York

Gardner, Martin (1968)
Logic Machines, Diagrams and Boolean Algebra, Dover Publications, New York

Gengle, Dean (1984)
The Netweaver's Sourcebook, A Guide to Micro Networking and Communications, Addison-Wesley, Reading, Mass.

Gleick, James (1987)
Chaos, Making a New Science, Viking Penguin, Inc., New York

Grabbe, Eugene M., Simon Ramo and Dean Wooldridge (1958)
Handbook of Automation, Computation, and Control, Vol. 1, Control Fundamentals, John Wiley and Sons, New York

Hamming, Richard W. (1980)
Coding and Information Theory, Prentice-Hall, Inc., Englewood Cliffs, NJ

Hampden-Turner, Charles (1981)
Maps of the Mind, Charts and Concepts of the Mind and its Labyrinths, Collier Books, Macmillan Publishing Co., New York

Harman, Willis, and Howard Rheingold (1984)
Higher Creativity, Liberating the Unconscious for Breakthrough Insights, Institute of Noetic Science, Jeremy Tarcher, Inc., Los Angeles

Harrel, David (1987)
Algorithmics, Addison-Wesley, Menlo Park, CA.

Hartigan, John A. (1974)
Clustering Algorithms, John Wiley & Sons, New York

Haugeland, John, ed. (1987)
Mind Design, Bradford Books, MIT Press, Cambridge, Mass.

Hillis, W. Daniel (1989)
The Connection Machine, MIT Press, Cambridge, Mass.

Hiltz, Starr Roxanne, and Murray Turoff (1978)
The Network Nation, Human Communication via Computer, Addison-Wesley Publishing Co., Advanced Book Program, Reading, Mass.

Hofstadter, Douglas R. (1980)
Goedel, Escher, Bach: An Eternal Golden Braid, Random House, New York

_____ (1985)
Metamagical Themas: Questing for the Essence of Mind and Pattern, Basic Books, New York

Hope, Keith (1968)
Methods of Multivariate Analysis, University of London Press, Ltd., London

Howson, Colin, and Peter Urbach (1989)
Scientific Reasoning: The Bayesian Approach, Open Court, La Salle, Illinois

Huntington, Edward V. (1921)
The Continuum and Other Types of Serial Order, Harvard University Press, Cambridge, Mass.

Ipsen, D. C. (1960)
Units, Dimensions, and Dimensionless Numbers, McGraw-Hill, New York

Jambu, M., and M. O. Lebeaux (1983)
Cluster Analysis and Data Analysis, North Holland Publishing, Amsterdam & New York

Johnson, George (1986)
Machinery of the Mind, Inside the New Science of Artificial Intelligence, Time Books, Random House, New York

Johnson-Laird, Phillip (1988)
The Computer and the Mind, An Introduction to Cognitive Science, Harvard University Press, Cambridge, Mass.

Jolley, J. L. (1968)
Data Study, McGraw-Hill, New York

Kay, Alan, et al (1984)
"Computer Software", Scientific American Magazine (special issue on software), Vol. 251, No. 3, September, 1984

Khanna, Tarun (1990)
Foundations of Neural Networks, Addison- Wesley, Reading, Mass.

Khoshafian, Setrag, and Razmik Abnous (1990)
Object Orientation: Concepts, Languages, Databases, User Interfaces, John Wiley & Sons, New York

Kline, Morris (1982)
Mathematics, The Loss of Certainty, Oxford University Press, New York

Kitcher, Philip (1984)
The Nature of Mathematical Knowledge, Oxford University Press, New York

Kowalik, Janusz S. (1988)
Parallel Computation and Computers for Artificial Intelligence, Kluwer Academic Publishers, Boston

Krol, Ed (1992)
The Whole Internet Catalog & User's Guide, O'Reilly & Associates, Sebastopol, CA

Kuhn, Thomas S. (1970)
The Structure of Scientific Revolutions, Second Edition, International Encyclopedia of Unified Science, University of Chicago Press, Chicago

Laurel, Brenda (1990)
The Art of Human-Computer Interface Design, Addison-Wesley, Reading, Mass.

Leler, Wm. (1988)
Constraint Programming Languages, Their Specification and Generation, Addison-Wesley, Reading, Mass.

Leshan, Lawrence, and Margenau, Henry (1982)
Einstein's Space & Van Gogh's Sky, Physical Reality and Beyond, Collier Books Macmillan Publishing Co., New York

Levine, Howard, and Rheingold, Howard (1987)
The Cognitive Connection, Thought and Language in Man and Machine, Prentice Hall Press, New York

Liskov, Barbara, and John Guttag (1986)
Abstraction and Specification in Program Development, MIT Press, Cambridge, Mass.

Lorin, Harold, and Harvey Deitel (1981)
Operating Systems, Addison-Wesley, Reading, Mass.

Lucas, Peter, and Linda van der Gaag (1991)
Principles of Expert Systems, Addison-Wesley, Workingham, England

Mandelbrot, Benoit B. (1983)
The Fractal Geometry of Nature, W.H. Freeman and Co., New York

Martin, James (1981)
An End-User's Guide to Data Base, Prentice- Hall, Englewood Cliffs, NJ

_____ (1977)
Computer Data-Base Organization, 2nd Ed., Prentice-Hall, Englewood Cliffs, NJ

_____ (1981)
Computer Networks and Distributed Processing, Software, Techniques, and Architecture, Prentice-Hall, Englewood Cliffs, NJ

_____ (1981)
Design and Strategy for Distributed Data Processing, Prentice-Hall, Englewood Cliffs, NJ

_____ (1977)
Future Developments in Telecommunications, Second Edition, Prentice-Hall, Englewood Cliffs, NJ

_____ (1990)
Information Engineering, vols. 1,2,3, Prentice-Hall, Englewood Cliffs, NJ

_____ (1981)
Telematic Society, A Challenge for Tomorrow, Prentice-Hall, Englewood Cliffs, NJ

Marx, Melvin H., and William A. Hillix (1979)
Systems and Theories in Psychology, Third Edition, McGraw-Hill, New York

McNeill, Daneil, and Paul Freiburger (1993)
Fuzzy Logic, Simon & Schuster, New York

Meadow, Charles T. (1973)
The Analysis of Information Systems, John Wiley, New York

Meyer, Bertrand (1988)
Object-Oriented Software Construction, Prentice-Hall, New York

Minsky, Marvin (1986)
The Society of Mind, Simon and Schuster, New York

Mozer, Michael C. (1991)
The Perception of Multiple Objects: A Connectionist Approach, MIT Press, Bradford Books, Cambridge, Mass.

Nicholls, John E. (1975)
The Structure and Design of Programming Languages, Addison-Wesley, Reading, Mass.

Pagan, Frank G. (1981)
Formal Specification of Programming Languages, a Panoramic Primer, Prentice-Hall, Englewood Cliffs, NJ

Pagels, Heinz (1988)
The Dreams of Reason, The Computer and the Rise of the Sciences of Complexity, Simon and Schuster, New York

Parsaye, Kamran, Mark Chignell, Setrag Khoshafian, and Harry Wong (1989)
Intelligent Databases, Object-Oriented Hypermedia Technologies, John Wiley & Sons, New York

Peat, F. David (1987)
Synchronicity, The Bridge Between Matter and Mind, Bantam Books, New York

Peitgen, H. O., and Richter, P. H. (1986)
The Beauty of Fractals, Images of Complex Dynamical Systems, Springer-Verlag, Berlin

Peled, Abraham, et al (1987)
"The Next Computer Revolution", Scientific American Magazine (special issue on parallel computing), Vol. 257, No. 4, October, 1987

Posner, Michael (1989)
Foundations of Cognitive Science, MIT Press, Bradford Books, Cambridge, Mass

Penrose, Roger (1989)
The Emperor's New Mind, Penguin Books, New York

Penzias, Arno (1989)
Ideas and Information, Managing in a High-Tech World, W. W. Norton & Co., New York

Quarterman, John S. (1990)
The Matrix: Computer Networks and Conferencing Systems Worldwide, Digital Press

Rand, Ayn (1990)
Introduction to Objectivist Epistemology, Second Edition, Meridian, Penguin Books, New York

Rapaport, Matthew (1991)
Computer Mediated Communications, John Wiley & Sons, New York

Restle, Frank (1959)
"A Metric and an Ordering on Sets", Psychometrika, Vol. 24, No. 3, September, 1959

Rheingold, Howard (1991)
Virtual Reality, Summit Books, Simon & Schuster, New York

Rosch, Eleanor (1988)
"Principles of Categorization", in Readings in Cognitive Science, edited by Collins and Smith, Morgan Kaufmann, San Mateo, CA

Rucker, Rudy (1977)
Geometry, Relativity and the Fourth Dimension, Dover Publications, New York

_____ (1983)
Infinity and the Mind, The Science and Philosophy of the Infinite, Bantam Books, Toronto

_____ (1987)
Mind Tools, The Five Levels of Mathematical Reality, Houghton Mifflin, Boston

_____ (1984)
The Fourth Dimension, A Guided Tour of the Higher Universes, Houghton Mifflin, Boston

Rumelhart, David E., James McClelland, and the PDP Research Group (1987)
Parallel Distributed Processing, Explorations in the Microstructure of Cognition, Vols. 1-2, Bradford Books, MIT Press, Cambridge, Mass.

Schiffman, Susan S., M. Lance Reynolds, and Forest W. Young (1977)
Introduction to Multidimensional Scaling; Theory, Methods and Applications, Academic Press, New York

Schrage, Michael (1990)
Shared Minds, The New Technologies of Collaboration, Random House, New York

Sharples, Mike, David Hogg, Chris Hutchison, Steve Torrance, and David Young (1989)
Computers and Thought, A Practical Introduction to Artificial Intelligence, MIT Press, Bradford Books, Cambridge, Mass.

Simon, Herbert (1982)
The Sciences of the Artificial, Cambridge, MIT Press

Singh, Jagjit (1959)
Great Ideas of Modern Mathematics, Their Nature and Use, Dover Publications, New York

Smith, Edward E., and Douglas L. Medin (1981)
Categories and Concepts, Harvard University Press, Cambridge, Mass

Sokal, Robert R., and Peter H. A. Sneath (1963)
Principles of Numerical Taxonomy, W. H. Freeman and Co., San Francisco

Sowa, John F. (1984)
Conceptual Structures: Information Processing in Mind and Machine, Addison-Wesley, Reading, Mass.

Steen, Lynn Arthur (1980)
Mathematics Today, Random House, New York

Tank, David W., and John Hopfield
"Collective Computation in Neuronlike Circuits", Scientific American Magazine, December, 1987, pp104-114

Taylor, David (1992)
Object-Oriented Information Systems, Planning and Implementation, John Wiley & Sons, New York

Tversky, Amos (1988)
"Features of Similarity", in Readings in Cognitive Science, edited by Collins and Smith, Morgan Kaufmann, San Mateo, CA

Wegner, Peter (1968)
Programming Languages, Information Structures, and Machine Organization, McGraw-Hill, New York

Wexelblat, Richard (1981)
History of Programming Languages, Academic Press, New York

Wilder, Raymond (1980)
Introduction to the Foundations of Mathematics, Second Edition, Robert E. Krieger Publishing Co., Huntington, NY

Winograd, Terry, and Fernando Flores (1986)
Understanding Computers and Cognition: A New Foundation for Design, Ablex Publishing, Norwood, NJ

Winston, Patrick (1979)
Artificial Intelligence, Addison-Wesley, Reading, Mass.

_____ (1984)
Artificial Intelligence (Second Edition), Addison- Wesley, Reading, Mass.

Wolfram, Stephen (1988)
Mathematica, A System for Doing Mathematics by Computer, Advanced Book Program, Addison-Wesley Publishing, Redwood City, CA

Zimmerman, H. J. (1987)
Fuzzy Sets, Decision Making, and Expert Systems, Kluwer Academic Publishers, Boston