Spatial Synthesis:  A Research Program

Sandra L. Arlinghaus, Ph.D.
Adjunct Professor of Mathematical Geography and Population-Environment Dynamics
School of Natural Resources and Environment; Taubman College of Architecture and Urban Planning
University of Michigan, Ann Arbor, MI;

William C. Arlinghaus, Ph.D.
Department of Mathematics and Computer Science
Lawrence Technological University, Southfield, MI
“Spatial Analysis” is a term in current use in a variety of disciplines:  from geography to regional analysis, to economics, to anthropology, to (no doubt) a host of others [1].  Merriam-Webster’s online Collegiate Dictionary defines “analysis” as a “separation of a whole into its component parts” [2].  Often, however, one wishes to consider not only separation but also composition:  the composition of the whole from a set of parts.  Thus, the same source defines “synthesis” as “the composition or combination of parts or elements so as to form a whole.”
We take the occasion of this Winter Solstice issue to invite the world at large to come together and offer a synthesis of ideas involving spatial concepts and theories, as a part of a broadly-based research program.  Volume I of this work will concern the concept of spatial hierarchy.  Book 1 (by the authors of this article) of Volume I, to appear, is entitled Centrality and Hierarchy:  Regular Lattices, Geometry, and Number Theory.  Other topics, that we might foresee, involve more books on Centrality and Hierarchy within Volume I as well as Volumes on topics such as (but not limited to):  Distance and Geodesic; Adjacency and Connection; Minimax, Absolute/relative, and Density; Scale, Orientation, and Dimension; Partition, Separation, and Diffusion; and, Transformation and Symmetry.
The authors of this article would assemble, edit, obtain reviews, and work to obtain a publisher for a series of eBooks entitled “Spatial Synthesis.” In doing so, they would draw on their recent experience in publishing an eBook, and in developing websites, to make the final product one that employs a variety of interactive tools for communicating information on the internet [3, 4].  Issues involving agreements concerning publication would be dealt with at the outset according to the format of the publisher.  If you would like to submit an idea for preliminary review, for suitability for inclusion, or if you would like to suggest yet other directions for this synthesis of spatial concepts and theories, please feel free to e-mail us or send e-mail attachments to:  We wish to have this work be synthetic: from its method of creation through its content formulation.  Please consider joining this venture in spatial synthesis.
  • 1.  Berry, Brian J. L. and Marble, Duane F.  Spatial Analysis:  A Reader in Statistical Geography, Englewood Cliffs:  Prentice-Hall, 1968.
  • 2.  Merriam-Webster’s Online Dictionary,
  • 3.  S. Arlinghaus, W. Arlinghaus, and F. Harary. Graph Theory and Geography:  an Interactive View Ebook.  (Wiley-Interscience Series in Discrete Mathematics and Optimization)  New York:  John Wiley & Sons, 2002. ( )
  • 4. Solstice, Pirelli INTERNETional Award Competition, SemiFinalist, 2001. (