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Computing Space VI: The Many Languages of Space or How to Read Marble and Dacey

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Today’s post is the sixth in a year-long series called,”Computing Space,” which highlights new mapping technologies and new areas for cartographic innovation, along with stories of the lives and work of many of the mostly unknown cartographers, geographers, mathematicians, computer scientists, designers and architects who both now, and in the past, have had a hand in the development of computer cartography and its applications.

 Philosophy is the theory of multiplicities, each of which is composed of actual and virtual elements. Purely actual objects do not exist. Every actual is surrounded by a cloud of virtual images.

                                                                                                                –G. Deleuze, The Actual and the Virtual

The important and seminal papers from the earliest history of computer cartography and geographic information science (GIS) still read by students today are few and far between, even though many of them contain deep conceptual ideas on the nature of geographic space and how it might be modeled in a digital environment. Some of these papers, like Max J. Egenhofer and Robert D. Franzosa’s, Point Set Topological Spatial Relations and Michael Goodchild’s, Geographic Information Science, both published in the International Journal of Geographical Science and Systems, are recognized as classics in the exposition of the state-of-the-art and set the stage for the development of spatial analysis in the 1990s. Many of these older papers are continually referenced in journal articles and were written during a time when the theoretical underpinnings of what is GIS today were already established, but were increasingly being cast in a more formalized, and highly abstract mathematical language.

Section from Egenhofer and Franzosa, Point-Set Toplogical Spatial Relations.
Section from Egenhofer and Franzosa, Point-Set Topological Spatial Relations.

Earlier papers, from say the 1960s, are however, less credited and seldom referenced, and are more conceptual, as geographers and computer scientists were still thinking through and experimenting with the wide variety of computational and algorithmic tools that might be useful in spatial analysis and cartography. Former posts on this blog have dealt with some of the early publications that provided an outlet for analytically inclined researchers at the Harvard Laboratory for Spatial Analysis and Computer Graphics and from the University of Michigan Community of Mathematical Geographers.

Today’s post will concentrate on a very early paper in the history of GIS, written in 1965, by Michael F. Dacey and Duane F. Marble,  from Northwestern University. Their paper, which was widely read at the time, is one of the most conceptually rich treatments of the foundations of Geographic Information Systems from these early years, at least in the mind of this blogger. The paper’s title, Some Comments on Certain Technical Aspects of Geographic Information Systems, gives little hint of the deep foundational and philosophic underpinnings that it contains. Instead of speaking about what today’s readers might imagine when they hear the word “technical,” the paper instead takes a more visionary approach linking some of the thinking taking place in the philosophy of logic, geometry and language to computer oriented spatial problems and cartography.

Title Page from Dacey and Marble, Some Comments on Certain Technical Aspects of Geographic Information Systems. From the Nick Chrisman Collection, Geography and Map Division, Library of Congress

Dacey and Marble take the word ‘map’ to be a bit of a basket concept, and use it as a generic term that refers to any of “the wide variety of methods used for representing spatially located information.” When speaking about the definition of a Geographic Information System (something that had yet to be clearly defined in the way we think of it today) however, they do not limit their ideas to mere maps, but rather take a more design oriented and functional approach, writing that any such system must take into account “the manifold aspects of collection, codification, storage, retrieval and analysis of spatially located and other kinds of data.”

In the introduction of the paper, the authors split the research and the central problems then facing scholars trying to establish the foundations of GIS into two areas that they believe are fundamental to the design and operation of any future computer based mapping and spatial analysis system . The first, concerns the formal structure of a system that would enable the collection, storage and retrieval of spatial “located” information. In using the word “located” Dacey and Marble are not only speaking of strictly of geospatial data, but include such things as “images and photographs” that could be spatially tagged. Their second class of problems, and the one treated in more depth in their short paper, concerns the description and analysis of information “having spatial arrangement and distribution.”

It is here that the paper breaks interestingly new ground and can be seen in many ways as one of the first attempts to speak about geographic objects in a GIS in a formal, and what could be termed, mereotopological (more on this term below) way[1]. The paper divides itself into two broad but very related areas discussing,  what feels on first reading  like an ontology of spatial representation, and which the authors call Spatial Statistics and Spatial Languages.

In the beginning of the section on spatial statistics, Marble and Dacey write:

The description or analysis of spatially located information, is, in many cases, largely the study of the geometric patterns formed by the arrangement and distribution of objects.

Here we have the beginnings of a kind of spatial thinking that is about objects, and one that takes objects and spatially oriented events as prior to space itself.  This means, that for the purposes of analysis, there is no way to understand a geographic space unless one has a handle on what objects it contains, how they are structured, how they relate to one another, and how to represent them. For Marble and Dacey, the kind of formal methods that must be employed to understand objects in a GIS, requires a kind of spatial thinking that is about how spatial objects are locked together into the spaces they occupy, how they interact, and most critically, what kind of geometries need to be studied and incorporated into a computational environment in order to  study geographic phenomena. In simple terms it is what we want to analyze that defines the space of analysis and not the other way around. This opens new areas for research and new cartographic applications that go beyond just thematic two-dimensional mapping. At the time this was not an easy or simple question and had great ontological implications for how one might represent the structure of geographically relevant objects and related spatial information, of whatever dimension, in a computer data base.

The second part of the paper is dedicated to an exposition on the topic of spatial languages. The authors explain that this part of the paper summarizes some of their research that was conducted earlier in the 1960s and which was inspired by the book Fundamental Theory, written by the astronomer, Arthur Eddington in 1946. The section they quote sets the stage for the remainder of their paper:

We have to express in mathematical symbolism what we are doing when we mention things; for if we have no measurement conception of what we are doing, the result of our measurement would not persuade us to believe anything in particular. All our results are derived from the condition that the conceptual interpretation which we place upon the results of measurement must be consistent with our conceptual interpretation of the process of measurement; we have to define symbols with properties that correspond precisely to the conceptions produced.

According to our authors this remark (especially, in my reading at least, the last line) generated a reconsideration of the symbols used on maps and the concepts underlying those symbols. In other words, what are the underlying semantics and meaning of those symbols, how do they refer to the real world, and how might they be codified in a programming language.

Their investigation resulted in a recognition that the models used for spatial relations in maps use a “language” that is very different from everyday language and also from the formal logic used by programmers. The locus of this difference, for Marble and Dacey, resides in the fact that it is not a simple generalization to go from everyday spatial language to a meaningful and analytically implementable two-dimensional computer representation of that language. Our everyday way of speaking about objects in space is just not formal enough and is too filled with ambiguity to be useful in a digital computer and therefore, a new and more rigorous way of spatially programming must be developed.

It is in this realm that I find Dacey and Marble’s paper far ahead of its time. Writing about the need for a formal two-dimensional language to represent cartographic models  the authors point out that this revived in them an interest in linguistic structure and that some kind of two-dimensional language is needed in order to create a functional GIS (we can read into this deep connections with the philosophy of Gottlieb Frege and Ludwig Wittgenstein). Searching for possible languages and knowledge representations, they look to the new field of pattern recognition and find, as one would expect in 1965, that the two-dimensional syntactic structures used for representing simple patterns are inadequate for dealing with the information and complex semantics of maps.

Some of the papers that Dacey and Marble reference show the depth of their research and how widely they read in their attempts to find a spatial language that in a GIS might formalize the knowledge needed to make and analyze a map. For example, they reference the paper Space, Time and Individuals, written the philosopher N.L. Wilson, which describes, in highly abstract and mathematical terms, a one-dimensional language for the representation objects and individuals in space that might be useful for computer applications. They also reference the work of the philosopher Rudolf Carnap and his book the Introduction to Symbolic Logic and its Applications in which he develops the semantics for spatial languages.

Section from Wilson's Space, Time and Individuals Papers laying out the initial formal axioms for an object in space-time.
Section from Wilson’s Space, Time and Individuals paper, published in the Journal of Philosophy in 1955, laying out the initial formal axioms for an object in space-time.

There are many untold stories in the history of GIS and how its conceptual, logical and mathematical foundations came to be developed. There were many dead ends, many conceptual doors that opened and closed, and many ideas on how our everyday notions of space could be made more formal and axiomatic that had to be explored before today’s amazingly flexible and useful GIS systems and applications could come into being. Reading their paper today, gives us not only historical insight into the technical side of Marble and Dacey’s thinking, but it also opens a window onto the wider philosophical underpinnings of how and why GIS came to be what it is today.

[1] Mereotopology is the combination of the formal logic of the notions of parts, wholes and boundaries as they pertain to objects, combined with the mathematical structure of topology. It is used to study the formal structure of objects and their algebraic properties. For a good introduction to the rapidly expanding research in Mereotopology see Roberto Casati and Achille C. Varzi, Parts and Places: The Structures of Spatial Representation (Cambridge, MA: MIT Press, 2003). This is one of the most critical areas for ontological research into cartographic and spatial representation in modern GIS. Historically interested and mathematically inclined readers should look into, Biacino L., and Gerla G., 1991, “Connection Structures,” Notre Dame Journal of Formal Logic 32: 242-47; Clarke, Bowman, 1981, “A calculus of individuals based on ‘connection’,” Notre Dame Journal of Formal Logic 22: 204-18 ; ——, 1985, “Individuals and Points,” Notre Dame Journal of Formal Logic 26: 61-75; Cohn, A. G., and Varzi, A. C., 2003, “Mereotopological Connection,” Journal of Philosophical Logic 32: 357-90; Forrest, Peter, 1996, “From Ontology to Topology in the Theory of Regions,” The Monist 79: 34-50; Gerla, G., 1995, “Pointless Geometries,” in Buekenhout, F., Kantor, W. (eds), Handbook of incidence geometry: buildings and foundations. North-Holland: 1015-31; Roeper, Peter, 1997, “Region-Based Topology,” Journal of Philosophical Logic 26: 251-309; Smith, Barry, 1996, “Mereotopology: A Theory of Parts and Boundaries,” Data and Knowledge Engineering 20: 287-303; ——, 1997, “Boundaries: An Essay in Mereotopology” in Hahn, L., ed., The Philosophy of Roderick Chisholm. Open Court: 534-61; Varzi, A. C., 1996, “Parts, wholes, and part-whole relations: the prospects of mereotopology,” Data and Knowledge Engineering, 20: 259-286; ——, 1998, “Basic Problems of Mereotopology,” in Guarino, N., ed., Formal Ontology in Information Systems. Amsterdam: IOS Press, 29-38; ——, 2007, “Spatial Reasoning and Ontology: Parts, Wholes, and Locations” in Aiello, M. et al., eds., Handbook of Spatial Logics. Springer-Verlag: 945-1038.


  1. Thanks as always for the erudite and illuminating exploration of the origins of GIS. It is no surprise that a technology that rich and complex has a similarly rich and complex genesis (yikes! what is the plural of genesis?). I had not expected the glancing allusion to Wittgenstein, but there you are!

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