Spatial Core Concepts

abstract: Gilberto and Werner have asked pertinent questions relative to the various efforts to formalize spatial concepts for Geographic Information Science.

cognition vs. formal geometry


External Realism

Not assuming a shared external reality which is observable by everybody makes GIS pointless.

Objects vs Process

Human cognition considers, for reasons of cognitive economy, all observations which are not in the same (spatio-temporal) frequency spectrum in which humans exist, as static objects. A scientific understanding of reality - without the limits of human frequency focus - is necessarily a spatial-temporal universe populated by processes. The two views, the cognitive and the formal-scientific one, are incommensurable. Conversions of observations between them are approximately possible.

note: Humans exist in a millimeter to hundred meter and 10 Hz to 10e-5 Hz (once per decade) temporal spectrum.

Gilberto's questions:

From an email from Gilberto Camara to me after Werner's "Retirement event" (June 1, 2021 at UCSB).

note: Gilbeto is Gilberto Camara, Werner is Werner Kuhn, Martin is Martin Raubal, Andrew is Andrew Frank, Galton is Antony Galton, David Mark is David Mark, Goodchild is Mike Goodchil. Las Navas is the Las Navas del Marquez (in the Avila Province of Spain) where the 1988 meeting was held [ref]

Gilberto's email:

... the subject of “core concepts” is a fascinating one. As a provocation, I would like to pose questions which I believe need to be addressed by “core concepts” research:

(1) “Is there a reality independent of our representations?” (2) “What is the place of time in GIS Theory?" (3) “Should GIS Theory be restricted to the study of computer representations of geographical reality or should it also be concerned with cognitive representations? (4) “Do the core concepts need to include mathematical formalisms?" (5) “What is the role of data analytics on GIS Theory?" (6) “How best can GIS Theory support transdisciplinary research?”

The first is the “Searle question”. It hinges as to whether GIS Theory should be based on External Realism. If it does, the explanation of core concepts needs to distinguish between observations and representations. Werner actually said as much in his work "A Functional Ontology of Observation and Measurement” (which I like a lot): “everything starts with observations”. Starting from observations implies that fields and objects are not a duality, but belong to different ontological tiers (as Andrew proposes). Adopting External Realism makes it easier to answer questions such as “do mountains exist?”. Also, this view better explains the linguistic nuances of geographical concepts, as explored in the work of David Mark. Those that reject External Realism are faced with the problem of incommensurability of representations.

The second is the “Galton question”. It implies establishing the relation between events and objects. In a “space + time” world, objects exist and events modify them. In a “spacetime” world, objects are all there is. Adopting a “space + time” view leads to some ontological choices: should objects exist before events happen? Can we talk about “processes”? Is there such a thing as a “spatial process”?

The third is the "Las Navas question". Linking GIS Theory to computer representations has important benefits for GIS practitioners, but narrows the field of research. Hence the Las Navas research agenda, which places spatial information as a basic component of Cognitive Science. Thirty years from the landmark 1991 meeting, what is your appreciation of its consequences? Interestingly, it was only in the 2010s, after smartphones became ubiquitous, that spatial cognition concepts became technological mainstream (e.g, Martin’s work at ETH). Thus, if one considers that GIS Theory should include both matters of computer representation and of spatial cognition, the core concepts need to include notions of both disciplines.

The forth is the “Frank question”. Andrew has always insisted on the importance of formal models as a basis for understanding the translation from external reality to computer representation. IMHO, formal models are essential to build mental abstractions. Words only are not enough. Formal descriptions can be done in Haskell, R, Python, or simply with an abstract data type notation, but they can hardly be eschewed in the core concepts.

The fifth is the "Goodchild question”. Mike was primarily interested in spatial analytics, for good practical reasons: analytics and modelling are the primary uses of GIS. Can one teach core concepts without discussing spatial autocorrelation, map algebra, and agent-based modelling?

The last is the “Kuhn question”. Werner has an immense curiosity and an incredible energy of reaching out to other sciences. Still, the question remains: do we start from computer representations which are shared by different disciplines or start with abstractions (e.g, fields) which are semantically loaded? To establish a dialogue with an archaeologist, do we start with a map in QGIS or with a list of concepts?

My reactions:

My first reaction was (email june 4, 2021):

my first reaction is to ask, which of these questions are independent of each other?

i assume that the question 1 (Searle) is assumed by everybody in questions 2 and up. gis without assuming a joint reality seems pointless to me.

then I would assume that one could show that Galton's question implies other things, which limits what can be done with time + space (in terms of the next questions: especially for Goodchild's and Werner's questions.

question 1: Searle's question

My position starts with accepting a joint external reality, observable by everybody - but not necessarily observed in the same way and with the same results. Important for my thinking is the ability of everybody to act on the joint reality, to change it in some ways and that the changes are observable by others. Werner's stress on observation is necessary but incomplete without actions by one observer and the observable changes they produce for other actors.

I do not remember how much Werner stresses actions (It is clearly part of Raubal's observe - decide - act scheme in his dissertation). Actions with observable effects on the joint reality are the base for all forms of communication between individuals; semantics of actions and observations are intrinsicly linked.

Algebraic formalisations (a later question) link observations and actions to fix the semantics of pairs of actions and observations, where some specific action produce some specific observable changes.

The joint external reality is existing independently of any observer; there is nothing we can know about it except what we (individually) observe. The result of observations are local to the observer and cannot be shared; they appear as "real" and some researcher call this "reality" or they take external representations of the result of observations are "reality" (what I would call representations).

I have a hard time to see a meaningful discussion when one does not assume an external, observable and actionable reality. What is one then discussing? If not external reality exists, what is the object of the discussion? If the external reality is not joint (i.e. everybody has his own) then everybody can assert properties observable in his reality without conflict with the observations of others.

question 2: Galton's question

As Gilberto puts it, it is to clarify the relation between events and objects. I restate is as a decision between a space-time universee with "things" (events, processes) existing in (three) spatial dimensions and one temporal dimension or an universe, in which Objects with (three) spatial dimension exist in time.

In the NCGIA, the research was focused on geographic space and time and 'time' was split off into a specialist meeting (I 7) whereas 'space' was the connecting theme of the NCGIA. The 'time' specialist meeting, which I was postponed till the admiral said "Andrew, I think it is time for Time", to which I could only say "Aye, aye, sir".

During this time, I came to the conclusion that separating the research between space and time was hindering research progress. The object GIScience studied had grown beyond the early examples (cadastral parcels and political units, soil types etc.). The ease with which to observe point positions even dynamically thorough GPS added trajectories of moving objects influenced the CHOROCHRONOS project and lead me to formalized spatio-temporal (toy) universes. I compared my approach with the SNAP - SPAN approach of Barry, which on the surface seemed (falsely) to be symmetric between a universe of snapshots (SNAP) and processes (SPAN).

I thought at the time, that from the physical world, typically modelled as a space-time universe formalized as Partial Differential Equations (PDE) a universe with "object-processes" (in space time regions) was formalizable and would encompass most the object models formalized (for database usage). (Details later xx).

However, I was not able to build reasonably interesting, but still toy universes with object and processes without hitting an "complexity explosion" - in the real world (or in a model based on PDE) everyting is connectd to everything. When mapping the PDE model ot an object model, complexity overwhelms everything. I looked into PDE of multiple scales (in space and time: to connect coarse and fine models) but nothing I saw was convincing me to rein-in the complexity explosion.

I evidently undrstood Galton's question as a either-or question and felt I knew what to choose but could not convince myself that this choice would work (neither could I see others having overwhelming success with their choices). I think I had laid out methods how to progress from the point-time observations of properties to objects with properties changing in time - but any construction of an, even small, example was lost in an explosion of complexity.

The two options: space-time vs space and time

Having agreed that an external observable reality exists, a discussion of models is reasonable. Note: I assume that no direct knowledge - other than observation of properties at space-time locations - of external reality is possible. I think this is very close to Goodchilds 'geographic space' model, which assumes that for each point in space and time properties have observable values. [ref]

Space-time models

Physics and engineering have an extensive, successful experience with space-time models. Such models represent a continous space with observable properties at points undergoes continous changes of properties at locations. All knowledge is knowledge based on observerations collected in a framework, which I call models; models collect data to answer questions like 'what is the value of property x at location y and time t' in some compact, efficient form. Such models, sometimes dynamic and sometimes, when the processes of interest slow, snapshot models. Models are often built with a specific (spatial or temporal) resolution. Theses models are based on formal mathematical theories and implemented approximatively with computer representations. The specific approximations are selected in reaction to the necessities of the application. Difficulties to integrate data from different models are well known and handled case-by-case.

PDE as a model of external reality

I take the model of space-time modelled with PDE in physics; this model has been very successful to predict observable behaviour of reality. It is widely used in engineering and predictions are in most cases accurate. This model includes observations of points (in space-time). The PDE model can be studied as of infinite resolution (but not instantiated, i.e. represented in a computer system) or with a coarse instantiation of a raster; multiple models with different raster size are possible. Converion between are possible in some cases: coarser to finer without loss, but not from finer to coarser. note: Without loss means that an observation of a property of the model remains the same after a transformation.

Models with vector geometry

Similar models are possible with point, lines and regions with various theoretical underpining (for example as cell complex); such models are often called topological The transformation of raster models to topological models has been studied and is approximatively possible.

Space and time

Models of objects existing in space and evolving in time seem equivalent (and, transferable from space-time models, although not without loss). Such models seem prevalent in human discourse, in planning and science (PDE are 'nicer' but userd only in few applications where they are indispensable: statics, hydraulics and similar enginering problems).

The advantage of conceptualization the world as objects is abstraction and the human cognitive conceives the world as (slowly changing) objects in which humans move; a conceptualization of the world as mostly static is economical, it reduces the cognitive load. A conceptionalization of the world as dynamic is not necessary, because only object which change with a (spatio-temporal) frequency comparable to the frequency of human movement and changes require a conceptionalization as dynamic. Objects which change slower (or are much larger than humans) are, relative to a human, static; objects which are change faster (or are much smaller than humans) are dealt with as aggregates.

note: Language has the class of "mass noun" which serves to collect small objects into a single larger objects, e.g. grass, gravel, etc.

Why are only objects with a dynamic in a frequency similar to human beings perceived as dynamic?

how to make the argument

For an observer with a certain frequency (spatio-temporal) of observation, - objects which change much less than the frequency of the observation appear as non-changing, i.e. static. - objects which change with higher frequency are conceived as objects with statistically varying properties (e.g. )

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