**MAIRIE DOUFEXOPOULOU
**

This work presents a theoretical viewpoint on the involved foundation perspectives about configurations of the meaning of “space-time” in context of its professional use. There exist diverse human activities, which are based on a configuration and knowledge about “space” / “place” including a description of particular types of properties of space. These features are used for different professional objectives. Hence there are several differences about the given perspectives to a meaning of these terms. In addition there exist several forms by which a representation of space is used in association to a particular objective. These are characterized according to objective and subjective viewpoints, in which the objective forms are used for the representation of space, while the subjective ones are based on various technological / philosophical and professional perspectives.

An approach is to classify these perspectives is to consider two main viewpoints: (i) when space/time is the “object” for spatial mapping and (ii) when a particular mapping form is used for geo-referencing “places”, at which different geographical “information” or qualification measures and/or properties about “space” are appointed.

These viewpoints, illustrate the basic difference between a) spatial mapping and b) geography.

Consequently any representation approach of the space-time includes a type of an objective perspective to describe the space through a Mathematical form, which is coupled to a subjective one, which depends on the type of the properties which characterize a given part of “space”. The subjective perspectives are founded on philosophical and professional viewpoints. Hence any mapping form of space is used to determine “places” at which many different types of geographical “information” or qualification features are illustrated.

Consequently any general estimation process for a positioning of simple “places” in “space” or of geographical “information” at a “place” is characterized by an interchange of the priority of importance between the positioning and the illustrated “information”. This feature is expressed by the form of the used estimation functions in context of generalized prediction. Under this viewpoint the terrain relief stands either as only an “object” to map in which the dimension of height above a zero height level may receive the role of a physical variable in the role of an important parameter. This varying in space/time surface is used also in placing measures for the description of space or the description of geographical data. Thus the terrain relief receives a dual role as 1) a mapping “object” or 2) as a contributing parameter for geographical phenomena having a static or a dynamical (=variable in time) attitude

This contribution aims to illustrate to various sorts of users of space and / or place that in all types of interpolation for general prediction of places and of spatial “information” an efficient expertizing with 1) use of: Mapping disciplines or mapping “products” 2) the Geographical Information Systems (GIS) and 3) Global Positioning Systems (GPS) is needed. However the various professional experts are not always familiar with the aim of using a space-time representation for different professional uses. The link of “space” and “place” to the use of their representation is provided in context of the perspective of the professional discipline. .

**A link between perspectives of using the space to its representations**

The meaning of „place” expresses a restricted consideration of positioning in “space”. Such a consideration includes a perspective about a Mathematical structure of space used for its description and a perspective, which depends on the given meaning to its use for particular professional objectives. Hence the positioning coordinates in space include a variable and/or a parameter which depend on its particular use. The meanings of “place” and “space” (quantified or qualified) deserve a particular definition in the various sciences or disciplines and a viewpoint about the “space” associates to its professional use (scientific, technical, planning, problem solving).

Consequently all perspectives to consider “space” may be divided into „objective”, which associate to a given Mathematical or Physical frame and to „subjective”, which associate to its particular use. Any description of “space” through a Mathematical viewpoint embeds applications aiming for its mapping, in which a description of possible qualifications introduces physical or conceived properties in context of the various professional goals.

A relationship between the objective and the subjective viewpoints may be illustrated by adopting Lefebrvre’s principal work (1974), which provides an ideological basis about their connection. Actually it provides how conceived or perceived manifestations of space can interact. That work had introduced important implications for an analysis about space on ideological base.

Although the present contribution does not deal with mental perspectives about the space, a way to connect the geographical “space” with its mapping forms seems that should be founded on an enlarged definition about its use ( e. g A space for place in sociology, Annual Review of Sociology, 26 pp.463-496) as „a set of coordinates with an added structure”. In practice such a definition is composed by a set of coordinate for “places” in association to an associated structure of space. Thus “places” are characterized by qualified content of „information”, which depends on the use of space..

Lefebvre’s argument in The Production of Space is based on the perspective that that „space” is a social product and as such it may extend to include complex objectives of use in which an approriate conceptual link between the mapping disciplines and the use of various mapping forms of „space” in professional applications is provided. This consideration implies that a research perspective from space to processes of its production or any of properties involves all past and present available forms of the objective mappings of „places” of „objects”, Lefebvre considered 3 classes of perspectives: 1) the spatial practice (the perceived space, called “first spacë”) 2) the representation of space ( the conceived space, called „second space”) and 3) representational spaces (the lived space as is conceptualized by scientists, planners, social engineers or other users). Consequently all the representational spaces include a mapping form and experienced space through its perspective in the frame of use. Among possible representational forms of mapping the space a perceived space through the natural space, there are Mathematical forms to use. All these forms are founded on a physical description of „space”, which is based on a coordinate system for the identification of „places” at which physical and geographical „objects” can be measured or estimated.

In practice most systems in use to describe the space in objective forms are founded on the Mathematical mappings, which are expressed by a variety of different coordinate frames.

Consequently any perception about „space” with a goal either a) to produce or b) to use a particular mapping form aim to support a wide range of applications and perceptions about „space”. These combine a particular mapping form with various types of „information” or „objects” at „places”. Any mutual connection between the meanings of „space” and „place” follows two perspectives depending on the order of given importance about the „place” and about an „object”/„information” at the “place”. This order provides a basic difference between the disciplines of Geography and Mapping in theory.

In practice this difference is not clear through any interconnection of technological „tools” such as Global Positioning Systems (GPS) and Geographical Information Systems (GIS) for the types of geo-referenced „objects”. These „tools” have been developed during the last decades of 20th century and their extensive use in many different applications since only few decades revealed a confusion to all the professional users of „space” and „place” about the complex systems of relationships / characteristics among the represented „places” and among „objects”/„information”. This is caused because of that such structures may receive physical, mathematical, social, political, economic, cultural or personal perspective (Gieryn, 2000). Thus a connection between „places” to mapping forms of the „space” depends on professional perspectives about the use of a geographical part of „space”. A complete representation form about “space” includes a geometrical perspective of description on and /or around the Earth. This is based on the human perception, which involves (i) the location of an observer with respect to the Earth and (ii) a coordinate system, which describes a region of „space”. In practice few types of geometries or topologies are in use to relate the perceptions about „space” to the no material qualifications. Hence any form of a Mathematical representation of „space” in its mappings may support any professional use of „places” where particular qualified properties are of interest. .

All perspectives about the “space” have been initiated from human need: a) a need to know where we are in Universe and b) how the Earth is. These originally philosophical perspectives are used for practical needs to know “where”, “how”, “what” characterize any professional objectives within a particular mapping form. Such a practical need is based on a particular perspective related to the professional goal. There are applications, for which the various existing mapping forms of the Earth and the Universe may be used. These are analog, digital or imaging representations. Consequently they are characterized by formal Mathematical differences, which are implemented through many types of technological “means”.

The involvement of human perception about the dimension of height above Earth is based on the direction of local plumb-lines. The height as a coordinate of “place” is measured along such a natural (curved) line from a zero level surface. Hence the need to express the direction of the gravity force at any “place”, involves the determination of a particular zero level surface connected to an adoption about the shape of the Earth or of a part of horizon. In addition it serves to estimate the impact of a physical “space” (gravity space) to its geometric perception and thus it interconnects Relativity to Newtonian Physics. Two models about the Earth’s shape are in parallel use: 1) a regular and homogenous body and 2) a physical body, with a shape that expresses an approach about the position of a Mean Sea Level (MSL) and represents the horizon. However this horizon can be determined with respect to the regular body! Consequently both Earth’s models are interconnected!

Independently of the used Earth’s model any mapping of space aims to geo-reference many sorts of geographical “objects” or “values”. . Geographical “objects” at different “places” are expressed in various forms or through symbols. Thus any form for positioning any geographical “information” within a particular part of space consists of a Mathematical description about “space” which depends on its physical and also a user’s approach. Also the use of a particular description of the space through any mapping form to support a use depends also on the form and the type of used “information”.

Any variation of the positions/locations or of “information” throughout a mapped part of space may then be expressed by two types of functions: a) those which describe relative or absolute positions through a type of geometry that describes the structure of “space” through geometry and b) functions or values, which determine possible relationships among geographical “information” in context of the very qualified structure of the “space”. Hence all geographical data are described according to subjective or professional perspectives about a conceived geographical space using perceived mapping forms. Consequently any type of mapped “information” varies according to its particular properties, although the perspective about the mapped space is based on geometry/topology properties.

Therefore any estimation of i) new positions or ii) new values of geographical “objects” in a part of space interrelates both perspectives: a) a particular mapping form or topology structure and b) a conceived perspective according to which geographical “objects” are illustrated or recorded in this part of space.

A crucial issue is how a particular contribution of a perspective of space for professional use is described. The description includes: a) The objective mapping or topologic representations and b) any subjective or conceived perspectives, which depend on particular geographical “objects”. Any common description of both perspectives illustrates the dual role of space: as a coordinate system to describe relationships for distances, areas and volumes, and as conceived “reality” to describe possible relationships among the represented geographical “objects”. Much less contribution comes from the impact of the (unknown) interior structure of the Earth upon the Earth’s gravity field, which touches upon only the “curved” structure of gravity space.

Consequently all objective forms to represent the “space” illustrate Mathematical structures, while any subjective or conceived perspective associates to its mental or subjective use. Such a consideration includes a rigorous description of the Earth’s topographic surface. The mapping forms of this surface are used in context of applications in engineering, Space Science and for many other complex practical applications which are supported by a use of Geographical Information Systems.

A first approach is a philosophical perception, about the viewpoint what is defined as space in a mapping discipline or in Science. A second approach is the type of a mapping form (e. g analogue, digital, local, regional or global geographical scale). The importance of an objective mapping form may deteriorate towards subjective or mental perspectives about the “space” in spite that the approaches interrelate.

Soja explains, “I define Third-space as an-Other way of understanding and acting to change the spatiality of the human life, a distinct mode of critical spatial awareness that is appropriate to the new scope and significance being brought about in the rebalanced trialectices of spatiality–historicality–sociality.”(Soja, Edward W. Thirdspace. Malden (Mass.): Blackwell, 1996. Print. p. 61)

The type and the geographical extend of any mapping form about “space” and “place” depend – as said – on the exact objective of an application; hence the precision of any description about a perceived space includes both objective and subjective perspectives. Therefore types of coordinate systems, which describe an objective form of “geometry” of space-time or a topology of spatially depending “information” (user determined) may vary. In practice all are determined by using measures of various physical properties, geographical variables or measures about user defined properties of “space” which are varying in a common space-time continuum.

The dependence of height coordinate through the direction of plumb-line introduces the dualism between the two possible Earth’s models, which describe the “space” through 2.5D, 3D or 4D coordinate systems. Any Mathematical representation with a particular model of space or through its mapped form may then be conceived as a model space. Its mapped form is compared to any empirically observed space or a measured “real” space (a physical space such as gravity space).

The impact of the Earth’s gravity field may vary in its importance according to the particular demands of the needed precision to describe space-time coordinates and also for a variation of the terrain relief as a parameter for some physical and dynamical processes on and around the Earth This is mostly needed in association to dynamical phenomena on or around the Earth and for the establishment of height systems.

Hence any perspective about the “third” space includes an “objective” geometry and is also user dependent (“subjective” to a particular professional objective). In the second case, the topologic structure becomes more important than the “real” geometry. The professional use about the geographical space (e.g. physical space, social space, town-planning space, civil space, economic space) is defined through the type of needed geographical variable’s).

Consequently the data processing for all types of measures within space under a particular description of it includes an estimation of the impact of “real” geometry and “real” physics of space upon a particular geometry structure of a particular model space. Within such a mapping form a estimation about the variation of geographical variables is based on. Thus there are applications for which a very detailed mapping is needed and applications which can be based on quite general forms of mapping. The impact upon any geometric structure of space is composed by: 1) an impact of the gravity field in positioning 2) an impact of all measuring / instrumental errors and/or 3) impacts of any instrumental, environmental origins. Small differences between a “real” geometry and a measured space at various places are expressed through a probability model.

At present the description of the “geometry” of “space” is mostly based on coordinates from a Global Positioning System (GPS), which may be adapted to any other existing local, regional or mapping coordinate frames that have been established in the past. The Earth’s topography stands as the unique physical entity, which keeps a common role in the description of space, either as object of any mapping or as a geographical variable. In fact the topographic relief stands as unique physical interface among three objectives such as: 1) Mapping 2) geographical use of space 3) physical surface for measuring geographical variables.

Users of space are not fully familiar about all the representation forms of mapped space or its Geographical perspectives. This is caused by the practice where they apply computer based algorithms, which are based on various coordinate frames through GPS coordinates, national coordinate systems or positioning and several national Cartographical systems. These associate to several platforms which support Geographical Information Systems (GIS) and several types of computer interfaces, which support a use of different computer based environments.

The content of this analysis is based on a monograph about “space”, which is at stage of advanced preparation. According to the knowledge of its authors it is a first holistic approach about “space” and “space with respect to the Earth” (georeferenced) for engineers, geographers and Earth scientists. The aim of this presentation is to connect the mental and technological perspectives about the use of “space” with the goal to reveal the existing large differences in its conceiving among the variety of professional users. It is composed by four parts: 1) The Philosophical perspective 2) Forms of mappings 3) Geographical and professional objectives 4) The perspective in probability models in context of the spatial distribution of mapped coordinates and geographical “information”.

**On philosophical perspectives**

The transition between a philosophical view-point about “space” to a representational form of it involves two main perspectives: i) The most known – and limited – which relates to the mapping disciplines and ii) a particular one, which is connected to the numerous spatial qualifications of “space” that may characterize any feature, “object” or property which varies within. The second enlarged perspective is subdivided to (i) perspectives upon the type of qualification (physical or human qualification) and to (ii) perspectives related to probability distribution for the particular geographical “objects”.

The mapping disciplines concern to available forms of spatial mapping (e. g printed and electronic maps, satellite imaging, GPS positioning, GIS platforms) used in any context within a geographical or engineering approach. Hence this perspective is founded on physical and mathematical representation approaches in context of mapping forms. This perspective is based on one of the two main viewpoints with regard to the basic definition of space according to Newton or Kant. However as objective forms of representation about space they include in most cases also subjective or user defined features within a region. A starting perspective is connected to the more recent viewpoint of (Soya,1996) and to the earlier (Lefebre,1992) about space.

Soya’s and Lefebvre’s works consider most the geographical conception of space, while Kant’s and Newton’s perceived space is adaptive through different Mathematical forms to its mapping approaches. For Soya the perceived and the conceived space are not separable in the so-called “third space”, which is an empirically observed space. The “first space” represents a philosophy in connection to natural sciences, while the “second space” concerns mainly a conceived perspective, which deals with the mental or ideological properties of space. Both properties are connected – for professional use – close to the geographical perspective of using the “space”, which may be supported by any mapping form. As the perceived physical space to map is based on human perception about the dimension of height; all existing mapping forms include at some extend the impact of the Earth’s gravity field, which affects the geometrical representation through the coordinate systems.

Geometry has been the first Mathematical branch to describe the “first space” much earlier than the invention of coordinate algebra. In fact the invention of coordinate Algebra by Descartes and Fermat to describe and model geometric objects is founded upon the earlier work of Fibonacci who was born as Leonardo Pisano (Sigler, 2202) It was he, who replaced the Latin numbering system and described physical structures with ordered sequences of numbers (Sidney Smith, B.) This perspective involves the Earth’s models, which differ in their features according to the professional aims of their practical use. The “second space” is a rather new field in a frame of art, culture and human disciplines and it concerns most to a Geographical approach.

Although the theorizing about space is recent branch which attracted the cultural theorists (e.g. Prieto, 2012; Gruenbaum, 1973), the conceptual interrelationship between “first space” and “second space” may be illustrated to any general reader or simple user of “space” through the Lefebvre’s tripartite division (Lefebvre, 1992) in particular as a perceived space, which concerns to spatial practice. This a finally conceived space includes both perspectives (mapped and qualified) and also the lived spaces, which are empirically representational spaces; hence the representational spaces carry the complex properties of empirically observed space in association to any “objective” form for a professional use.

Prior importance is given to the foundation of the philosophical perspective about mapping approaches of a perceived space. Such a perspective is expressed in practice by objective mapping form for a description through the coordinate systems according to a particular Mathematical approach, with the use of one of the viewpoints of Newton or Kant.

For these viewpoints a representation form in practice ends up as a perceived 2.5D, 3D or 4D space and thus all mapped forms include the sensed height coordinate which represents a measure of duality between the physical space and its geometry. Newton’s perspective is based on the belief that space (time) are self-existing entities, while Kant claimed in his Critique of Pure Reason that the two entities are only a result of what can be expressed through observations and through the determination of relationships of things. In spite of the existing large conceptual difference between these two perspectives, mapping producers and the users of various mapping forms about space, do not follow consciously any philosophical perspective. They simply apply operational models, which describe a particular approach for parts (or regions) of space with regard to an Earth’s model or to any other professionally conceived model of space. In practice – either for simple spatial mapping or for professional use of a particular mapping form – the form is either an analog or a digital approach of a perceived model space and includes a description about the topographic relief, in addition to the impact of the Earth’s gravity field upon the determination of places.

Quite many Mathematical problems have been involved in the representation of physically complex spaces. Hence each form of mapping describes different structural properties of the space and not all forms are appropriate for a particular professional use. Several users of particular mapping forms about space are concerned more with the conceived/mental space and consider the geo-referenced “places” of qualified features of space as sets of coordinates with respect to an available frame. Such features can be only physical properties, geographical “objects” and other professionally related properties according to the aim of a particular professional objective.

Consequently the perspectives to consider space and place use in common the mapped “products” of space or “means” of technology and Space Science for this purpose, such as satellite imaging, digital maps, GPS coordinates, GIS and – at a large extend – all earlier traditional printed maps and coordinate systems according to nationally used mapping systems. The next paragraph presents a viewpoint about the main features of available mapping forms.

**Available forms of the mapped space**

Any place within a particular description of the space is uniquely described with a coordinate system, which is used for “places” in analog or digital form in association to a particular structural geometric form. Such descriptions concern of the “first space” and for practical use the space is represented by rigorous Mathematical models limited in 2.5D or 3D dimensions. In practice engineers or geographers deal about space within existing mapped forms via some projection of a mathematical model space on a flat surface. For particular objectives the descriptions are simply a background to describe possible relationships among the various geographical “objects” or relationships among conceived properties about the “second space”. Hence any mapped space including a geo-referenced “second space” illustrates a “third space”, which is an empirically observable lived space.

With regard to the “first” space its available mapped forms may vary between traditional printed maps or topography diagrams until the most recent digital illustrations of regions, which result from processing satellite imagery. All this available variety of forms about a mapped space is based on quite many sorts of reference frames, which have been developed in context of an adopted coordinate system.

The existing variety of mapping forms has been developed through the time by following the evolution of Science and Technology in context of modeling the “space” and also in context of the measuring instrumentation or observational possibilities according to physics, history, philosophy. The perspectives meet at the existing representational forms of space.

A first means of mapping geometry has been the Euclidean, which limited the geographical extend for its application due to the Earth’s curved (and irregular) surface to local regions. Hence the described places through Topography (flat Earth) are rather limited in the geographical extend. Consequently the local topographic plans and the Earth’s mapping had to be connected by an Earth’s model and/or its Cartographic projection onto a mapping plane.

This reason caused the demand to be based on a Mathematical representation of the Earth’s shape and of the terrain relief. The Earth’s shape and size and the illustration of the terrain relief were for long the important “objects” of mapping through the use of grids about the 2D geographical coordinates φ, λ and by the use of a dual height system about geometric heights h and/or heights H above an approach of the Mean Sea Level (MSL) as a converted geometric measure of the Earth’s gravitational potential energy. In context of projected geographical coordinate systems φ, λ upon a mapped Earth’s surface there are relevant distortions about meridians, which have impacts on the evaluation of particular geometry elements of the mapped space, depending on the particular Cartographic

projection.

Disciplines such as Topography, Geodesy, Cartography or Satellite Imagery have been developed independently from each other for mapping different sizes of geo-referenced space in the course of time. Existing survey plans, topographic maps or world maps represent the most common “objects” of mapping parts of space, which concern to printed forms of mapping. Not so long ago the accuracy to locate “objects” by using such mappings was limited because of several observational or instrumental restrictions as well as of many difficulties in calculations.

The invention of using the curved geometries and the extension of Newton’s physics by relativity improved the conceived models of space in the context of an ability to apply differential geometry for its description (e.g. Marussi, 1949). However in practice little improvement was achieved due to limitations in the direct measuring of long distances on the ground and within the space “out” of Earth as well as in the measuring between spatial “places’. Also an impact of Earth’s gravity field could be estimated only for raw physical Earth’s models and quite few measures about functions of the gravity field. During the past six decades the available forms of mapping the “first” and “third” space have been tremendously extended in many new forms: Space Science, the invention of laser, the use of radars, satellite imaging are few examples available to producers and users for all kinds of mapping forms about the “first space” and/or the users of a complete “third space”. Such forms are presently available in analog or digital forms of representation. These are produced from satellite imagery, or are continuously provided through technological means such as Google maps, GPS receivers.

Consequently users and producers of mapped forms about space do need expertizing more about the combination of different “products” based on Information Technology than to obtain experience about differences between perceived or conceived “space” or about their modeling. A conversion of all available mapping forms into a unified description of space is founded on GPS coordinates and is presented in GIS platforms, which register “third space” as a fully organized system for geo-referencing geographical “objects” is what is needed to support any particular professional objective for the use of space.

Most of the present users of mapped “third space” deal in practice with “ready to use” software interfaces and other products for the purpose to adapt mapped forms of “first” or “third” space under a common coordinate system or into common data base structures.

**Geographical and professional perspectives**

Any mapped form of a “first space” may be used to place “objects” within representational spaces (“third space”) and to accomplish particular needs for professional applications. These may be classified in three groups as: a) Geographical b) Scientific, Engineering and of c) general interest. For any of them the importance of “place” varies according to the goal of using the space. The range of variation is qualitative (in context of the professional use) and quantitative (in context of the accuracy of coordinates within a used mapped form of space).

Hence the suitable representation forms of space may vary according to their use for which the perspectives about the importance of a place and of the resolved details of the terrain relief may vary also according to the actual professional goal.

In broad sense, for applications within groups (a) and (c) the size of representation space may vary between local, regional and global geographical extend, while for applications of group (b) the size of a region rarely exceeds a regional geographical extend with mapping scales to vary between 1:100 to 1: 5000 Another perspective is a classification of professional applications between groups (a), (c) and (b) regarding the importance of the mapping with respect to the importance about the kind of the located “objects” within a particular mapping form. For applications of group (b) the existing mapping forms of space may have higher or at least equal importance than the illustrated “objects”; hence the accuracy of coordinates of location and the accuracy of the observable “objects” receive a variable importance.

In contrary for the applications of groups (a) and (c) the kind of “objects” has higher importance than the used mapping form of space, which may remain raw and simple. In particular the geographical space is named according to the professional goal in which an application belongs (e. g Physical Geography, Social Geography, Economical Geography, Culture Geography).

Finally a mapped geographical region for scientific or for engineering use deserves high or medium positioning accuracy all-over the mapped region, whatever is its size. Usually this demand is coupled with the need to achieve a consistency about the representation of terrain relief features, which can be resolved with a particular mapping form in context of the relief as a parameter. This need associates to time dependent dynamical processes such as weather forecast, evolution of Earth’s dynamical activities etc.

After all the professional perspectives to characterize the space (civil space, agricultural space, town planning space, social space etc.) can be named after a professional objective (e.g. civil space, agricultural space, town planning space etc.)

**The perspective in probability models**

In professional applications the “space” stands as either a variable or a parameter, and all the users meet with an error optimization. As “error” one defines small discrepancies between any model and an empirically observable situation In the case of representational spaces, there are two different perspectives in context of two mathematical terms “resolution” and “accuracy”. These terms illustrate the variation of residual values (discrepancies) between a description form of “space” and/or its empirical observable features (geographical “objects”) throughout a used mapping form. The accuracy of a “place” through coordinates is measured in context to a particular mapping form. The resolution of the mapped “objects” (including the variation of terrain relief) is determined through the geometrically closest distance of space or the size of the smallest pixel, which contains observational “information” in context to the variable geographical “object”. Both terms concern to empirically observable “space” or to the mapping model itself with regard to their rigorous description.

Consequently any residual small quantity in a context of coordinates and/or geographical “objects” is a member of a probability model. The models carry different probabilistic laws:

1) a Gauss model about only the random measuring errors;

2) a stochastic model about all other possible errors about the model’s parameters;

3) a variation of the illustrated geographical “objects”, which concerns to the sort of the variable object.

Hence in practical applications of using the “space”, there is an appropriate probabilistic model about such residuals. This is the reason why so many probabilistic models have been proposed in context of various applications in Earth and Space disciplines, Geography, Engineering etc.

The fact that any form of Mathematical description about any model of “space” provides a mapping form as an optimized solution of a direct and inverse problem for spatial representation (due to the physical nature of the space) leads to adopt probability models for the discrepancies. These are mostly expressed by linearized forms of two term probability models. A brief explanation and a basic foundation to illustrate a basic approach to this topic is the basic definition about the “space”. One may follow its definition in relativistic Physics as “time-space continuum” because through this definition all ranges of accuracy about the coordinates may be included. This “continuum” is conceived – as previously mentioned – through the two principal perspectives with respect to the philosophical approach of the analytic form of the representation of space. The first is Newton’s perspective; the space is an intuited reality, while the second follows Kant’s approach, which defines as “space” any determination of relationships among “objects” (including thus the coordinate set).

In practice in all professional uses there are associated standard probabilistic models about the optimization of discrepancies. These models are based on the “correctness” of relationships among “objects” within a mapped part of “space”. The term of probability model about the parameters of the model “space” concerns to stochastic variables, while the term, which describes the measurement errors, follows a Gauss distribution. This is only a quite general description because there exist several perspectives how to treat rigorously the linear combination between these two terms.

**A concluding remark**

Through the previous presentation about the various perspectives to consider the space (perceived, conceived physical, geographical) it has been evident that in applications to solve professional problems, the needed demands of accuracy about “places” with respect to any coordinate frame may receive higher or equal importance than the accuracy of measures about any “object” located at a place or of measures about a particular qualification that characterizes a “place”. This class of problems is an object of Earth disciplines (e. g mapping the space or an investigation about dynamical processes related to the Earth’s) or of geo-referenced processes (e. g climate and weather forecast, water and sea motions)

For another class of professional problems the spatial mapping forms simply are used to support the geo-referencing of geographical “objects” although the space may receive also conceptual properties. Hence the importance about the accuracy of a “place” through positioning coordinates is secondary comparing to the need of having an accurate measure about “objects” at particular places. For this class the type of physical or geographical qualifications about the “space” characterizes all subjective, ideological or user-determined criteria in its use.

Consequently both terms “space” and “place” may receive quite various meanings among the professional users. The meanings comply with the particular objective within the discipline in which the professional application is classified.

In spite of the philosophical perspective about space in sociology or Mathematics, there is a quite extended use about “space” and “place” among many practical problems and there are varying demands about the accuracy of “places”.

It is recommended that the numerous experts and users of present technological products, as GPS, GIS, computer interfaces and other “products” from Information Technology, to maintain a close professional contact with the final users of their data processing results. The final users of a particular representation about “space” are those, who can provide an exact answer about the rates of the needed accuracy and resolution of the spatial mapping forms in accordance with the demands of their own objective.

**Used Literature**

Abbott, A. (1997): Of Time and Space: The Contemporary Relevance of the Chicago School. (Social Forces Vol. 75, No. 4 pp. 1149–1182)

Gieryn,T. (2000): A Space for Place in Sociology

(Annual Review of Sociology Vol. 26 pp. 463–496)

Goodchild, M. F.( 2004): GIScience, Geography, Form, and Process.

(Annals of the American Association of Geographers Vol.94 No.4 pp. 709–714.)

Gruenbaum, A. (1973) Philosophical problems of space and time (Boston Studies in the Philosophy of Science Vol.12 Springer Verlag Berlin-Heidelberg London)

Lefebrve,H. (1992): The production of space ( Wiley-Blackwell, Oxford pp.464)

Marussi, A. (1949): Fondements de la Geodesie differentielle absolue du champs potential terrestre (Bulletin Geodesiqu Vol. 14 pp. 411-439)

Prieto, E. (2012): Literature, Geography and the Postmodern poetics of place (Palgrave Macmillan, e-book)

Sidney Smith, B. (retrieved 23.1.2016): Fibonacci sequence. http://platonicrealms.com/encyclopedia/Fibonacci-sequence

Sigler,L.E. (2202): Fibonacci’s Liber Abaci: Translation into Modern English of Leonardo Pisano’s Book of Calculation (Springer Verlag, Berlin-Heidelberg-London)

Soja, E. W. (1996): Thirdspace (Blackwell, Cambridge – Massachusetts pp.61)

*This presentation stands as a first release of the content of a Monography in advanced preparation about the perspectives of the space-time for professional users. Thanks are given to Gabor Bartha, who helped out the present editing. M. Doufexopoulou*

* Athens, 5.2.2016
*