One of the motivations for the use of such partitionings is their ‘objectivity’. It is also asserted that there are advantages for analysis purposes over the irregular spatial polygons defined by political jurisdictions.

• There is no doubt that there are notational simplifications; one can index a cell of an array in the same fashion as in matrix algebra.
• The major advantage however is pedagogical, and results from the fact that in such a scheme every country in the world has exactly the same number of neighbors. The analytical results can be extended to the more realistic variable number-of-neighbors case but the insight is more easily gained in the cellular case.

Abstract: This paper discusses empirical and analytical rules to select a suitable grid resolution for output maps and based on the inherent properties of the input data. The choice of grid resolution was related with the cartographic and statistical concepts: scale, computer processing power, positional accuracy, size of delineations, inspection density, spatial autocorrelation structure and complexity of terrain. These were further related with the concepts from the general statistics and information theory such as Nyquist frequency concept from signal processing and equations to estimate the probability density function. Selection of grid resolution was demonstrated using four datasets: (1) GPS positioning data— the grid resolution was related to the area of circle described by the error radius, (2) map of agricultural plots—the grid resolution was related to the size of smallest and narrowest plots, (3) point dataset from soil mapping—the grid resolution was related to the inspection density, nugget variation and range of spatial autocorrelation and (4) contour map used for production of digital elevation model—the grid resolution was related with the spacing between the contour lines i.e. complexity of terrain. It was concluded that no ideal grid resolution exists, but rather a range of suitable resolutions. One should at least try to avoid using resolutions that do not comply with the effective scale or inherent properties of the input dataset. Three standard grid resolutions for output maps were finally recommended: (a) the coarsest legible grid resolution—this is the largest resolution that we should use in order to respect the scale of work and properties of a dataset; (b) the finest legible grid resolution—this is the smallest grid resolution that represents 95% of spatial objects or topography; and © recommended grid resolution—a compromise between the two. Objective procedures to derive the true optimal grid resolution that maximizes the predictive capabilities or information content of a map are further discussed. This methodology can now be integrated within a GIS package to help inexperienced users select a suitable grid resolution without doing extensive data preprocessing.

What makes it [raster structure] especially attractive is that most of the technical characteristics are controlled by a single measure: grid resolution, expressed as ground resolution in meters. The enlargement of grid resolution leads to aggregation or upscaling and decrease of grid resolution leads to disaggregation or downscaling. As grid becomes coarser, the overall information content in the map will progressively decrease and vice versa.

Tente imaginar alguma coisa que existe fora do tempo e que não tem extensão no espaço. A mente humana não pode produzir tal idéia. Nada pode ser percebido excepto através destas formas, e os limites da física são os limites da estrutura fundamental da mente. Assim, já vemos que não podemos conhecer fora do espaço e do tempo.

Mas além das formas da sensibilidade, Kant vai nos dizer que há também o entendimento, que seria uma faculdade da razão. O entendimento nos fornece as categorias com as quais podemos operar as sínteses do diverso da experiência.