What is Tobler’s first law of geography?

What is Tobler’s first law of geography?

“Everything is related to everything else, but near things are more related than distant things.”

The first law of geography was developed by Waldo Tobler in 1970.

This observation that Tobler made is closely related to the ‘Law of Universal Gravitation’ and the ‘Law of Demand’. The concept was first applied by Tobler to urban growth systems. It was not popularly received when it was first published.  

Source- Geography


The Earth’s surface is almost infinitely complex, and it would be impossible to characterize even a small part of it. Instead, geographers and others often indulge in spatial sampling, selecting a comparatively small number of locations. To collect data, and assuming that the gaps between such observations can somehow be filled.

If every location had characteristics that were completely independent of those of its nearby locations, this would clearly be impossible. But in reality, characteristics tend to vary fairly slowly over the Earth’s surface, such that the characteristics at one location tend to be similar to those at nearby locations. Of course, what exactly is meant by “nearby” and “similar” remains to be seen, and depends on the particular characteristics of interest. Weather, for example, tends to vary very little over distances less than 1km, but it varies greatly over distances of 1000km; soils, on the other hand, can vary substantially over distances as short as 10m.

Tobler originally stated the First Law (TFL) in the form “All things are related, but nearby things are more related than distant things”. The important message is in the second part, and because “related” carries unnecessary connotations of causality TFL is better stated as TFL“nearby things are more similar than distant things”. thus forms the basis of the process known as spatial interpolation or the formal process by which the gaps produced by spatial sampling can be filled.

One way to gain insight into is the significance of TFL through a simple thought experiment. In a world in which TFL was absent nearby places would be as different as distant places. It would be necessary to step only a vanishingly small distance away from one’s current location to encounter the full range of conditions on the Earth’s surface, from the height of Mount Everest to the depths of the Marianas Trench, and from the summer temperatures of Death Valley to the winter temperatures of the South Pole. A world without TFL would be an impossible world from the perspective of human existence.  

Several methods have been devised for characterizing TFL and the property it addresses, which is known generally as spatial dependence. The field of geostatistics, also known as the theory of regionalized variables, was devised by statisticians as a way of formalizing the principle known informally as TFL, and of optimizing the process of spatial interpolation that relies on it. The variogram (or more correctly semivariogram) is defined as a function describing the increase of variation in a phenomenon with increasing distance. In the absence of TFL variation over short distances is as large as variation over long distances, and the variogram is flat. With phenomena that obey TFL, however, variation is generally observed to rise monotonically until it reaches a maximum value known as the sill, at a distance known as the phenomenon’s range.

Spatial dependence can be described as the most important property of any spatial pattern. It can be useful in distinguishing the impacts of hypothesized processes. Since the presence of strong, positive spatial dependence at a particular scale implies that the processes causing the phenomenon are similarly persistent at that scale. Smoothing processes such as glaciation and diffusion processes such as migration both result in patterns with strongly positive spatial dependence. While sharpening processes such as economic competition result in the opposite. But this kind of inference is scarcely sufficient to explain the growth of interest in TFL. In recent years, which relies instead on much more utilitarian arguments concerned with GIS (A geographic system of information) design.


In a world, without TFL every point’s characteristics would bear no relationship to those of its neighbors. In order to represent any geographic data set in a GIS, it would be necessary to characterize every point. The result would be an impossibly large data set. TFL allows spatial patterns to be captured by sampling. Since spatial interpolation can always be used to fill in the gaps.

TFL is the basis on which all contour maps are made. The basis on which each day’s weather maps are compiled from point data. It allows large areas to be characterized as homogeneous. It is represented in a GIS as polygons rather than as multitudes of points, achieving massive degrees of data compression. In other words, TFL is the basis of the armory of tricks. With which GIS databases represent what is in principle an infinitely complex world.

The specific details of any phenomenon’s spatial behavior, as represented for example in its variogram. They are the basis on which the density of sampling is determined. Since points spaced closer together than the range of the phenomenon. They will yield observations that are to some degree redundant. It is also the basis for such parameters of GIS representation as pixel size, minimum mapping unit, and spatial resolution. No wonder, then, that the growth of GIS stimulated a renewed interest in TFL and its implications.

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