Where’s Waldo? What’s Tobler? Why’s it a law?

Every geographer and geographic information scientist has heard the phrase “everything is related to everything else, but near things are more related than distant things” at one point in his or her career. Some have even had to endure the determined repetition of this one phrase in nigh every lecture, every workshop, every colloquium, the single words chiselling away at our long-term memory to sculpt our perception of the underlying principles of geography. Waldo Tobler’s “first law of geography” is just so intuitive and simple that it makes sense, period! But is it really that intuitive? Does it merit the term law?

Everything is related to everything else

This seems trivial but let’s think about the implications for a second. In essence, this implies that no matter the area of interest, no matter the scale of analyses, no matter the tools used, the different dimensions of a given circumstance are entangled, are related. This leads to the complex network of interactions that constitute our world. This is of particular importance since this calls for careful consideration when trying to isolate individual variables or when trying to correlate two sets of data. In my opinion, it is important to emphasise this omnipresent net of entangled relatedness, especially since analysing these interactions is one of the major contributions of the geographic discipline to the scientific community.

Near things are more related than distant things”

Seems intuitive and kind of catchy. One simple sentence being at the core of a myriad of spatial interpolation algorithms and spatial statistics. Especially questions of spatial autocorrelations become relevant where Moran’s I might ring a bell. This is of particular importance seeing the growing number of openly available spatial datasets resulting in a frenzy of geographers wildly correlating various variables and building spatial models trying to explain some snippet of reality.

However, despite seeing all the valuable contributions this one phrase has brought to the discipline of geography, in particular geographic information science, we must also have a closer look at the dangers of oversimplifying the inherently complex networks of reality. We live in a world with borders and boundaries, more than we think, and this is exactly where I argue Tobler’s law breaks down.

This leads to a major paradox, that Tobler’s Law is always true and at the same time always false for any and every given location. It all depends on scale and focus. For the fun of it, let’s call this Schrödinger’s Map on which for any given location, the first law of geography is true and false as long as we do not define the scale of investigation.

Schrödinger’s cat is not amused

Let me give you an example: if we take a few water molecules, the more distant hydrogen atoms of different water molecules are probably more related to each other than the closer oxygen molecules. But if we zoom out just a bit and look at a glass of water, well, if we are still interested in the water molecules then yes, of course, the water molecules are more related with each other than the glass which prevents them from spilling onto my desk. But then again, if we change the scale once more, the water in the glass sitting on my office desk is probably more related to the water in the lake on the other side of town than to the keyboard I’m typing on, would you agree?

These boundaries are not only limited to physical features but also tend to pop up all over the place. Think of the various diasporas around the globe, think of china-town or little Italy. Especially with the increased ability of humans to move around in the world and new forms of technology such as mobile phones, Skype, Twitch and YouTube the concepts of near and far seem to be dissolving into questions of global interactions where relating near and far things seems all the more controversial.

Constant dropping wears away a stone

Maybe I just have a problem with the term “law”. The laws of thermodynamics, those are, if anything, what I consider laws. Tobler’s Law, in my humble opinion, is less a law but more a general guideline which needs careful consideration case by case. Waldo Tobler was a great scientist who has made major contributions to the discipline of geography in general and geographic information science in particular. I am not trying to say otherwise! All I suggest is to consider the phrase “everything is related to everything else, but near things are more related than distant things” more as a guiding principle of geography and less as a bounded law. In my opinion, Tobler’s first law of geography is simply put spatial autocorrelation broken down into its essence, simple and understandable.

Further Reading:

Thanks @rwesterh87 and @giva_uzh for the links

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