Tobler’s Law: Critical Questions to Ask

Tobler’s first law of geography (TFL), that near things are more related to each other than distant things*, is employed in spatial models used to demonstrate, explain, and predict phenomena. The law is employed when designing migration and trip models, population center growth patterns, meme spread, and causes of disease, to name a few.

In its essence, TFL is the basis of most spatial analytical procedures. TFL, while not claimed to be immutable fact, is often considered to be close to it. Indeed, TFL is, in general, a concept that has wide applicability and usefulness.

However, not much has been said with regard to disputing what seems to be a unanimously agreed-upon viewpoint, and perhaps there are some important questions that arise if we take the stance of Devil’s advocate. Sometimes when we universally accept a model, missing pieces are never discovered and even downright wrong implications are held as true.

To draw a parallel with the financial markets, options markets are occasionally “underpriced” since they presuppose that prices for commodities or stocks or currencies hover around the most recent prices in a bell-curve like behavior. Extreme price changes are not priced into the model** underlying options prices, and therefore offer opportunities for someone who anticipates an extreme price change in the future (such as when a firm comes under investigation, or a key product is recalled.) Some hedge funds have made large sums of money taking advantage of this fact.

Getting back to Tobler’s first law, it would be prudent to allow ourselves to ask certain questions of it in order to better ascertain the risks we are exposing ourselves to when classifying the world in such a way–just as it is good to have a thorough understanding of the risks and opportunities in the options market before betting the farm.

Using an example from ecology, one might apply TFL to a model and incorrectly assume that nearby ecosystems are more related to one another than far-away ecosystems. In a hyper-local model, one could be mostly right in this assumption. However, at some point trouble is encountered, such as when the goegraphy changes abruptly via a mountain range, stream corridor, or seashore, for example. Nearshore ecology is more likely to be similar to nearshore ecology elsewhere in a country than it is to the nearby backshore ecology, for example.

Of course, Tobler himself has stated that TFL is not necessarily true in every instance.*** The questions we should be asking are:

1. How can TFL fail us?
2. What could TFL miss?
3. If TFL fails us or obscures an important truth, what would be the implications?
4. Would these implications be inconsequential or very large?

* There’s another part to the law that states that “everything is related to everything else”, which is not addressed in this post.
** See the Black-Scholes model, which is still used, but which does not allow for extreme changes in price that can actually occur.
*** Sui, Tobler’s First Law of Geography, a big idea for a small world?

  1. #1 by gBeth on December 30, 2012 - 10:31 am

    Good questions. I’ve read that the concept does work for things like wikidpedia article relationships (there was a study somewhere…) but the big problem is that it really isn’t a law at all. A law has to be true all the time and we know there are exceptions.

  2. #2 by Gretchen on December 30, 2012 - 12:37 pm

    New twitter comments:
    @thisismikep these questions can be asked because Tobler’s law is not a law but a variable to control in many models.

    @justinholman Good post but I think you need to address spatial scale and resolution. TFL may only fail due to data limitations.

    @PATCmaps TFL does not apply to cyberspace. Or does it?

  3. #3 by CindyF on December 30, 2012 - 1:33 pm

    This has me thinking of scale of spatial data. Does this always apply when we go down to atomic level or beyond to global analysis? With only basic chemistry years ago, seems that it might not work there. In grain of sand, for example, the closest thing would be space, not other grain of sand, right? In planets, space, is closest not other planet? So wouldn’t this “law” be limited in scope? Come on physicists, set me straight! :)

Comments are closed.