Transportist: Adopting the Concept of Entanglement in Spatial Interaction
Updating our appropriations
Waldo Tobler, (a student of Bill Garrison) famously said
"Everything is related to everything else, but near things are more related than distant things."
This has come to be known as The First Law of Geography.12
Transport geography and modeling have long adopted the “gravity model” metaphor from classical (Newtonian) Physics. [I won’t do a full history of gravity models today, but note that it goes back to the 1800s and has been rediscovered multiple times in geography].
Modern physics has brought us the idea of entanglement, or what Einstein derided as “spooky action at a distance”. I don’t understand quantum mechanics, (and neither does anyone else), but I will adopt the metaphor.
Are there places that are distant, and are more connected than a simple gravity model or proximity relationship would predict? And the answer, of course, is yes. The reason here is not so much that people are continuous “fields”, but instead a much more discrete answer that people belong to social networks.
There are ties due to migration, for instance, which means Australia is still closer in some ways to the United Kingdom than to its immediate neighbours Papua New Guinea or Indonesia despite Indonesia’s higher population.
Similarly, there are ethnic neighbourhoods in any world-class city. The relationships (trade, travel, friendships, familial) between the various “Chinatowns” in Sydney (including Hurstville, Burwood, Eastwood, Chatswood, and Chinatown/Haymarket among others) are greater than between each of those neighbourhoods and their nearer neighbours.
There are also ties due to employment, so people are more likely to be neighbours of people they work with than a random model would predict, as Nebiyou Tilahun showed in his dissertation.3
We could specify a gravity model for people of Chinese heritage in Sydney, and it would be statistically significant. But there are also many hidden networks. So while we have this first law, we also need to temper it with knowledge of relationships that tie beyond just proximity.
There are numerous ways to model this.
If we think about the general form of the accessibility measure (A_{i}):4
C_{ij} is the cost
O_{j} is the opportunity
g,f are functions.
We want to specify a g(O_{j}) that selects for affinity. Each individual has their own weighting of opportunities, their g function is personalised, so maybe g_{i} which measures the social distance between the individual and the opportunities they care about, or are aware of, rather than the physical distance? How attractive is the opportunity personally (aside from network cost information)? [We of course can’t and probably shouldn’t forecast this.]
The g function could even be a place rank-ish type of function, which weights the opportunities (connected places) partaken by their Social Network more strongly than the connections in general.
For instance, in a recent paper, we use a correlation matrix as a spatial weight matrix, rather than a simple adjacency or traditional accessibility matrix, to better explain changes in number of jobs and workers in blocks in Minneapolis.5
A second note is that geography is place-based. Transport analysis is network-based. Some links are complements (upstream and downstream) … traffic on one is highly positively related to traffic on another. Some links are competitors (parallel links), traffic on one is inversely related to traffic on the other, after controlling for total demand.
“Every link is related to every other link, but complementary links are more positively related, and substitute links are more negatively related than distant links."
would be a somewhat less-than-elegant way of reframing the First Law of Geography for Networks.
Coming full circle, if there are places that are entangled by social relations beyond what would be explained by distance alone, are there links that are entangled? Well of course. In addition to an analytical or theoretical approach, where the weights between links are specified by the analysis, empirically a Network Weight Matrix (implemented as a network element correlation matrix) can show the relationship between links, and this can be used for short-term traffic forecasting6 or for the prediction of network evolution (for instance of tram networks)7.
Just as the classical physics of Newton shaped transport thinking in the mid 20th century, a few decades after it fell out of fashion, we might now start thinking about appropriating other more modern physics ideas and analogising from them to build more realistic transport analysis tools.
Tobler W., (1970) "A computer movie simulating urban growth in the Detroit region". Economic Geography, 46(Supplement): 234–240.
There is a of course a discussion on the Second Law of Geography, but nothing has achieved the same standing.
Tilahun, Nebiyou and David Levinson (2011) Work and Home Location: Possible Role of Social Networks. Transportation Research part A 45(40) 323-331. [doi]
What, equations in my newsletter? Even more, LaTeX typeset equations in my newsletter!
Li, Manman, Cui, M., and Levinson, D. (2023) Interaction between development intensity: An evaluation of alternative spatial weight matrices Urban Science 7(1), 22. [doi]
Ermagun, Alireza, and Levinson, D. (2019) Spatiotemporal Short-term Traffic Forecasting using the Network Weight Matrix and Systematic Detrending Transportation Research part C. 104, 38-52. [doi]
Ermagun, Alireza, and Levinson, D. (2019) Development and Application of the Network Weight Matrix to Predict Traffic Flow for Congested and Uncongested Conditions. Environment and Planning B: Urban Analytics and City Science.
46(9) 1684–1705 [doi]
Ermagun, Alireza, and Levinson, D. (2018) An Introduction to the Network Weight Matrix. Geographical Analysis. 50(1), 76–96. [doi]