Gradial: Or the Unreasonable Network

The reasonable network adapts itself to the world; the unreasonable one persists in trying to adapt the world to itself. Therefore all progress depends on the unreasonable network.1

The physical location of network infrastructure is one of the most permanent decisions cities make. The Cardo Maximus in the old city of Jerusalem is still a main north-south shopping street, constructed when Emporer Hadrian rebuilt the city in the 130s CE.

A street right-of-way, once created is seldom destroyed. A segment of that infrastructure is designed to be optimal at a moment of time, with a particular land use (either the realized development of today or an imagined place of tomorrow), enmeshed within a particular network context of all the other nodes and links, compatible with a particular technology. That it functions at all when land use, networks, and technologies change radically, as they do over centuries, is testament to the general flexibility inherent in networks. But the implication is that if it is optimal for the world in which it was designed, it is unlikely to be optimal as that world changes.

Some adaptations do occur. Streets designed for horses were adapted for streetcars (trams) and bicycles and cars and buses and pedestrians.

Still, it may be the best that can be done. Embedded infrastructure, the dictionary example of sunk costs,2 cannot adapt much to the world around them. Instead we expect the world to adapt to the infrastructure.

Following Shaw, we might say such infrastructures are `unreasonable’, in that they cannot be reasoned with.

Many, if not most, planned cities have been laid out with a network of streets “with the sombre sadness of right-angles,” as Jules Verne, quoting Victor Hugo, described the American grid in Salt Lake City, of streets at 90-degree angles to each other, in his classic road trip story: Around the World in 80 Days. Street grids don’t plan themselves, so while all street grids were planned, not all plans result in street grids.

Organically developed3 cities are often more naturalistic, radial cities, with streets feeding the city from the hinterlands, allowing more than 4-directions of entry. All roads lead to Rome, as the saying goes. The Romans themselves were a bit adverse to this organic radial system once they got their own growth machine going, laying out encampments and new settlements on the grid system. The radial system leading to and from the town would bend once it reached the town gates. But as cities themselves were generally not conceived of as whole, but rather themselves emerged, often as conurbations of smaller settlements, towns, and villages, there are often radial webs centered on town A overlapping radial webs centered on town B. Rome was famously built on seven hills, which can be read as meaning Rome is a conurbation of seven earlier villages. (See Elements of Access, Chapter 3.3)

Each of these networks typologies has its advantages and disadvantages.

Washington DC Metro. The center is a space, not a point. A `triangle’ is formed by L’Enfant Plaza (Yellow/Green with Orange/Blue/Silver), Metro Center (Red with Orange/Blue/Silver), and Gallery Place (Red with Yellow/Green)


We observe that radial networks are optimal to maximize access for many-to-one types of movements (suburbs to central city). So rail transit networks, which serve the high loads demanded by, and making possible, high density city centers tend toward being radial. But when they are large they are usually not so radial that all the branches meet at one junction. From a network design perspective, intersecting more than two lines at a station can lead to other types of conflicts, and many systems are designed with triangular center to avoid overloading a single transfer station. Washington DC’s largely radial Metrorail system, shown in  the first figure, illustrates this design. Cities are spaces, not points.

In contrast, the 90-degree grid is reasonably well-suited to maximize access for scattered trips, what network analysts would call a many-to-many pattern. We see this especially in dispersed point-to-point (suburb to suburb, within city to within city) flows that are enabled by and reinforce the grid. This is the network for the automobile. The Los Angeles freeway grid, the famous Milton Keynes arterial grid, and numerous other  late twentieth century cities have been designed in a grid-like way (though not so orthogonal that Victor Hugo would object). Even though the topology is not as efficient from a distance perspective as say a 60-degree mesh, by remaining out of the city core it can keep speeds higher.

But in response to the landscape that emerged with the automobile, transit planners like Jarrett Walker (2012) have called for more grid-like transit networks, so people can move, via public transport, from suburb to suburb without going through the city centre. This is relatively easy to reconfigure for buses, the very definition of  mobile capital, while very difficult for the more capital intensive rail networks with their physically embedded infrastructure.

Still, core radial lines will always be the backbone of transit systems so long as at least one important center justifies a disproportionate amount of service.

So how can we grid the radial, or square the circle, so to speak?

A better network topology might be the 60-degree, hexagonal pattern. (Ben Joseph 2000) But remaking street grids for existing cities is tough-going, as property rights are well established, and requires efforts like those of Haussmann in 19th century Paris. (Willms 1997).

Possible system layouts: (a) hub-and-spoke; (b) grid; (c) hybrid. Source: Figure 1 in Daganzo (2010)

Instead, we have overlapping network topologies, ideally which are grade-separated in some fashion, so trains are radial and don’t intersect streets or motorways, and bus services can be more grid-like, and rapid or express bus networks serve the market niche in-between.

Thus the original street level networks are still topologically grids, but the services running on that grid, while still largely parallel and perpendicular, are compressed near the center, so the bus lines, for instance, bend towards the center, as illustrated in the second figure. The regulatory layer of through streets for automobiles may be constructed to defer to the orientation of bus services.

There are no optimal network configurations independent of the enveloping land use pattern or the technological regime. Similarly there are no optimal land use allocations independent of the network pattern or technology. Finally, there is no optimal mode independent of the land use or network. All three of these systems are interlocking. Moving one requires adapting the others.

The unreasonable network forces the land use pattern to adapt to it, such that relocating network elements is more costly than keeping them in place. Similarly, in many ways the network, designed for a given technology, is very hard to adapt to a different technology. That doesn’t stop people and cities from trying, the misfit we see with the automobile in the urban core is the product of failing to acknowledge this unreasonableness. But as the number of European cities restricting cars in the city center are showing, the unreasonable network wins out over technology too.

The Grid/Radial Gradial network is also Gradual. These systems seldom change all-at-once, instead they gradually evolve over decades, centuries, and millenia.


1. This is an adaptation of a famous George Bernard Shaw quote.

The reasonable man adapts himself to the world; the  unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.

2. The economist’s adage that “sunk costs are sunk” means that once something has been built, and that money spent, it no longer factors into benefit-cost analysis about how prospective decisions should be made, except to the extent it changes the costs of various options. Logically, you shouldn’t go to a concert just because you bought tickets if you don’t want to go, though if you are considering going to a concert or a bookstore after you bought the tickets, you don’t need to account for paying for the tickets again. You might also consider the `opportunity cost’ of going as the loss from not scalping the tickets. You shouldn’t throw good money after bad. But the sunk infrastructure cannot be unbuilt.

3. Organic development is often largely systematically unplanned, though obviously some degree of planning often goes into laying out a street, even if it is disjoint from any other decisions. When we think of `planning,’ we are generally referring to longer-term more strategic type spatial plans, that consider interactions between prospective decisions, rather than short-term tactical plans that optimize a single decision alone decontextualized from the rest of the city.