Intro

Perhaps the city is the most complex machine created by humans. The roads, houses, water, and energy are well connected, and a great number of humans gather here to take care of their homes. What’s surprising is that the creation of a city like this continues to evolve with time, rising and falling, rather than being created as a whole through a single plan. Of course, there are cities that are made into planned cities from the start, but it is actually almost impossible to control the process of changing even those cities. It’s as if at birth, the shape of the brain is similar to that chosen form through the evolution of a great number of years, but as we grow up, the connections and functions of the brain continue to change little by little, so that everyone has a completely different individuality. In that respect, cities and the brains of humans are quite similar.

Then, I recently read a paper that did a serious study of similarities between the brain and the city. It is the paper published by Mark Changizi and Marc Destefano in 2009 titled “Common Scaling Laws for City Highway Systems and the Mammalian Neocortex”.

Although the analysis was limited to the city’s highway system, it is an interesting paper that figures out the similarities between the brain of mammals and the city’s highway system. While this may be a coincidence, it is more reasonable to assume that this kind of similarity in a system of complexity may have occurred rather than merely by chance, as the structure represented by nerves and roads evolves to work an efficiently similar way.

Why is the brain and road infrastructure similar?

Let’s first take a brief look at the main components of the brain and their roles. The neocortex of mammals, including the human brain, consists of what is called a grey matter. The gray matter, consisting of the cell body of nerve cells, has short dendrites and long axon, like tentacles, to connect with other nerve cells, and when the dendrites of various neurons are gathered together and formed in bundles, white roads seem to connect to parts of the brain. This is called white matter. By quantitatively dissecting the brain, we can measure the volume of these gray matter or white matter, the number of nerve cells and synapses, the surface area, the diameter of the axon, etc. The relationship between these figures is somewhat consistent, even for different mammals. For example, if the area of the neocortex is S, the number of total nerve cells N increases by 0.75 square of S and multiplied by a constant b. It is not important that each of these figures is important, but that there is some mathematical relationship between the surface area of the brain and the entire nerve cell of the brain. A number of similar relationships are found, such as the number and surface area of synapses in the brain, the number of synapses per nerve cell, the surface area, the average diameter of the axon and the average speed of the data transmitted through the axon. Perhaps these figures are the most efficient proportion of the brain’s evolution into the cerebrum in the form of thin plates. In other words, the least energy needed to sustain this connection while maintaining a high level of interconnectivity has been selected through evolution.

The recent surge in interest in network science in research on urban roads is no different from this. In fact, the connection structure of the Internet is not much different. When you think about the Internet, you call it the Information Highway. Researchers like Marco Dorigo studied the problem of finding the shortest route for ants from their nests to food through a kind of swarm intelligence algorithm, which gives similar implications. Ants solve this problem by secreting a chemical called pheromone, and once they find food, they back home and drop pheromones so that other ants can track it. The more ants gathering after detecting pheromones, the more pheromones dropped, and the more clear the way for ants to return home. Pheromone is volatile and disappears quickly, so once all the food is collected, there is no way out. This volatility makes shorter paths more attractive than longer ones, and naturally shorter ones are chosen. In 1992, Dr. Dorigo’s group developed an algorithm called the ACO (Ant Colony Optimization), which began to help solve various problems by simulating a group of ants roaming around by spraying pheromones in certain areas. There is also a PSO (Particle Swarm Optimization), invented by James Kennedy and Russell Eberhart in the mid-1990s. Feeding the balconies with birds, the first bird will find it and fly, and soon a large flock of birds will gather. They developed the algorithm by looking at the closest associates of artificial birds who randomly flew around and found food. These simple ideas are now applied to a number of areas, including video analysis, antenna design, and even diagnostic systems in medicine and machine breakdown analysis.

If you think about it this way, it is not easy to first think about, but very persuasive, that Mark Changizi and Mark Destefano in 2009 found a big commonality between the city’s highways and brain neurons. Neurons transfer information in the form of electrical signals to different locations in the brain and highways serve as an infrastructure for shipping people and objects from place to place in cities. Just as each neuron plays a key role in the overall functioning of the human brain, so does the role of the road in the city. Not only the simple connection structure but also the way it works, there are many similarities. The city’s road system is revamped in various ways for political and economic reasons, and the signal system is also changed. Sometimes bus-only lanes are installed and subways are opened. As such, city roads are pressured by choice from outside, and the brain responds to these changes with sensitivity and consistency. If a city fails to respond properly to these changes, or if its connection to an inner-city is blocked or its connection to an outside city is in trouble, it will lead to a sharp decline in the population.

Results of the analysis of 60 cities

What Changizi and Destepano focused on was an analysis of 60 cities in the United States to compare how similar they are to the various rates of squared relationships, known anatomically, of typical neocortical cortexes held by the brains of mammals.

The first analysis was the relationship between the size of the city and the number of highways. This can be thought of as similar to the relationship between the surface area of the brain and the number of neurons. Surprisingly, the figure was 0.759, close to 0.75, a figure is known for its relationship with the surface area of the brain and the number of neurons. The next comparison is based on the number of entrances and exits on the highway, considering the number of synapses in neurons. Similarly, since the entry and exit of a vehicle on a highway are made through the entrance and exit of a highway, this can be considered a similar concept to the relationship between neurons and synapses. The figures surveyed for the relationship between the urban area and the density of highway entry and exit were calculated between 1.066 and 1.210, which matched the figure of 1.125 representing the relationship between the surface area of the brain and the total number of synapses. Even the figure is almost at the median value of the figure calculated in 60 cities.

Another characteristic of the neuronal axon is that it is myelinated. Myelin is a substance that surrounds the neuronal axon, which makes the bundle of axon look white because the color is white. That's why it's called white matter. When myelinated, the transmission of information through the axon is more effective and faster. In the case of highways, increasing lanes will allow the vehicle to move faster and more effectively. Lane lines on highways relative to the area of land increase by 0.174 square coefficients, which can be compared to the 0.125 of the diameter of the axon with the surface area of the brain increases. Considering this figure alone, it is a rather large difference, which is why highways are a two-dimensional world and neurons are a three-dimensional pathway. As the city got bigger, the surface area of the highway was naturally widened, and the square factor was about 1.4333. The coefficient between the surface area of the white matter of the brain and the surface area of the entire brain is 1.375. There are more interesting figures, but when you organize them and draw a table, they are as follows. It is surprising that more square counts are expressed in exact proportion.

Credit: Common Scaling Laws for City Highway Systems and the Mammalian Neocortex (2009)

Conclusion

It would be nonsense to suggest that we need to study brain science to understand the city with these commonalities. But let’s think of the brain as a kind of network and the city as a kind of network and look at the similarities. When you think about future urban planning or future cities, you will find out a lot by understanding these network sciences. And it is easy to imagine that network science and other studies related to complex systems will play a common role in conducting research on cities and brains.