Geography is the Fractal Objective Function of Humanity
Why settlements naturally arise at the confluence of two rivers, underexplored consequences of the rise of AI, and how it all ties together.
The study of geography in the abstract might seem outdated or even futile. After all, building an understanding sufficient to inform a bridge design or military offensive requires an in-depth knowledge of the peculiarities of the terrain in question. How should drainage be managed given this soil structure? How defensible is the high point overlooking that river? However, as we’ll see, the self-similar fractal nature of geography allows us to discern common patterns which Humanity responds to across different levels of organisation. Understanding these patterns can therefore reveal much about our history and provide a framework to analyse future actions and policy as we continue to shape the physical and digital landscape for our purposes.
What is an objective function?
An ‘objective function’ (or its mirror, the’ loss function’) describes the reward (or penalty) at each point in a decision space. It defines the fundamental problems and opportunities of every optimisation exercise. Though individuals may not conceive of it this way, all life constantly grapples with objective functions. Trees grow towards the light while their roots grow and spread to maximise water and mineral intake for a given energy investment, all while minimising exposure to harmful stimuli such as arsenic or other stressors. Herbivores are constantly trading off risk and reward as they venture further afield from a place of safety to exploit greener pastures. Objective functions define our expected payoffs in poker, the costs and benefits of a company extending its logistic network, and the problem that machine learning software adapts to solve.
Why does geography define our objective function?
Water is critical for life. Areas with plentiful freshwater resources are also, to a first approximation, most able to support a rich abundance of plants and animals. The richer the area, the more food available for humans. The more food is available, the larger our families and communities can be and the more specialised and productive we can become.
Floodplains in particular, bringing water and nutrient-rich soils from further upriver, are the most productive areas on the planet and provide excellent drought-resistant ground for high-yield grain crops such as rice, wheat, and barley. These crops are necessarily dried and stored after harvest to provide food throughout the year. Consequently, we see the construction of grain silos and defensive measures to protect this great resource and the rise of more elaborate social orders to manage it – from warrior castes to early bureaucrats predicting floods and allocating water resources for irrigation across land holdings. In other words: civilisation, arising first in the floodplains of the Fertile Crescent, and again probably independently in the likes of the Lower Yellow River in Ancient China.
Surface water also plays a critical role as both an inhibitor and enabler of transportation. Crossing a fast-flowing river while heavily laden with goods is nigh impossible. Draught animals require an ever-greater proportion of a load for their feed as travel distance increases (‘the wagon equation’). Consequently, transport by barge or ship remained the only viable method of long-distance transport of heavy goods until the advent of the railway during the 19th Century. Taking these points together, the geography of navigable freshwater defined the logistical landscape of our ancestors.
The grain farmer floats his surplus downstream on a small barge, while the sheep farmer living in rugged terrain drives his flock downhill to market such that the two may trade. The local optimum point for such a market is at the confluence of two rivers/streams or near a ford suitable for oxen, such that the catchment of local producers within a day’s journey or so is maximised. Secondary and tertiary supporting industries (e.g. tools, bread, lodgings) naturally arise at these points. Any further surplus can be traded downriver (assuming the river is navigable) to larger settlements sited according to the same principles.
Eventually, these rivers lead to the sea. Here, the river disgorges nutrients into an estuary rich in aquatic life. Humans built small boats to fish here and were incentivised by the geography to improve this technology and fish a little further out past one’s competitors. Eventually, these became good enough to venture beyond the estuary and a little way out to sea, opening up the possibility of extending the riverine trade route to nearby cities and islands. We were bound for the longest time to the weaker currents and easy navigation by landmark. Eventually, we cracked the secrets of navigation at sea, providing significant advantages to those blessed by sheltered deepwater harbours, and marking the beginnings of a global network of traders, shifting national alliances, and knowledge sharing.
Of course, there is more to geography than water. Plate tectonics shape the land and raise great mountain ranges out of the sea, only for them to be worn down again by rain and wind which is driven by solar energy from the Sun. These systems together form a great mega-system of energy and matter, all cycling and transforming across different timescales. Sometimes a great forest is submerged and subducted beneath the Earth’s crust by the movement of the plates and eventually arises millions of years later as a seam of coal. With attention, discernible patterns can often be observed across different spatial and time scales. Rain carves consistent fractal erosion patterns into the landscape, forming the basis of natural waterways. The wind blows out to sea at night and into land during the day. Seasonally, the redistribution of solar energy from the equator towards the poles creates consistent seasonal patterns of rainfall, cyclones, and trade winds to be managed and exploited.
In the aggregate, a great multi-dimensional model of the world’s geographical processes emerges. This model is the product of millennia of accumulated knowledge. It is sophisticated enough to predict the impact of rising carbon dioxide levels decades in advance, and the likely direction of chaotic storm systems days in advance (with further advances in the pipeline).
How has humanity adapted geography?
Geography has been interdependent with life since life first began. Life adapts to the geographic objective function and, in turn, shapes it. Trees hold the soil together to reduce erosion while converting carbon dioxide into oxygen (likely causing one of the first great extinction events). Beavers respond to their environment by creating dams to store winter food and protect against predators. In doing so, they have enormous effects on the local environment, flooding great tracts of land, changing river dynamics, and forcing life around them to adapt to the new contours of the function.
Few species have had as profound an impact on geography as humans. Just as we have adapted to geography as we’ve discussed above, so too have we adapted geography to better suit our purposes. Fallen logs, simple river ferries, and then great bridges connect two previously mutually inaccessible areas. Great dams and irrigation schemes improve the reliability of freshwater resources and increase crop yields. Paved roads improve informal tracks, reducing the time taken for transport and communication along that road. The travel time map shrinks. Trade and governance over longer distances become more practical, leading to consequent growth in economic specialisation and state capacity. A ratchet mechanism can develop if the economic surplus is reinvested. Infrastructure modifies the landscape and reduces costs, and improves local maximums of the objective function. The surplus grows and enables yet better infrastructure and technological development. Eventually, our economies became so sophisticated that we see the emergence of recognisably modern states commanding vast resources and radically reforming entire landscapes.
Storing and redirecting energy has always been of great importance to us. Gravity could be used in some limited ways to float objects downstream. Developing sails allowed us to harness the wind increasingly efficiently. Wood, coal, and peat could be burned for heat. However, for most of human history, most mechanical work was biomechanical, hence relying on an agricultural/pastoral surplus. This changed with the development of the steam engine in the 17th Century, which finally allowed meaningful work to be produced from heat. The industrial revolution was underway, and the following centuries saw radical changes in our ability to interact with geography. Coal, then oil, became the supreme natural resource. The wagon equation was finally overcome with the first steam railways in the early 19th Century. Geographically, we can think of this development as similar to a new bridge in joining together previously logistically disconnected locations. Highways traversed by motor vehicles fill a similar function, with much greater flexibility, as our network of roads grew to reach nearly every point of economic significance.
More recently, the development of electricity and its associated infrastructure has enabled the transfer of energy at low cost. Modulating the frequency and amplitude of these energy transfers allowed near-instant communication, previously limited to runners or crude signalling systems, across long distances in ever-increasing fidelity to an ever-increasing number of networked locations. Organisations previously constrained by time lags and bandwidth can now coordinate globally in real-time. State power, previously limited by the extreme illegibility of its domain, is increasingly limited not by the availability of information but rather by its ability to process that information and act. The ongoing development of AI will reduce these constraints too, and thus herald a new age of previously inconceivable state capacity.
In some ways, the digital age has created a new landscape distributed across server farms and other digital devices. In other ways, these developments are no different to any other piece of infrastructure that alters the landscape and changes the objective function. Some costs are reduced, some are imposed (e.g. maintenance), and new maxima come within reach for cultures to explore, adapt to, and exploit.
Exploration, Exploitation, and Path Dependence
Cultures adapt to the objective function and converge upon a local maximum. As the function changes over time, adaptations ideally need to be updated or abandoned, or they can become maladaptive. Some degree of maladaptation can be accommodated if there is a large surplus. However, accumulate too much and a culture can find itself outcompeted or otherwise unable to sustain itself. The disappearance of the Greenland Norse provides one such example. As the climate and economic environment shifted, the continuation of cultural practices more relevant to their homeland became increasingly costly. At the same time, opportunities to learn from the local Thule people largely went unexplored, ultimately leading to their total collapse.
We can consider two broad sets of cultural adaptations that respond to the objective function: exploration and exploitation. Exploration is the process of making the function more legible. Exploitation optimises the returns of existing knowledge. Exploration strategies tend to be more useful as the function changes and new frontiers become available. Exploitation tends to become more adaptive as the contours of the objective function become more stable and well-understood. These modes are not necessarily mutually exclusive across a distributed culture. Still, in practice, limited resources and cultural mythos tend to create a bias towards one or the other (c.f. Polynesian myths of discovery and Germanic tales of danger and the grim consequences of sin).
Even where broad adjustments to a changing function take place, many older traditions and adaptations tend to linger, creating a degree of path dependence where new local maximums are reached from the position of the old.
Implications of this Framework
Humanity optimises the objective function at various organisational levels: from individuals and family units to small businesses, communities, municipal and state governments, and finally to transnational organisations.
From an optimisation perspective, private sector individuals and organisations have a range of advantages over states. Firstly, competition puts pressure on outdated or dysfunctional adaptations, forcing updates or risking replacement. Second, thanks to proximity and keen interest, they usually understand the local contours of the objective function much more deeply. After all, profit can be made where there are discrepancies between local and global knowledge. Markets thereby make distributed information legible. The price of commodities reflects the cumulative impact of flooded farmland in India, supply-chain difficulties in California, and the future expectations of everybody engaged in that market. Without markets, this fractal information often remains illegible. Consequently, wherever states have attempted to direct production, shortages quickly occur.
Nevertheless, states are both inevitable and desirable of sufficient scale to provide mechanisms for resolving coordination problems. For example, contract law enforcement increases the costs of defection and generally allows private parties to conduct business in a high-trust environment. Eminent domain allows infrastructure to be updated as cities grow. There are generally two kinds of situations where government intervention is useful. First, in cases where the benefits are distributed but costs are concentrated, and hence no single party is incentivised to act. Second, where the benefits are concentrated, but costs are distributed (leading to free-rider problems). These are typically most conveniently resolved by the government through expenditure and regulation respectively.
Path dependency is evident everywhere in our public expenditure and regulatory frameworks. Old laws often continue to compromise the ability of our public infrastructure and private markets to operate effectively, with little to no commensurate benefits.
The costs of regulating land use or responding to a community seeking to protect the character of their neighbourhood were relatively low a century ago. As our cities have grown, zoning practices in many English-speaking cities have failed to reconsider the opportunity costs, causing a significant imbalance in housing supply. Prohibitive zoning has failed to respond to the changing objective function, increasing the costs of housing, with all the attendant impacts on human wellbeing that entails. The design of city streets is bifurcated into either like-for-like replacements or costly prestige projects involving expensive materials and the latest gimmicky design features. In contrast, simple opportunities to marginally improve the geography with every renewal project are continually ignored.
"Urban planners should be held responsible for unaffordable high price/income ratios in the same way that… police are held responsible for high crime."
-Alain Bertaud. Order Without Design, How Markets Shape Cities
As long as public sector organisations avoid catastrophe, there are relatively few incentives for states to properly understand the objective function, let alone seek to improve it methodically. As the world’s complexity continues to grow and becomes increasingly illegible to any individual, results are increasingly dependent not on elected politicians but on the capacity of public officials to provide quality advice and execution. Unfortunately, this capacity has been in relative decline in recent times.
Starting in the mid-20th Century, as enormous value was generated by new industries, returns for top individuals in the private sector began to outpace public sector salaries dramatically. At the same time, reactions to perceived public official overreach, especially when pursuing enormous high-modernist projects that poorly accounted for local conditions, led to a raft of new rules and bureaucratic processes to constrain the power of any future planners seeking to follow the lead of Robert Moses. With lower pay, lower prestige, and a more frustrating bureaucracy to navigate, it should be no surprise that talented individuals increasingly filtered themselves away from a career in public service.
There are signs that the pendulum is beginning to shift, both as local governments become increasingly amalgamated and the theoretical capacity of these institutions grows with increasing revenue thanks to broader economic growth. Meanwhile, modern technology has fundamentally transformed the objective function and presents many relatively straightforward opportunities to create significant value for the public.
Ultimately, it is not enough to simply point out that our public policy is suboptimal. and that a sane zoning policy, improved traffic monitoring system, or better street design would be beneficial. The real task, which I hope to contribute to in coming posts, is overcoming the political and operational barriers to implementing these changes.