Geography is the Fractal Objective Function of Humanity
Why settlements naturally arise at the confluence of two rivers, how group migration is like training AI, and the evolution of the modern world.
The study of geography can sometimes seem obsolete, superseded by more specialised disciplines. After all - building a bridge or planning a 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, a more general understanding of geography allows us to discern common patterns which Humanity responds to across different levels of organisation - from the individual to the state. Understanding these patterns can tell us much about our history, and provide a framework to analyse 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. 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 trade 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 incentive structure of an institution. Wherever individuals are implicitly or explicitly rewarded/punished for different actions, there’s an objective/loss function at work.
Imagine the horizontal axes above tracking ‘danger’ and ‘lack of food’ across a landscape. The height of the graph reflects how unsuitable the area is for habitation. A group of herbivores migrates away from predators and seeks greener grass until it arrives at a local minimum where any further migration is negative. Most species will have some mechanism to ‘scout around’ (e.g. quasi-random dispersal of seeds) to avoid being trapped in a shallow basin where a more optimal basin is nearby.
Artificial Intelligence works the same way. We define a loss function, and a model is trained using this same process of ‘gradient descent’ to minimise that loss. In practice, we’re usually seeking to minimise a prediction error of some kind, such as for weather prediction, computer vision, or ‘next word’ predictors like ChatGPT.
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’). Before long, the entire cargo is eaten by your horses along the way. 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 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 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 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. As rail was supplemented1 by our network of roads growing to reach nearly every point of economic significance, our objective functions have been reshaped so completely that the importance of rivers has been all but forgotten.
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 by the speed of a person on a horse), 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 understand what it means, and how it should inform action. 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 has altered the physical or information landscape. 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’ peoples 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 for public
Humanity optimises the objective function at various organisational levels: from individuals and family units to small businesses, communities, municipal and state governments, and even transnational organisations. Lower levels of organisation tend to be more flexible, and have a deeper understanding of the local landscape. Higher levels have advantages of scale, and are often better placed to address the coordination problems of lower levels.
From a societal perspective, lower levels also ‘benefit’ from greater competition. Where states often run on outdated ideas for decades, until compounding errors bring collapse, competition2 puts pressure on dysfunctional adaptations, forcing updates or risking replacement. Further, competition incentivises local contours of the objective function much more deeply. After all, profit can be made where there are discrepancies between local and global knowledge. The engagement of individuals in markets makes distributed information legible in real-time. The price of commodities quickly 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 remains illegible. Consequently, wherever states have attempted to direct production, shortages or gluts have soon followed3.
Nevertheless, states fill an important role by addressing coordination problems like defence, and criminal justice that otherwise suffer from free-rider and perverse incentive problems. Contract law enforcement allows private parties to conduct business in a high-trust environment, knowing the state will come down hard on any defectors. Eminent domain allows infrastructure to be updated as cities grow. In general, there are two kinds of situations where government intervention is useful. First, where the benefits are distributed but the costs are concentrated, and hence no single party is incentivised to act4. Second, where the benefits are concentrated, but costs are distributed5. These are typically best resolved by the government through expenditure and regulation respectively.
Unfortunately, many such initiatives that are initially adaptive can lose relevance as the objective function changes, or scope creep sets in. A set of policies designed to address one coordination problem can grow to create a worse one. This sort of ‘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 housing supply shortage. 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 tends towards either like-for-like replacements or costly prestige projects involving expensive materials and the latest gimmicky design features. Simple opportunities to marginally improve the geography with every renewal project are often 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
Part of the problem is quality of the civil service. Politicians are much the same as they’ve ever been, or at least, are a reflection of the times6. Yet, at a time when the problems states face are more complex than ever, the capacity of public officials to provide quality advice and execution has been in decline.
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.
Given the relative levels of opportunity to deliver value, perhaps this shift from public to private sector was appropriate. The public has been able to coast successfully for many years on the legacy of high state-capacity years of the early-mid 20th Century. Meanwhile, the private has built the modern digital and high-tech economy taking fundamental technical advances (often funded by the state through legacy programmes like DARPA, NASA, and ITRI) and commercialising these products, bringing down the costs of what were experimental prototypes to such extent that 70% of the global population now own a pocket device with 100,000,000x the processing power of the Apollo Guidance Computer. Arguably our top talent was best allocated to these sorts of problems rather than to making what would have been, at the time, relatively marginal improvements to the efficiency of the state.
While the prices of consumer goods have generally declined7, prices have skyrocketed in highly regulated industries like healthcare and education. Delivery costs for infrastructure and other core public services have also risen substantially, usually in a manner divergent from underlying material and labour costs.
This is the natural result of public sectors adapted to the objective function of the mid-20th Century, and diminished by a few generations of entropy. States have been shielded from the usual feedback mechanisms by unprecedented economic growth, which compensates for declining efficiency, and the changing nature of inter-state conflict. As the objective function changes, the divergence has become more marked. Thus, the value of attracting talent back to public service has risen substantially, as have the benefits of updating public practices for the 21st Century and the age of AI.
Unfortunately, the strategic and operational knowledge base of how to deliver effective reform has mostly passed on with the retirement of the long-tenured public servants, and their proteges, of yesteryear. Hence the need for rebuilding projects such as this blog.
Road and rail complement each other, since the flexibility of roads usually comes at the cost of efficiency. Over a well-utilised network, rail freight is much cheaper than road, and freight sent via rail (where practical) reduces road congestion and maintenance costs which are both disproportionately affected by trucking. Both modes are significantly more expensive than modern shipping.
For most of human history, states were both much smaller and engaged in much more direct competition than they are now. A state with poor economic policies, say, would find itself outcompeted in the next war, providing a mechanism for the abolition of terrible policies and the development of better ones. While I’m very glad to live in an era where inter-state conflict is rare, it’s unfortunate that there’s little incentive for even the most dysfunctional of modern states to adapt and change. Democratic competition provides one of the few mechanisms for feedback that exists at the state level, but is only effective to the extent that the public’s perception of the state-level objective function, and the strategies of the candidates to address it, actually correspond to reality.
Even an AI central planner with perfect information about the present is insufficient to solve this problem. The preferences of consumers change over time, and supply is often constrained in unexpected ways. Local shortages or gluts occur constantly, and prices need to change to reflect these new realities. If a ship transporting parsnips crashes during a bumper crop of carrots, lower carrot prices will encourage people to make the switch, while higher parsnip prices will create natural rationing, while incentivising people to import more parsnips to resolve the shortage. The only supercomputer capable of resolving these sorts of problems in advance is one with perfect information of the future - i.e. an omniscient God.
For example, education. Society benefits from an educated population, but while individuals can fund scholarships and private schools, the costs (if not necessarily the delivery) of universal education can only be managed by the state.
For example, free rider problems, and the tragedy of the commons. Situations where individuals benefit, but to the detriment of society as a whole are difficult for non-state actors to manage.
One major caveat here is the changing nature of media. While I think the impact here is often overstated, the shift from print, to radio, television, and finally social media has had two clear impacts on politics:
First, the escalating immediacy of the dominant medium has encouraged lower time preferences - politics has become overly focused on ever shorter news cycles rather than long-term success (even to the detriment of electoral success, e.g. in the case of Boris Johnson’s inordinate focus on the big media story at the time of whether Big Ben would Bong for Brexit). Second, the pervasiveness of modern media is a major problem. Democracy may die in darkness, but only the hardest of weeds can grow in unrelenting sunshine. US Congressional Hearings are a great example. The results of these meetings should be reported of course, but televised coverage incentives nothing but grandstanding, and pushes the real decision-making forums behind closed doors, being the only place where decision-makers can be convinced of new ideas, make concessions without appearing weak on camera, and so on.
Combined, these discourage working to deliver outcomes. Everything from procurement decisions to scientific funding is based on legible markers of respectability and risk avoidance. Nobody was ever fired for buying IBM, even if it costs twice the price for half the results.
Or, as in the case of motor vehicles, prices have been relatively stable while safety ratings, fuel efficiencies, and general quality have dramatically improved.