There is a kind of intellectual cowardice in how most scholars treat geopolitics. They dress it up in the language of complexity, of nuance, of “it depends,” and in doing so they obscure what is, at its core, a mechanistic and predictable system.
Power is not mysterious. It is calculable. And if we are serious about understanding why nations rise, why empires fall, and why the same patterns repeat across centuries, we need to stop pretending that history is poetry and start treating it as physics.
This article proposes two formal relationships that describe how power operates across time and space. The first is a temporal one. Political output in any given period is a function of economic conditions in the preceding period, where that relationship is not linear but compounding.
Write it as P(t+1) = f(E(t)), where P is political capital, t is the current period, and f is a function whose shape depends on the specific variables of that state’s economy, population, and institutional strength. The second is a structural formula: Power = (2M + E + A) x S / (G x D), where M is military capacity, E is economic output, A is alliance depth, S is internal stability, G is geographic friction, and D is internal division.
These are not metaphors. They are the underlying logic of every major geopolitical event in recorded history, and the fact that no one has written them down in this form before is itself a symptom of the problem.
The Temporal Equation: Economics Precedes Politics
Always Ibn Khaldun, the fourteenth century Arab historian and one of the most underrated thinkers in intellectual history, described what he called asabiyyah, a form of collective social cohesion that rises and falls in cycles of roughly three to four generations.
What he observed empirically in the dynasties of North Africa and the Islamic world was that economic prosperity generates political confidence, political confidence generates overreach, and overreach destroys economic foundations, which then destroys political stability. He described the equation without calling it one.
The Soviet Union’s collapse in 1991 was not primarily a political event. It was the lagged consequence of economic stagnation that had been building since the Brezhnev era of the 1970s. Oil revenues masked the dysfunction for a decade.
When those revenues declined and the structural rot became undeniable, Gorbachev had no political tools left that could compensate for what the economy had already decided. P(t+1) was already determined. The economics of (t) had spoken.
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The same logic runs through the Weimar Republic. Germany’s political implosion in the early 1930s was not caused by Hitler’s rhetoric, though his rhetoric was the vehicle. It was caused by the economic catastrophe of hyperinflation in 1923, the brief recovery of the mid-1920s built on American loans, and then the cascading collapse after 1929 when those loans were called in.
Karl Polanyi, in “The Great Transformation,” argued that the political extremisms of the twentieth century were market dislocations wearing political masks. He was right. The function f(E(t)) in Weimar Germany had a near-vertical slope because its economic variables, debt, unemployment, currency failure, created a political output that normal democratic institutions could not contain.
This temporal dependency is not unique to failed states. China’s political transformation since 1978 follows the same equation in the opposite direction. Deng Xiaoping’s reforms generated an economic variable so powerful that it produced political capital sufficient to sustain a one-party government through Tiananmen, through the 1997 handover, through the 2008 financial crisis.
The Communist Party of China has survived not because of ideology but because its economic output has continually regenerated its political legitimacy. The moment E(t) stops delivering, P(t+1) becomes a crisis.
The Structural Equation: Power Is Arithmetic, Not Art
The formula Power = (2M + E + A) x S / (G x D) has several properties worth explaining before applying it. Military capacity is weighted at double because coercive force remains the final denominator of international relations. Hans Morgenthau knew this. So did Thucydides, who put the bluntest version of it into the mouths of the Athenians at Melos: the strong do what they can and the weak suffer what they must.
This is not an endorsement. It is an observation that has held across every civilizational order from Mesopotamia to the present.
Economy and alliances are additive but unweighted individually, because neither alone constitutes power. A wealthy state with no military protection and no allies is a target, not a power. A state with a powerful military but no economic base to sustain it collapses within a generation.
The Habsburg Empire in 1914 had a military but a fractured economy and a crumbling alliance with Germany that was less partnership than dependency. It scores poorly on the additive numerator.
Stability is a multiplier because it is the force that converts potential into actual power. Pakistan has nuclear weapons, a large military, and a significant economy by regional standards. It consistently underperforms its theoretical power because its stability coefficient is low. Internal coups, civil-military tensions, provincial insurgencies, and judicial crises divide the numerator before it can compound.
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Japan, by contrast, with a constitutionally restricted military and a geography that makes it an island fortress, maintains a stability multiplier high enough to sustain significant geopolitical weight despite its pacifist posture.
Geography is a divisor because it is friction. Napoleon understood this when he entered Russia and forgot it at the same time. The Wehrmacht relearned it in 1941. Geography does not determine outcomes but it taxes them. Britain’s geographic insularity gave it a low G value, meaning the divisor was small, which amplified its effective power for three centuries disproportionate to its landmass.
The United States similarly benefits from two ocean buffers. Russia, conversely, has a vast and indefensible steppe border that forces it to spend political and military capital on buffer states, permanently taxing its net power output.
Internal division is the second divisor and arguably the most dangerous variable in the contemporary period. Aristotle, in the Politics, identified stasis, internal factional conflict, as the primary cause of constitutional collapse. He was describing ancient city-states but the variable transfers cleanly. The United States today carries a rising D value.
Its nominal power remains extraordinary when you look only at the numerator. But the denominator is growing. Political polarization, institutional distrust, and the weaponization of information create an internal division coefficient that reduces effective power output even as military spending and GDP remain high. This is not partisanship. It is arithmetic.
Why Theology and Philosophy Saw This Before Mathematics Did
Augustine of Hippo argued in “The City of God” that earthly power is inherently contingent and self-consuming. He was making a theological point about the ultimate insufficiency of political order, but he was also describing a dynamic system with negative feedback loops.
The Roman Empire, which Augustine watched dissolve around him, fell precisely because its power equation collapsed. Military overextension raised G. Barbarian integration raised D. Economic debasement of the currency destroyed E(t), which then destroyed P(t+1). Augustine read the equation in theological terms. We can now read it in formal ones.
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Hegel’s dialectic, for all its obscurity, also encodes a version of this. The thesis of a dominant power generates its antithesis. The synthesis is a new equilibrium at a higher or lower level of complexity. This is a narrative version of the feedback between P(t) and E(t) across successive periods. Hegel did not have the tools to formalize it. We do.
Kautilya, writing the Arthashastra in ancient India roughly contemporaneous with Aristotle, produced what is arguably the most sophisticated pre-modern theory of statecraft. His mandala theory of concentric rings of friend and enemy states is a qualitative description of the alliance variable A in the structural equation.
He understood that alliances are not relationships, they are strategic assets that depreciate, appreciate, and must be actively managed as part of a power portfolio.
Existing Evidence
Apply the structural equation to the present moment. China’s power score is rising because its M is growing rapidly (second largest defense budget), its E remains the second largest GDP by nominal measure, its A is expanding through the Belt and Road Initiative, and its S has been artificially stabilized through authoritarian consolidation.
Its G value is complicated by Taiwan, the South China Sea, and the Himalayan border, and its D value, while suppressed, is building beneath the surface in Xinjiang, Hong Kong, and in the demographic pressures of a post-one-child-policy society.
The United States’ score, by this formula, is still higher than any competitor when the full numerator is calculated. But the denominator is the problem. A rising D value is not theoretical. It is measurable in legislative dysfunction, in judicial legitimacy crises, and in the kind of domestic political violence that was once considered a feature of weaker states.
Russia’s equation tells a story of a state that has prioritized M to the point of starving E, while G remains its permanent structural burden and D is suppressed rather than resolved.
Geopolitics is not inscrutable. It is not the exclusive domain of diplomats, generals, or strategists with access to classified briefings. It is a system governed by relationships that can be modeled, analyzed, and to a meaningful degree predicted. The equations proposed here are not the final word. They are a framework, and frameworks that can be falsified are more honest than theories that explain everything and therefore explain nothing.
The next time a state rises or falls, before reaching for cultural explanations or great man theories of history, run the numbers. Check what E(t) was doing three to five years prior. Look at the stability multiplier and both divisors. The answer will usually be there, waiting in the arithmetic, which is exactly where Thucydides, Kautilya, and Ibn Khaldun left it for us twenty centuries ago.
*The views presented in this article are the authors’ own and do not necessarily reflect the views of The Diplomatic Insight.
Arnav Goyal
Arnav Goyal is a geopolitical analyst and author whose work has appeared in Real Clear Defence, the London Daily News, and IRE Journals (peer-reviewed, Vol. 9, Issue 3, 2025). He is the recipient of the Edinburgh Essay Award (Scottish Arts Trust, 2026), author of “Events That Could Lead To WW3: Explained” (Amazon, 2024), and founder of The Global Youth Nexus. He was ranked 62nd Best Debater Globally at the World Scholar’s Cup Tournament of Champions at Yale University. He can be reached at forarnavgoyal@gmail.com