Y = Arctg X: The Hyperbola of the World Order

Y = Arctg X: The Hyperbola of the World Order
Author Max Ostrovsky
Country The United States
Language English
Subject Civilization, Sociocultural evolution, World history, Universal history, Macro-historical, Comparative history, Political history of the world, Archaic globalization, History of globalization, Military globalization, Globalization, Global politics, World-systems theory, World Polity Theory, World War, International relations, Geopolitics, Grand Strategy, Balance of power, Hegemony, Empire, American Empire, Futurology, World War III, World government.
Publisher University Press of America
Pages 306

Y = Arctg X: The Hyperbola of the World Order is a nonfiction world history and world politics book by historian Max Ostrovsky with a "Foreword" by anthropologist Robert Carneiro. It aims to explain why certain civilizations existed as systems of independent states while others evolved into universal empires, what conditions cause the pendulum to swing one way or the other, what the drawn theory implies for the future of the modern civilization, and where we stand now.


  • Overview 1
  • Structure 2
  • Foreword 3
  • See also 4
  • References 5


An inexorable trend occurred throughout the human history: political units strove to grow larger in size and fewer in number. Leafing through pages of historical atlases, this trend strikes the observer. With scientific regularity appeared record-breaking empires in terms of both territory and population.[1] It looks as expanding pulsation of mathematically describable social trend.[2]

The implication of this trend is obvious and its significance is hard to overestimate. The trend actually represents a process of the ongoing political unification of the world. The projection of the trend into very close future suggests the appearance of a single world-wide empire.[3]

Y = Arctg X: The Hyperbola of the World Order analyzes the trend in order to offer an explanatory theory and project the theory into future. Based on four civilizations—Egypt, Mesopotamia, China and the Mediterranean—the theory is tested on the whole world. Beginning since the dawn of history, it proceeds through the present stage into future. It combines the theories devoted to the theme from the earliest, drawn by Shang Yang,[4] Kautilya,[5] and Polybius,[6] until the latest ones, by Edward Luttwak[7] and Zbigniew Brzezinski.[8]

The analysis finds that any political system with a firm agricultural foundation is pre-destined to politically unify and turn the state of unity into norm. A long list of secondary factors lacks determinative influence but merely deflects the process whether accelerating or decelerating it. The main secondary factor is geopolitical circumscription[9]—the degree to which a political system is spatially compact, static and isolated from other systems. The more a system is circumscribed, the sooner it unifies and the longer its unity persists.

Circumscription explains the difference between the European and the Chinese patterns. Circumscribed China mostly existed as universal empire while ever-expanding Europe perpetuated the model of independent states. The same had held true for the difference between Egypt and Mesopotamia.[10]

In history, two synchronous political processes occurred—external expansion and internal consolidation. Expansion complicated and sometimes outpaced consolidation. But the gap between the two processes was doomed to close due to the fact that the space of the earth is definite.

The space ended towards the 20th century. The sovereign void of the world ended. No outlet for further expansion was left.[11] The factor of circumscription became enacted and that moment our civilization headed straight towards overall unity. The Long Peace of La Belle Epoque was doomed; instead followed the era of World Wars. The time had come for great powers to clash in the fight of elimination.

This time, the centripetal factor of circumscription was multiplied by the modern technology of warfare and communication. The technological progress reduced space and caused the world to shrink in terms of time required to overcome distance. Due to technological progress within circumscribed space, warfare drastically increased and within less than a century we overcame the centuries-old balance of power and reached a unipolar hegemonic world order.

The macro-historical view reveals the true meaning of the unipolar moment we have witnessed. Underestimated by contemporary observers, the proclamation of the New World Order in 1990 signifies a milestone in the millennia-old trend of the political unification of the world.

The synthesis of the theory with modern conditions suggests that the genesis of the World State is much closer at hand than it seems to most of us. Persistent multipolar and bipolar worlds passed their event horizon. Modern conditions swing the pendulum into the opposite direction—towards ever greater political consolidation. That is, the present global hegemony is supposed not to dissolve back into multipolarity but to turn into global empire.[12]

How hegemony is transformed into empire is exemplified by transformations of similar hegemonies in the past—Rome[13] and Ch'in. Both adhered to the pattern of defensive imperialism, both began with isolationism (the earliest in history instances of the Monroe Doctrine) and both evolved from isolationism through hegemony into empire. The thesis shows that all three grand strategic transformations—of Rome, Ch'in and the United States—are essentially the same with the modern process being currently uncompleted.

The two previous hegemonies produced anti-hegemonic back-clashes, defeated anti-hegemonic powers and established universal empires. Mainstream theories of International Relations expect anti-hegemonic power-balancing in our world too.[14] This work indicates plenty of symptoms confirming the gathering storm, mainly over the Eurasian land mass. The restoration of multipolarity became a universal aspiration across this continent; the transatlantic split revealed its tectonic depth; strategic partnership between major Eurasian powers is evolving; and the geopolitical doctrine of Eurasianism in Russia rose like a phoenix.[15] The beating pulse of Eurasia is still beating.

The clash of civilizations is not plausible. Rather, the forthcoming clash is of Hemispheres—the Western based on North America versus the Eastern based on Eurasia. Turning to the school of geopolitics, this scenario is confirmed by the fondest of geopolitical theories.[16] The geopolitical motion of the Eurasian land mass seems to indicate that close is the moment when a fight for global power would erupt mightier than the earth has ever seen, an Endkampf of epic dimensions. The two Hemispheres would clash on four fronts, exchanging multi-megaton salvos across all four oceans.

In previous civilizations, warfare of any kind and scale was not eliminated but by universal unity. The nuclear warfare, as the record of human nature strongly suggests, will not be an exception. This book is devoid of maudlin sentiment or pious exhortation. It does not flinch to state: the mightiest war on this earth is yet to be fought, whether civilization is to survive or not. Either we will have a nuclear apocalypse or a nuclear genesis of the World State.

In case the world survives World War III in one piece physically, a certain winning people would weld it into one piece politically. The War would be followed by sweeping conquest and annexation by a victorious power of the most of the world. The universal annexation would proceed under the known device: "one world or none." All weapons of mass destruction would be outlawed. The rest of strategic armor would be monopolized by the central power. The hegemonic strategy would be discredited once and for all in favor of the imperial.

With shorter interruptions, the universal empires of ancient Egypt and China persisted for two-and-a-half millennia of their circumscribed existence, until they were engulfed by larger systems. The modern system, being global, is totally circumscribed. It can neither expand, nor be engulfed by a larger system, and this geopolitical condition will remain until the end of history. We are already in the global hegemony, we can expect its transformation into the global empire already within the span of this generation, but we should not expect its fall already after two-and-a-half millennia. Reversing the famous thesis,[17] the "unipolar moment" proved to be not moment but state and hence onward is not supposed to be interrupted but by rare and brief, albeit deadly and destructive, multipolar moments.

The image on the front cover (see above) shows two Egyptian gods, Horus and Seth, holding the hieroglyphic icon of unity. This 4000-year-old image illustrates the model of civilization which, besides being an exotic past, is our own very long future.

Y = Arctg X: The Hyperbola of the World Order differs from the post-modern research, alternating between case-studies devoid of broader implication and broader topics described in relativist terms. The present theory of history is an instance of Realpolitik and Geopolitik, leading to a sweeping determinist theory and a clear future project. The world-historical trend is mathematically expressed by one short formula.

This kind of theory seems to be debut by a professional historian. The science of history neither recognizes theories nor is used to multi-disciplinary approach. On the other hand, social sciences accustomed to theories take only a little note in primary sources. This theory, by contrast, is built on a firm factual basis of primary sources comparable in their quantity and diversity only to historical source-books. They range from the Epic of Gilgamesh to Herald Tribune, from Bible to Mein Kampf, and from the Shang bones inscriptions to the Pentagon tapes. The uniqueness of this theory of history is a combination of the primary-sources research common for historians with the theoretical and multi-disciplinary approach common for other social scientists.


The book is divided on three parts. The first part compares political patterns of four civilizations—Egypt and Mesopotamia between 3000 and 500 BC, and China and the Mediterranean between 500 BC and AD 2000.

The second part begins with the analysis of the comparison and outlines a dominant factor—the geopolitical circumscription. Then this factor is examined for the whole of world history. This examination demonstrates that the geopolitical factor is only the main secondary factor while the prime trigger of political expansion and unification is a firm agricultural foundation. The theory is confirmed by the phenomenon of the "Imperial Belt" formed in the Axial Age.

The third and main part is the implication of theory for the modern civilization. It demonstrates that the ancient "Imperial Belt" survives in the Industrial Age and argues that the survival of the world historical pattern can only be due to the fundamental role agriculture still plays for modern industry and consequently for military power.

The main implication of the theory is that the modern civilization is pre-destined to politically unify and turn the unity into persistent norm. It argues that presently we are half way through—we live in the global "hegemony." The whole question of the global "empire" today is only the question of transformation from hegemony into empire. How this transformation happens, why, and how long it takes is exemplified on two analogous transformations in the ancient Mediterranean and Chinese civilizations.

The conclusion draws the final formula of the development of the world order in history. Depicting a graph of the largest territory or population controlled by a single center in the past[18] and projecting the trend into future in accordance with the theory, we receive a hyperbolic curve expressed by a short mathematical formula: Y = Arctg X.


How the polities of Egypt, Mesopotamia, China, and the Mediterranean were finally unified is described here in exhaustive detail … Yet the innumerable details … are marshaled in disciplined ranks and files in the service of the larger picture Max Ostrovsky wishes to point. Changing the metaphor only slightly, we can say that with great deftness he has carefully plucked out myriads of relevant threads from his many sources and woven them into a rich, dense tapestry, the main patterns of which are boldly highlighted. But illuminating as is his portrayal of the evolution of early civilizations, it is but a prelude. His principal aim is to project the trend into the future. Still on the distant horizon but approaching nonetheless, he sees the emergence of a single world state… Just the labor required to assemble so vast a collection of facts is daunting. Yet this is not simply a masterful compendium of facts and quotations. It is the achievement of penetrating intelligence with a broad firm grasp of the world imparting to the narrative a clear direction and a strong purpose.[19]

See also


  1. ^ List of Largest Empires
  2. ^ Hart, Hornell, "The Logistic Growth of Political Areas", Social Forces, 26, (1948), 396-408; Naroll, Raoul, "Imperial Cycles and World Order", Peace Research Society, 7, (1967), 83-101; Marano, Louis A., "A Macrohistoric Trend Towards World Government", Behavior Science Notes, 8, (1973), 35-40.
  3. ^ Robert Carneiro, "Political Expansion as an Expression of the Principle of Competitive Exclusion", Studying War: Anthropological Perspective, (eds. Reyna, Stephen P. & Dawns, Richard Erskine, Gordon and Breach, New Hampshire, 1994); Robert Carneiro, "The Political Unification of the World", Cross Cultural Survey, 38/2, (2004), 162-177.
  4. ^ Shang Yang, The Book of the Governor of Shang Region, (tr. Perelomov, L.S., Moscow, 1993).
  5. ^ Kautilya, Arthasastra, (tr. Ramaswamy, T. N., Asia Publishers, London, 1962).
  6. ^ Polybius, Histories, (tr. Tijev, A. J., Ladomir, Petersburg, 1994).
  7. ^ Edward Luttwak, The Grand Strategy of the Roman Empire from the First Century AD to the Third, (Baltimore: Johns Hopkins University Press, 1976).
  8. ^ Zbigniew Brzezinski, The Grand Chessboard: American Primacy and Its Geostrategic Imperatives, (Perseus Books, New York, 1997).
  9. ^ Robert Carneiro, "The Circumscription Theory: Challenge and Response", American Behavioral Scientist, 31/4, (1988), 497-511.
  10. ^ Mario Liverani, International Relations in the Ancient Near East, 1600-1100 BC, (New York: Palgrave, 2001); Mario Liverani, Prestige and Interest: International Relations in the Near East ca. 1600-1100 BC, (Padova: Palgrave, 1990).
  11. ^ Halford J. Mackinder, The Geographical Pivot of History, (London: J. Murray, 1904); Fredrick Jackson Turner, The Frontier in American History, (New York: Holt, Rinchart and Winston, 1920).
  12. ^ Hegemony and empire are distinguished according to Thucydides-the former as controlling only external affairs of other states and the latter their both external and internal affairs. Thucydides, History, (tr. Stratanovsky, G. A., Moscow: Ladomir, 1981).
  13. ^ Edward N. Luttwak, The Grand Strategy of the Roman Empire from the First Century AD to the Third, (Baltimore: Johns Hopkins University Press, 1976).
  14. ^ Kenneth N. Waltz, Theory of International Politics, (McGraw Hill, 1979); Kenneth N. Waltz, "The Emerging Structure of International Politics,"' International Security, 18/2, (1993), 44-79;John J. Mearsheimer, "Back to the Future: Instability in Europe after the Cold War,"' International Security, 15/1, (1990), 5-56; Christopher Layne, "The Unipolar Illusion: Why New Great Powers Will Rise?" International Security, 17/4, (1993), 5-51; Christopher Layne, "The Unipolar Illusion Revisited: The Coming End of the United States’ Unipolar Moment", International Security, 31/2, (2006), 7–41.
  15. ^ Eurasia Movement; Alexander Dugin, Основы геополитики: геополитическое будущее России (Foundations of Geopolitics: The Geopolitical Future of Russia), (Moscow: Arctogaia, 1997); Alexander Dugin, "Манифест: Евразия превыше всего," (Manifest: Eurasia over All), http://newright.il.if.ua/evrazia.html Alexander Dugin, Проект Евразия, (Project Eurasia), )Moscow: Jauza, 2004); Mark Bassin, "Classical Eurasianism and the Geopolitics of Russian Identity" (2001) http://www.dartmouth.edu/~crn/crn_papers/Bassin.pdf Mark Bassin, "Eurasianism "Classical" and "Neo": The Lines of Continuity," src-h.slav.hokudai.ac.jp/coe21/publish/no17.../14bassin.pdf; Mark Bassin, "Geopolitical Culture in the Post-9/11 Era: The Masks of Prometeus Revisited", (2007), http://www.colorado.edu/IBS/PEC/johno/pub/nazi Mark Bassin, "Classical Eurasianism and the Geopolitics of Russian Identity," Ab Imperio 2, (2003), 257-267.
  16. ^ Halford J. Mackinder, The Geographical Pivot of History, (London: J. Murray, 1904).; Halford J. Mackinder, Democratic Ideals and Reality: A Study in the Politics of Reconstruction, (New York: Henri Holt & Company, 1919); Homer Lea, The Day of the Saxon. (New York & London: Harper and Brothers, 1912); Alfred Thayer Mahan, The Problem of Asia and the Effects upon International Politics, (Washington & London: Kennikat Press, 1920); Karl Haushofer, "Continental Bloc: Mittel Europa – Eurasia - Japan," 1941, in On Geopolitics, (tr. Usachev I. G., Moscow: Mysl', 2004]; Nicholas John Spykman, America's Strategy in World Politics: the United States and the Balance of Power, (New York: Archon Books, 1942); Nicholas John Spykman, The Geography of Peace, (New York: Archon Books, 1944; Henry Kissinger, Diplomacy, (New York: Simon & Schuster, 1994); Zbigniew Brzezinski, The Grand Chessboard: American Primacy and Its Geostrategic Imperatives, (New York: Perseus Books, 1997); Alexander Dugin, Основы геополитики: геополитическое будущее России (Foundations of Geopolitics), (Moscow: Arctogaia, 1997).
  17. ^ Charles Krauthammer, "The Unipolar Moment," Foreign Affairs, 70/1, (Winter 1990/1), 23-33.
  18. ^ List of Largest Empires
  19. ^ Robert Carneiro, "Foreword," Y = Arctg X: The Hyperbola of the World Order, (Lanham: University Press of America, 2007, p X-XI).
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