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Thucydides Roundtable, Book VI: The State with the Golden Arm

[by A. E. Clark]

T. Greer offers two metaphors for the restless dynamism which Alcibiades considered a necessity to the Athenian State in the summer of 415: a motorist’s climb up an icy hill, where if you do not keep moving forward you will slide back; and a child’s top, which must keep spinning or fall.

I believe these are good images for what Alcibiades wanted the Athenians to think.  Whether they are good images for the reality Athens faced (and needed to understand in order to make the right decision about Sicily) is another question.

A dynamic system can find equilibrium in a steady state. If enough angular energy continues to be imparted to the spinning top to compensate for the degrading effect of friction, that top will stand forever. A snapshot of the forces and resistances in play, if taken today, will be identical to the snapshot taken tomorrow or a year from now. The icy hillside is a little different, because it is hard to imagine the hill ascending forever. Apart from the geographic implausibility, as altitude increases both air pressure and temperature will fall, adding new difficulties to the vehicle’s operation.  But for a limited distance, assuming the gradient is constant and the ice uniform, it is likely that the motorist will find a steady-state solution: a constant speed that maintains traction up the hill.

Expanding empires encounter a complication that is absent from these examples.  By continuing to grow, they increase the burden of administration, the scale of required coordination, the potential for internal dissension, the number of things that can go wrong, and the vehemence of resistance to their reign. It is as if we said that the top must not only go on spinning but must carry a heavier weight with each passing hour; or that the car must ascend a hill that is becoming ever steeper. Reality enforces a limit on this kind of growth. In the parable of Icarus, closeness to the sun represents both the success of the enterprise and its catastrophic failure.

Dynamic systems in the social sciences are often modeled with mathematics. Such efforts require a great many variables whose values, as well as their partial first and even second derivatives, are linked in sprawling systems of equations. This science is a bit over my head, and I’m not sure it has ever proven notably successful in modeling social and economic realities. But there is a basic point central to this kind of math which many of us will remember from high-school physics: it is important to distinguish a value from its rate of change.  A car’s position is one thing (location); how that value changes with time is another thing (velocity); and how that rate of change itself changes with time is a third thing (acceleration). In this regard, Alcibiades shows some confusion:

we have reached a position in which we must not be content with retaining what we have but must scheme to extend it for, if we cease to rule others, we shall be in danger of being ruled ourselves.” (6.18.3)

“If we cease to rule others, we shall be in danger of being ruled ourselves.” This is exactly what Pericles had said at 2.63.2: “to recede is no longer possible . . . to let [our empire] go is unsafe.”  Pericles’ rationale was as much psychological as economic: to restore freedom to any of those from whom Athens had taken it would make them all restless, with a cascading effect.  Assuming that the flow of tributary income Y is proportional to the stock of subject territory S, Pericles is warning that neither must diminish: dS/dt < 0 would spell danger for Athens. But mindful of the burdens, distractions, and risks of expanding the empire, he has also warned his countrymen “to attempt no new conquests” (2.65.7) for the duration of the war: dS/dt > 0 is also dangerous.

Yet Alcibiades’ conclusion is different: “We must not be content with retaining what we have but must scheme to extend it.”  It is not S, but dS/dt, that he would keep undiminished! In fact, considering the scale of the Sicilian expedition, Alcibiades was actually calling for dS/dt to rise, as success in Sicily would have not merely continued but accelerated the imperial expansion.

Alcibiades seems to err, therefore, because his conclusion does not follow from his Periclean premise; yet it is possible that his counsel, fatal though it was, rested on something other than a mathematical mistake.

While many dynamic systems can settle into a steady-state equilibrium, others — intrinsically unstable — must accelerate until they collapse. Chain-letters and Ponzi schemes are examples of the latter in which a phase delay between revenues (R) and costs (C) is exploited to mask an insufficiency of revenues: R(t) pays off C(t – 1). If R(t) = k * C(t), where  0 < k < 1, then revenues must grow exponentially to keep paying the bills.

Another situation that promotes unstable growth is decaying efficiency with inflexible income requirements. Suppose a bank earns a certain profit by extending credit, and the profit per year is calculated as a proportion of the amount of credit extended.  Prescinding from many real-world factors, this will be the interest rate r. Now suppose r is halved. To keep the money coming in, the bank must extend twice as much credit. Suppose r is reduced to one-tenth of what it was . . . you see where this is going, and unless a good fairy has greatly increased the bank’s capital cushion, systemic risk will rise.  A declining rate of return on capital affects more than banks, of course. Individual investors seeking to preserve their income will employ greater leverage and incur a greater risk of being wiped out. (These examples are, of course, purely hypothetical.)

A third situation — or perhaps it is a special case of declining efficiency — occurs when a large part of the value of inputs consists in their novelty. We could also say that the recipient is densensitized over time.  The addict who is satisfied with one hit of speed on Monday will require more on Tuesday, and so on . . . The addict’s dose must increase with time. This analogy is not inapplicable to the life of nations.  Consider how Saudi Arabia used its oil revenues to fund and appease a parasitic class who might otherwise have challenged the Kingdom’s narrow oligarchy. These payoffs brought about both rising expectations and a rising birthrate. Internal social stability has become a pressing concern for the House of Saud.

Did Athens’ reliance on tribute as well as on the psychological gratification of conquest exhibit the rising requirements characteristic of a stimulation that grows stale? It is striking to read, in the appeal of the Corinthians at Sparta (1.70.2),

The Athenians are addicted to innovation

We might hesitate, because the notion of addiction here seems to have been imported by Crawley into the text, which simply describes Athenians as neoteropoioi, “making things new,” i.e., innovative or revolutionary. Yet the Corinthians’ eloquent character portrait of Athens implies what Crawley has made explicit. His interpretation is confirmed in the words at 1.70.8, which Hobbes translates “What they have, they have no leisure to enjoy, for continual getting of more.”

Athens had the personality of an addict. Alcibiades’ personal attachment to debt and racehorses, then, made him a fitting representative of his city. His words “unless you are prepared to change your habits” (6.18.3) and “to take one’s character and institutions for better and for worse, and to live up to them as closely as one can” (6.18.7) suggest he was conscious of this. That he believed it would be “the safest rule” for Athens to keep feeding its accelerating addiction is typical of the wishful, unrealistic thinking common to all addicts. Because the addiction was not his alone but had come to be shared by the mass of the citizenry, Nicias and the ghost of Pericles found themselves like many elders, counseling prudence and moderation in vain.

5 Responses to “Thucydides Roundtable, Book VI: The State with the Golden Arm”

  1. T. Greer Says:

    A great discussion. I purposefully left out an examination of whether Athens actually was best described by the dynamic Alciabades described. I am glad you took up the issue youself.


    “Expanding empires encounter a complication that is absent from these examples. By continuing to grow, they increase the burden of administration, the scale of required coordination, the potential for internal dissension, the number of things that can go wrong, and the vehemence of resistance to their reign.”


    Expansion can be this way. But it is not always this way–especially in a premodern world where wealth was seized more often than it was made. To take the example I spent the most time on in my discussion, the problem with the Qin initially was not that each new conquest made their empire more top-heavy. In fact, the opposite was the case: the more they conquered the wealthier they became and the larger their armies became. But eventually they conquered everything worth conquering. They reached a point conquest came up against the law of limited returns–it was possible to expand into the Ordos, or into southern marshes, but the people there were too few, their wealth too small, and their communities too isolated to contribute to the strength of the empire.


    The Romans are another example of the type. The conquest of Italy, then Sicily, the Inner Hispania, then Carthage, then Greece, then Gaul, then the greater east, then outer hispania, then the danube and panonnia only strengthened the Romans. Each brought an immediate surge of wealth into the empire and a longer term boost in population, trade, and taxes. (The exception to this was Britian–not coincidentally, the first place to be abandoned during the late empire’s fiscal crisis). The Romans did not conquer Germania because they lacked the power to–they did not conquer it because they recognized it would cost them far more than it would help them to bring the German barbarians into the empire.


    Was the Sicilian expedition truly ‘imperial overstretch’ then? Had the Athenians won what would they have gained? Would their top have become heavier, but spin the faster? Or would it simply become heavier?


    P.S. I am sure this has been modeled by dozens of political scientists by now. Peter Turchin has a section in Secular Dynamics where he questions the math behind the idea of imperial overstretch, but I don’t have a copy here in China.

  2. Lynn C. Rees Says:

    Overstretch is as overstretch does. Even Thucydides’ account suggests that, if a few contingencies turned, the Athenians could have taken Syracuse. Giving that wealthy city a good plundering might have given Athens just enough juice to solidify a defensible toe hold in Sicily and increase its power back in non-Magna Graecia. Given that communication was by sea rather than land, it would have been more scalable than contemporary Asiatic land empires. Similarly, if some contingencies had gone the other way, the war of the Batos hadn’t broken out, Varus had distrusted Herman the German, Tiberius had been more aggressive, the Augusta Faustina hadn’t disliked her son-in-law, Commodus had liked snow, &tc., Rome probably could have absorbed Germania up to the Elbe and attenuated the constant drip from the Urheimat in Scandinavia, especially if the Romans had adapted to navigation in the North and Baltic Seas. What Marcus Aurelius was doing in the 170s was little different from what Charlemagne did 600 years later, only without the mass baptisms.

  3. Grurray Says:

    Thucydides seems to make it clear after the speech by Nicias that the Athenians were descending into folly. With a Shinseki/Powell-you-break-it-you-bought-it reverse psychology argument, Nicias’ cleverness backfired, almost comically, fueling an enthusiasm for ‘conquests that would supply a never-ending fund of pay for the future’, which sounds close to peak delusion. The Athenians were even expecting to be ‘greeted as liberators’ in a sense, and supplied with troops and riches. I had to cringe when reading about how the Egestaeans fooled the advance Athenian ‘dupes’, like an ancient Ahmed ‘Slam-Dunk’ Chalabi.

  4. T. Greer Says:

    One of the interesting things about the Sicilian campaign is that the goal posts seemed to always be moving. It is hard to say just what would have counted as a “success.” The Athenians never agreed on that themselves. In retrospect “success” might have been something that allowed them to recoup some of the costs of the campaign–say maybe sacking Syracuse and getting a permanent toe hold on the island, as Lynn suggests? But would gaining a permanent toe hold on the island actually have helped them much, or just bogged them down permanently in another front fighting enemies they never would have had otherwise? Or would Sicily have rallied to the Athenians cause after Syracusan defeat?

  5. T. Greer Says:

    Also: re- Charlemagne and Marcus Aurelius–Following the lead of Peter Heather, I disagree. When Charlemagne went west the kingdoms he conquered were more densely populated, technologically advanced, and economically productive than their 2nd century antecedents, just as the Gauls were richer, more populous, and more advanced than the Germans.

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