It’s easier to accept John Nash than the goddess Namagiri

January 7th, 2017

[ by Charles Cameron — delighted to find Ramanujan is not alone in dreaming of mathematics ]

When the Hinduism Today writer above says people found Ramanujan‘s assertion that his equations were given him in dreams by the local goddess Namagiri “irksome” he was understing the case: many mathematicians are allergic to the idea of a goddess providing inspiration to a mathematician in a devotional dream state. Thus Krishnaswami Alladi, in his Review of the Movie on the mathematical genius Ramanujan, writes:

The legend is that the Hindu Goddess Namagiri came in Ramanujan’s dreams and gave him these formulae..

See? It’s a legend, a priori, since “goddesses” don’t exist.

John Nash, he of the Beautiful Mind, game theory equilibria, and the Nobel Prize, on the other hand — if he provides inspiration to a fellow mathematician in a dream?

Why, his solution can be acknowledged as such in a learned paper..

Thucydides Roundtable, Book VII: Syracuse Through the Eyes of a Samurai

January 5th, 2017

[by A. E. Clark]

The Sicilian debacle that unfolds in Book VII arises from more than one cause and offers more than one lesson: but this reader was struck by the recurring motif of timing, which the Athenians keep getting wrong while their adversaries usually get it right. An obvious approach to this subject is through the Greek word kairos, which denotes an opportune moment that must be seized promptly when it comes along. Wikipedia has an interesting overview of how this concept, which appears to have originated in archery or perhaps the craft of weaving with a shuttle, came to be elaborated in classical rhetoric and Christian theology. Its military applications are obvious. In his Funeral Oration, Pericles notes, tou de polemou hoi kairoi ou menetoi: in war, moments of opportunity do not linger. (1.142.1)

Thucydides makes it clear that Gylippus, from his first entrance on the scene, is a man of kairos.  “[H]e had arrived at a critical moment” (7.2.4); “at last he thought that the moment had come” (7.5.2); the word in both instances is kairos. The Athenians by no means lacked such insight, but usually they failed to act on it: it is worth reading carefully the analysis Lamachus gave at Syracuse in 415, after which he allowed himself to be overruled (6.49.1-4). The Athenians repeatedly tarry precisely when decisive action is needed. Thucydides credits Demosthenes with proceeding to Sicily “without delay,” but the account suggests otherwise: the general stops at various places to build forts, ravage territory, and collect troop increments of marginal utility (7.20.2-3, 7.26, 7.33). By contrast, in this fateful summer of 413, the Spartans begin their invasion of Attica “in the first days of spring, at an earlier period than usual.” (7.19.1)

After they have been defeated but when they can still escape, again and again the Athenians prove fatally dilatory. The generals disagree after Epipolae, and so do nothing (7.47-49). The Athenians finally decide to sail away when the enemy brings in a fresh army, but a lunar eclipse persuades the superstitious Nicias to defer the departure by 27 days (7.50.4). They let themselves be cheated of their last chance to slip away by land when they uncritically accept a spoofed message of disinformation telling them to wait (7.73.3-7.74.1).

The very Greek theme of kairos, then, reverberates through this drama: the Spartans and the Syracusans know how to seize it, while the Athenians don’t, and that spells the difference between victory and defeat. But I will confess that this is not what first occurred to me as I read Book VII. Instead I heard echoes of a work of strategy by an author who certainly never read Thucydides and was steeped in a profoundly different culture. Go Rin No Sho, the “Book of Five Rings,” by a masterless samurai of the early seventeenth century, subsumes both individual dueling and large-scale warfare under the same “art of the advantage.” Miyamoto Musashi knew about kairos, but he called it Crossing at a Ford.  Of particular relevance to students of Book VII, he explores with Delphic intensity the role of hyoshi: timing (or ‘rhythm’).

The way to win in a battle according to military science is to know the rhythms of specific opponents, and use rhythms that your opponents do not expect, producing formless rhythms from rhythms of wisdom. (transl. Cleary)

If that key passage from near the end of the Earth Scroll sounds too much like a fortune cookie, be assured that Musashi explores the matter in greater detail. He stresses pre-emption, the seizure of the initiative by attacking suddenly, or by interrupting the enemy’s attack at its very inception, or by exploiting momentary imbalances when you are attacking each other more or less simultaneously.

Unfortunately, I do not know Japanese, and the language of Musashi presents difficulty even for those who do. Go Rin No Sho was probably a set of notes meant to supplement allusively an oral teaching that is unavailable to us. The translations by Thomas Cleary and William Scott Wilson are both respected by experts, but they differ from each other enough to indicate that the text must not be entirely clear. Here are two fine articles by Musashi enthusiasts that unpack some of the subtleties:



In practice, Musashi was a past master at screwing up his adversaries’ timing and finding ingenious ways to fluster them. He often showed up late for his duels and is reported to have despatched his most formidable antagonist by wielding not a sword but a long bludgeon that he had whittled from an oar while being ferried to the battle-ground.

…start by making a show of being slow, then suddenly attack strongly. Without allowing him space for breath to recover from the fluctuation of spirit, you must grasp the opportunity to win. Get the feel of this. (transl. Wilson)

This style is perfectly exemplified in Ariston’s “lunchtime” trick (7.39.2 – 7.40.4), which hinges on syncopated rhythm.

In the disastrous night battle at Epipolae, the turning point seems to have been a sudden change in rhythm which unbalanced the Athenians. They got used to an accelerating advance ( . . . the victors immediately pushing on” 7.43.5), and committed themselves to it by forgoing any consolidation (“the Athenians now advanced with less order, wishing to make their way as quickly as possible” 7.43.7). Being brought to a standstill and driven back by the Boeotians was a disorienting change of pace.  (“The Athenians now fell into great disorder and perplexity” 7.44.1)

Musashi noted the frequency with which deadlock arises in warfare and suggested antidotes to it.

Letting Go Four Hands is for when you and an opponent are in a deadlock and no progress is being made in the fight. It means that when you think you are going to get into a deadlock, you stop that right away and seize victory by taking advantage of a different approach. (transl. Cleary)

and, more psychologically,

When fighting with enemies, if you get to feeling snarled up and are making no progress, you toss your mood away and think in your heart that you are starting everything new. As you get the rhythm, you discern how to win. (transl. Cleary)

This is what the Athenians needed to do during the climactic naval battle of 7.70-71, in which the two sides seemed evenly matched (in unbearable suspense to the onlookers) and the Syracusan victory did not come until “after the battle had lasted a long while.”

Musashi was not a merciful man.  He wrote,

  . . . when opponents are demoralized and weakening, you concentrate your force on crushing them . . . In the context of individual martial art too, when your opponent is not as skilled as you are, or when his rhythm is fouled up, or when he starts to back off, it is essential not to let him catch his breath. Mow him right down . . . The most important thing is not to let him recover.

The Syracusans’ resolve to exploit their first naval victory to the fullest (7.56.2) and later their relentless pursuit and annihilation of the fleeing Athenian remnants exemplify this ethos.

In Musashi’s time, schools of swordsmanship had different opinions as to what the warrior’s eyes should chiefly focus on. His adversary’s sword? His adversary’s eyes, or feet? In the Wind Scroll, Musashi says the eyes should focus on “the hearts and minds of the people involved . . . on the state of the opposing troops,” but in a broad vision that takes in “the conditions for battle . . . the strength and weakness of the occasion” so as never to lose sight of the big picture. The speeches of Gylippus and Nicias offer an interesting contrast: Nicias talks about his men, their fate, their virtue. Gylippus addresses the motivations of his troops and their advantages in the battlespace at hand but, notably, he also analyzes the state of mind of the enemy and shares the intelligence he has received about it. (7.66.3 and 7.67.4)

I invite Roundtable readers who have shuddered through Book VII to pick up the Book of Five Rings, with particular attention to the Fire Scroll, and see whether they too find it a surprisingly apt commentary on the Syracusan campaign.

Everything can collapse. Houses, bodies, and enemies collapse when their rhythm becomes deranged. . . when the enemy start to collapse you must pursue him without letting the chance go. (transl. Wilson)

Happy Christmas: Of Shia & Christian in Beirut and Aleppo

December 25th, 2016

[ by Charles Cameron — season’s greetings ]

Posted by Rami Al Khal on Tuesday, December 20, 2016

I trust you can see and hear this video, or at least click through to Le Liban c’est ça aussi : une chorale musulmane qui chante Noël dans une église and watch it. It presents, as the post in French tells us, a Lebanese Shiite choir singing Christmas carols in a church, and with it I offer you my Christmas greetings on behalf of one and all at Zenpundit, greetings secular, sacred, Maccabean, Nazarene, Muslim, or at the mall.


I’m, as you may know, in recovery from heart surgery and on kidney dialysis, and this year I received a very kind care package of renal-failure appropriate food from an anonymous source, so I’m reminded that while the mall, grocery store and food-laden table may not represent the “essence of Christmas” as my mother would have wished — the child born God to brighten our dark world — they can nonetheless represent generosity as well as commerce, a break in the relentless pursuit of dominance, human life as gift and giving.

On this day, therefore, of commercial, charitable and Christian celebration, we wish you all, according to your varied natures and our own perspectives, happiness this Christmas in the teeth of winter and the world.


That Muslim voices are raised above in a Christian church in praise of the Christian nativity offers a glimpse of hope for mutual respect in the strife-and faith-torn Middle East — but such matters as the overlapping and interconnections of faiths are never simple, and by way or remembering something of the nuance, here’s a quick sentence from COL Pat Lang‘s post at Sic Semper Tyrannis yesterday, Christmas in Aleppo – Attention Joe Scarborough:

One of our German correspondents on SST informed us the other day that there are now some Christian members of Hizbullah, the Lebanese Shia militia. This would make sense because after the 2006 war against Israel Hizbullah assigned priority of its own reconstruction money to Christians in south Lebanon.


To quote Charles Dickens:

It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity..

Best wishes & blessings to all..

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

December 19th, 2016

[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.

Thucydides Roundtable, Addendum: Wyne on Revisiting Thucydides’ Explanation

December 17th, 2016

[Mark Safranski / “zen“]

Ali Wyne

Ali Wyne of the Brent Scowcroft Center on International Security

Our friends at The Strategy Bridge are continuing their own explanation of the Peloponnesian War and Thucydides’ timeless take on it. Ali Wyne from The Atlantic Council responds to Dr. Frank Hoffman’s previous post at War on the Rocks on “Thucydides: Reading Between the Lines“:

Revisiting Thucydides’ Explanation of the Peloponnesian War

….Far from being incidental to the Spartan polis, slavery was among its central characteristics. Slaves—or helots, as they were known—widely outnumbered non-slaves, perhaps by as much as a factor of ten.[3] According to the director of the University of Nottingham’s Center for Spartan and Peloponnesian Studies, a “fundamental feature of Spartan society was that the Spartiate citizens lived as rentier landowners supported by a servile population…who worked their estates.”[4] Any disturbance to this arrangement threatened not only Sparta’s agrarian economy, but also, by extension, the leadership’s authority. The English classicist Francis Macdonald Cornford observed how centrally “the constant menace of revolt” figured in its decision-making: “To meet this danger, and not for the purposes of conquest, their military system was designed and maintained.”[5] Sparta spared no measure to achieve domestic tranquility: the University of British Columbia’s Nigel Kennell observes that it “regularly sent young elite soldiers out into the countryside as armed death squads to murder any helot they found on the roads after dark or any working in the fields they thought too robust.”[6]

As Cornford’s judgment implies, however, fear of a slave revolt did more than influence Sparta’s approach to internal order; it was instrumental in shaping the city-state’s foreign policy, for an external antagonist—or even mere opportunist—could attempt to turn the helots against Sparta’s leaders. As it happens, they scarcely required encouragement. According to Jean Ducat, France’s foremost authority on Sparta, there existed “a state of open war between the helots and the Spartans throughout the period from 520 to 460.”[7] Most notably, following an earthquake in the Eurotas Valley in 464 that destroyed much of Sparta, the city-state’s slaves joined forces with their counterparts in Messenia to attempt a coup. Even though strategic tensions between Sparta and Athens had been rising following their collective defeat of the Persians in 479, the former initially welcomed the latter’s assistance in suppressing the uprising. Soon, however, Sparta asked the Athenian contingent to leave, fearing that the democratic ideology of its members might encourage further helot subversion: British historian Paul Cartledge explains that “[t]he Spartans simply did not want several thousands of democratically minded citizen-soldiers running loose among their Greek servile underclass in their tightly controlled territory.”[8]

The paradoxical nature of Spartan culture and its leadership in the Hellenic world is something worth pondering.

The Spartans were at once the most Greek of the Greeks yet also in some respects rather weird and alien. Their religious zeal for attending to religious rites and habit of relying upon divinatory guidance to military campaigns has already been remarked upon in this roundtable. Similarly, A,E. Clark and T. Greer have debated the meaning attached to Spartan “honor” and it’s impact on Spartan moral reasoning. The upper classes of other Greek polities, including Athens itself, were often admirers of ascetic Spartan martial virtues, it’s Agoge and the despotic regimentation the Spartiates imposed on the lower classes and helots (we can include Thucydides to a degree among their number). I.F. Stone wrote of young Athenian aristocrats as “Socratified youth”, swaggering through the streets with red cloaks and clubs in imitation of Spartans. Even the Athenian hedonist noble par excellence, exiled Alcibiades, joined in Spartan customs with sufficient enthusiasm to charm his grim hosts.

But the Spartans were also strange. They were the only polity to enslave on a massive scale their fellow Greeks, which was both the basis of their power as well as their Achilles heel. They scandalized other Greeks with the boldness of Spartan women, their penchant for sadistic whipping contests and their eerie practice of living and working among the remains of their dead. Finally their harsh eugenic practices which made every Spartiate life almost too valuable to lose. These things made Sparta different from it’s allies and rivals, shaped the political judgement of Spartan leaders and the strategies by which they pursued victory.

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