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[ by Charles Cameron — two approaches to mathematics, two types of heroism, and their respective complementarities ]
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I wish to propose a clear analogy between the mathematician Grothendieck‘s two styles of approach to a problem in mathematics, and the Navajo Twin Gods, Monster-Slayer and Child-Born-of-Water.

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Steve Landsburg‘s post, The Generalist, compares two approaches to mathematics, as practiced by two eminent mathematicians:

If there was a nut to be opened, Grothendieck suggested, Serre would find just the right spot to insert a chisel, he’d strike hard and deftly, and if necessary, he’d repeat the process until the nut cracked open. Grothendieck, by contrast, preferred to immerse the nut in the ocean and let time pass. “The shell becomes more flexible through weeks and months — when the time is ripe, hand pressure is enough.”

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In the paras leading up to this one, Landsburg gives us the insight that these two approaches can be generalized as “zooming in” and “zooming out”:

Imagine a clockmaker, who somehow has been oblivious all his life to many of the simple rules of physics. One day he accidentally drops a clock, which, to his surprise, falls to the ground. Curious, he tries it again—this time on purpose. He drops another clock. It falls to the ground. And another.

Well, this is a wondrous thing indeed. What is it about clocks, he wonders, that makes them fall to the ground? He had thought he’d understood quite a bit about the workings of clocks, but apparently he doesn’t understand them quite as well as he thought he did, because he’s quite unable to explain this whole falling thing. So he plunges himself into a deeper study of the minutiae of gears, springs and winding mechanisms, looking for the key feature that causes clocks to fall.

It should go without saying that our clockmaker is on the wrong track. A better strategy, for this problem anyway, would be to forget all about the inner workings of clocks and ask “What else falls when you drop it?”. A little observation will then reveal that the answer is “pretty much everything”, or better yet “everything that’s heavier than air”. Armed with this knowledge, our clockmaker is poised to discover something about the laws of gravity.

Now imagine a mathematician who stumbles on the curious fact that if you double a prime number and then halve the result, you get back the number you started with. It works for the prime number 2, for 3, for 5, for 7, for 11…. . What is it about primes, the mathematician wonders, that yields this pattern? He begins delving deeper into the properties of prime numbers…

Like our clockmaker, the mathematician is zooming in when he should be zooming out. The right question is not “Why do primes behave this way?” but “What other numbers behave this way?”. Once you notice that the answer is all numbers, you’ve got a good chance of figuring out why they behave this way. As long as you’re focused on the red herring of primeness, you’ve got no chance.

Now, not all problems are like that. Some problems benefit from zooming in, others from zooming out. Grothendieck was the messiah of zooming out — zooming out farther and faster and grander than anyone else would have dared to, always and everywhere. And by luck or by shrewdness, the problems he threw himself into were, time after time, precisely the problems where the zooming-out strategy, pursued apparently past the point of ridiculousness, led to spectacular, unprecedented, indescribable success. As a result, mathematicians today routinely zoom out farther and faster than anyone prior to Grothendieck would have deemed sensible. And sometimes it pays off big.

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I no longer have — alas — a copy of Where the Two Came to their Father, the first volume in the Bollingen Series, with its suite of 18 sand paintings beautifully rendered in silkscreen by Maud Oakes, but their respective black and blue colorations lead me to suppose that the illustration at the head of this post, taken rom that series, shows the twin heroes, Monster Slayer (black) and Child Born of Water (blue) whose journeys and initiation are the subject of the rituasl “sing” recorded in that book.

The theme of two male hero twins is central to the mythologies of the American continent, according to Jospeh Campbell, who contributed a commentary to Oakes’ recording of Jeff King‘s performance of this ceremony, and lacking both the King > Oakes > Campbell book and Gladys Reichard‘s two volumes on Navaho Religion, I must draw on brief quotes from miscellaneous web sources to dramatize the differences between the twins.

Monster Slayer is the doer of deeds, similar in nature to other masculine, not to say macho, heroes — while Child Born of Water is the contemplative of the pair:

The Sun [Jóhonaa’éí] gave them prayersticks and then told them that the younger of the two (Born for Water) would sit watching these prayersticks while the older (Monster Slayer) went out to kill the monsters. If these prayersticks began to burn, this would signal that his brother was in danger and that he should go to him to help.

Reichard explains:

Monster Slayer (na’ye’ ne’zyani) (I) represents impulsive aggression, whereas Child-of-the-water represents reserve, caution, and thoughtful preparation.

A measure of their respective strategies, and of the ways in which the insights of Child Born of Water can succeed where the brute force tactics of Monster SLayer fail, can be gleaned from this section of their story, also I believe taken from Reichard:

When The Twins visited Sun the second time, he said he was willing to help them, but this time he wanted them to return the favor: “I wish you to send your mother to the west that she may make a new home for me.” Whereupon Monster Slayer, believing himself equal to any task, replied, “I will do so.I will send her there.” Then Child-of-the-water reminded them both: “No, Changing Woman is subject to no one? we cannot make promises for her. She must speak for herself? she is her own mistress. But I shall tell her your wishes and plead for you.”

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One commentator glibly suggests that the joint presentation of the hero as twins is “a clever reminder that progress depends upon cooperation between our mind and our heart” — but the psychologist Dr Howard Teich offers a far more depthful interpretation: that the two twins represent two forms of masculine heroism, one the familiar macho hero of war movies, and the other wiser and subtler, the possessor of traits commonly attributed to the feminine — and hugely undervalued — in our culture.

Dr Teich suggests we must (urgently) abandon the division of virtues into “male” and “female” types, reognize that these types are complementary rather than rivalrous, that both are necessary functions of both males’ and females’ psyches, and begin to integrate the wholeness that both strategies together represent, in our own approaches to our lives in general, to the natural world around us, and indeed to warfare — unsurprisingly, since we first encounter the twins in the ceremonial specifically devised by the Navajo to protect young warriors on their way to battle, and to reintegrate them in harmony and balance on their return.

As Teich puts it:

Monster Slayer and Child Born of Water, as these Twin Heroes are called, are the most sacred of all the legendary heroes in Navaho mythology. It is rare for the Navaho even to speak of the twins; their presence is to be felt rather than observed, and their lessons absorbed rather than applied. Although the lessons the twins hold may be countless, their particular manifestation of a deeper, more complex image of masculinity deserves the reader’s especial attention.

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I’d like to suggest that in the same way that there are “zooming in” and “zooming out” styles in mathematics, and “monster-slayer” and “born of water” styles of heroism, there are in fact twin traditions of understanding the world which we might term scientific and poetic, or in Teich’s terms — and those of the alchemists — solar and lunar.

A unified or “solunary” vision will encompass the virtues of both.

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Dr Teich’s review of the King > Oakes > Campbell book under the title A Dual Masculinity was irst piublished in The San Francisco Jung Institute Library Journal, Vol. 13, No. 4, 1995. He now has a book out treating these themes: Solar Light, Lunar Light.

Oh, and please don’t expect me to know anything more about Grothendieck’s mathematics than I read in Landsburg’s article.

[ by Charles Cameron — coloring outside the lines of the challenge ]
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Civ4 Dune mod, “Worm attack”, from Desura

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I’m all in favor of the Atlantic Council‘s Art of Future War Project:

It is a moment to seek out new voices and ideas from artists who can range much farther out into the future. Artists are adept at making sense of disorder while also having the ability to introduce a compelling chaos into the status quo. In other words, they are ideally suited to exploring the future of warfare. Writers, directors and producers and other artists bring to bear observations derived from wholly different experiences in the creative world. They can ask different kinds of questions that will challenge assumptions and conventional ways of tackling some of today’s toughest national security problems. Importantly, they can also help forge connections with some of most creative people in the public and private sectors who otherwise struggle to find avenues for their best ideas.

That’s excellent, and as a poet and game designer with a keen interest in war and peace, I hope to contribute.

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Funny, though, their first challenge looks, to my eyes, just a little bit back to the future:

The Art of Future Warfare project’s first challenge seeks journalistic written accounts akin to a front-page news story describing the outbreak of a future great-power conflict.

Why would we want to produce something “akin to a front-page news story” at a time when news stories are already more web-page than front-page, and perhaps even tweet before they’re breaking news?

In any case, the good people at Art of Future War offered some clues to those who might want to take up their challenge, and I took their encouragement seriously —

The historical creative cues included below are intended to inspire, not bound, creativity.

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Their first clue did indeed inspire me, though not to write anything akin to a front-page news story, “between 1,500 and 2,500 words long”. The clue they gave was the Washington Times lede I’ve reproduced in the upper panel below —

while the lower panel contains the quote their clue led me to, by an associative leap of the kind artists are prone to — drawing on the vivid imagery of Peter Brook‘s play, The Mahabharata, which I had the good fortune to see in Los Angeles, a decade or three ago.

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My own leap backwards — to an ancient and indeed originally oral epic, the Mahabharata, rather than to century-old newsprint — won’t win me the challenge, since it doesn’t answer to the rules, nor will it provide useful hints as to what war will look like a decade from now.

The sage Vyasa, who wrote the Mahabharata at the dictation of the god Ganesh, might have been able to predict the future of war — I certainly cannot.

What I can do, and hope to have done, is to suggest that the whole of human culture has a bearing on war and how we understand it.

James Aho‘s Religious Mythology and the Art of War should be on every strategist’s reading list, as should Frank Herbert‘s Dune (see gamer’s mod image at the top of this page), JAB van Buitenen‘s Bhagavadigita in the Mahabharata and Brigadier SK Malik‘s The Qur’anic Concept of War — and Akira Kurasawa‘s Kagemusha on the DVD shelf, too:

There, I have managed to contribute something useful after all.

[ by Charles Cameron — a wargame so different from chess and go… ]
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A modern version of Hnefatafl, via Sources and Methods

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As I noted in a comment at the time, I was deadly envious of Zen‘s recent post, The VA bows Before Mjolnir, but I feel a little better now that I can make my own post about Hnefatafl, which Kristan Wheaton recently characterized as The Ancient Viking Game Every Intelligence Professional Should Play.

Prof. Wheaton’s key findings:

• It is an asymmetric game.  As you can see from the board above, one side starts in the center and the other side surrounds it on all four sides.  One side outnumbers the other by about 2:1.  The sides even have different victory conditions (the player with the pieces in the center need to get the “King”, the large playing piece in the middle of the board, to one of the corners.  The other player is trying to capture the King).  It is not too hard to see a game such as this one incorporated into courses, classes or discussions of asymmetric warfare.
• It is a conflict simulation.  Most historians agree that there were relatively few large scale battles involving Vikings. Instead, most of the time, combat resulted from raiding activities.  Hnefatafl seems to reflect the worst case scenario for a Viking raider:  Cut off from your boats and outnumbered 2:1. 
• It provides a deep lesson in strategic thinking.  Lessons in both the strategy of the central position (hundred of years before Napoleon made it famous) and in the relative value of interior vs. exterior lines of communication are embedded in this game. 

I really, really like the asymmetry of this game — WTG, Norsepersons!

The Department of Veteran’s Affairs has approved Mjolnir, the hammer of Thor the Norse God of Thunder, for use on gravestones of US military personnel.

“The Department of Veterans Affairs got out of the deciding game,” Pitzl-Waters says. The new rules stated that as long as a soldier filled out the proper paperwork and the symbol they wanted was linked with an existing religious community, a soldier could have any emblem they wanted on their tombstone. “You can’t just put, say, a Metallica logo on your headstone, but otherwise, the VA shifted the onus off of themselves in deciding what is or isn’t an ‘appropriate’ religion.”

In theory at least, Thor’s hammer was an acceptable symbol of faith in the eyes of the VA for the first time ever. But there was a dark side to the rules change. Like blót, the ancient Norse ritual sacrifice used to worship the gods, the Department of Veterans Affairs required blood to be spilled before Thor’s hammer could be officially added to the list. A soldier needed to die.

….Details are thin: His name was Shane, and he was a sergeant in the Marine Corps. He came from an extremely private family of Odinists, and he died in August 2012. After his death, his mother campaigned for the VA to not only allow Shane to have the symbol of Mjölnir placed on his headstone but for the same right to be extended retroactively to her husband, Mark, who had been buried by the Department of Veterans Affairs under a blank headstone under stricter rules. After ten months of red tape, the VA finally relented, and where once the space had been left empty, Mjölnir was carved into both of their headstones.

It’s a weird thing, when you think about it. That somewhere within a sea of headstones at Calverton or some other national cemetery, two soldiers–father and son–lay buried beneath the emblem of their faith: a magic, flying hammer that just also happens to be a pretty cool comic book weapon millions of people around the world know pretty well. 

Read the rest here.

Hat tip Feral Jundi

[dots connected by Lynn C. Rees]

Sigh

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? Raises question ?

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What did Lucius Aemilius Paullus know and when did he know it?

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Ask Colonel John Boyd, USAF (1927-1997)…

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Namedrop John Boyd

What do most respondants think?

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Uncritical Insight

John Boyd is a cheerleader jumping up and down on the sidelines chanting “faster! Faster!! FASTER!!!”.

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Uncritical Insight (cont.)

This reduces Boyd to:

1. Go fast.
2. Go faster.
3. Go ludicrous speed.
4. Profit!!!

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? – Raises Question  – ?

Is this man a cheerleader?

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? and ?

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Critique

NO

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Notice

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Key Asymmetry

When Boyd smiles, he’s 100 million light years away from being a cheerleader.

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Key Asymmetry (cont.)

If a Boyd particle barely brushed a cheerleader particle, it would annihilate it, leaving behind nothing but:

1. a tremendous burst of energy
2. plans for a better fighter plane than the F-35 at 1/1,000,000th the cost.

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Critical Insight

To understand Boyd, understand the battle of Leuctra (371 B.C.)

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Message

Boyd argued victory came by creating of a fatal disconnect between enemy and reality through:

• mental isolation
• moral isolation
• physical isolation

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Message (cont.) 

All three are critical to the originality of Boyd’s thought:

Boyd was thinking outside the box.

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Message (cont.) 

This box:

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Message (cont.) 

More particularly, this box:

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Message (cont.)

Battle of Cannae (216 BC)

Hannibal Barça put 50,000 or so Roman legionaries inside the box.

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Message (cont.)

Few Romans ever thought outside that box again.

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Problem

The physical kill box of Cannae became the mental kill box that military thinkers of the nineteenth century and early twentieth century kept their brains in.

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Problem (cont.)

This is your brain:

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Problem (cont.)

This is your brain on Cannae:

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Worse

Schlieffen, Chief of the Great General Staff of the Second Reich from 1893-1906, was obsessed with Cannae.

He even wrote a book on it.

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Worse (cont.)

Schlieffen used an exhaustive checklist when planning future military operations.

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Worse (cont.)

1. Does my plan destroy the enemy army like Buonoparte?

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Worse (cont.)

Satisfying those stringent requirements led to the Schlieffen-Moltke Plan:

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Worse (cont.)

Its results were mixed.

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Critique

Schlieffen’s plan failed because it only aimed at physical annihilation of Franco-British forces.

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Critique (cont.)

It’s moral and mental isolation (or annihilation) components were few or vestigial.

This absence dominated the Western Front for the next three years.

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First Cut

Boyd suggested that the German development of infiltration techniques in the later half of the war countered this.

Instead of the long bombardments château generals thought would physically annihilate the enemy trench line, barbed wire, and fortifications…

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First Cut (cont.)

The artillery barrage that accompanied German infiltration attack was sudden and unexpected…

…providing suppression as much through sudden mental or moral disorientation as through physical destruction.

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First Cut (cont.)

Instead of the physical impact of large ranks of infantrymen trudging across No Man’s Land…

Small teams of infiltrators dribbled across the lines in small groups, causing moral and mental derangement by attacking the enemy from the flank or rear in unexpected places at surprising times.

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Traditional Greek Order of Battle vs Leuctra’s Order of Battle

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Battle of Leuctra

Boyd referred back to Leuctra rather than Cannae as a guide:

Epaminondas‘ seemingly simpler act of stacking his left 50 deep and weakening his right was just as effective as Hannibal’s more technically complex but brittle double envelopment at Cannae.

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Battle of Leuctra (cont.)

Epaminondas created a fatal disconnect between Spartiate and reality through a balanced attack:

• physical isolation (more husky Boeotians to beat on the Spartan right)
• moral isolation (that’s against the rules!)
• mental isolation (the best Boeotian troops were on the left, not, as was tradition, on the right)

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Key Take Away

Epamimondas won a more efficient victory than Hannibal:

He mauled the Spartans just as effectively as Hannibal mauled the Romans …

Without the enormous luck and complexity involved in pulling off a double envelopment.

? 40 ?

And that’s why the NSA records (meta)data on all Americans.