zenpundit.com

[by Mark Safranski, a.k.a. “zen“]

Friend of ZP, Kanani Fong sent me early access to watch and review Kilo Two Bravo, due to be released November 13th. It is the true story of a platoon of British paratroopers who are caught in a minefield by the Kajaki Dam in Afghanistan’s deadly Helmand Valley. As I have just finished a monumental, six month long, project from Hell, this weekend seems to be a timely moment to settle down and watch. Looks intense. Review pending.

[ by Charles Cameron — Aristotle, the Ismailis, CG Jung ]
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Two is the first number:

From the tenth-century Rasa’il Ikhwan al-Safa’ (Epistles or Treatises of the Brethren of Purity) as found in Seyyed Hossein Nasr & Mehdi Aminrazavi, eds., An Anthology of Philosophy in Persia, vol. 2, Ismaili Thought in the Classical Age:

We say that one is the source and generator of the numbers because when one is removed from existence all the numbers are removed with it, but when the numbers are removed from existence, one is not removed. We say that two is the first whole number because numbers are a plurality of ones, and the first plurality is two.

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I am delighted to find myself in the company of the Ismailis, having written in On two, one, seven plus or minus, and ten – towards infinity:

When I worked as senior analyst in a tiny think-shop, my boss would often ask me for an early indicator of some trend. My brain couldn’t handle that — I always needed two data points to see a pattern, and so I coined the mantra for myself, two is the first number.

One isn’t a number until there are two, because it’s limitless across all spectra and unique, and because it is its own, only context.

One isn’t a number unless there’s a mind to think of it — in which case it’s already an abstraction within that mind, and thus there are, minimally, two. At which point we are in the numbers game, and there may be many, many more than two — twenty, or plenty, or plenty-three, or the cube root of aleph null, or (ridiculous, I know) infinity-six…

Go, figure.

Two is the first number, because the two can mingle or separate, duel or duet: either way, there’s a connection, a link between them.

And in Of a non-comparative use of the DoubleQuotes method:

Putting it bluntly, one point is pointless — things could go anywhere from there. Two points suggest a line, a link, a connection — a possible, maybe even plausible, trend.

It’s that sense I have of two being the beginning of thought that makes me so fond of the DoubleQuotes format — and of Arthur Koestler‘s insight about creation occurring at the intersection of two spheres..

If I’m a fundamentalist about anything, it’s the notion that it takes two to tango!

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Furthermore..

From CG Jung, A Psychological Approach to the Dogma of the Trinity, in Psychology and Western Religion:

The number one claims an exceptional position, which we meet again in the natural philosophy of the Middle Ages. According to this, one is not a number at all; the first number is two. Two is the first number because, with it, separation and multiplication begin, which alone make counting possible. With the appearance of the number two, another appears alongside the one, a happening which is so striking that in many languages “the other” and “the second” are expressed by the same word.

And from Leonardo Tarán, Speusippus of Athens: A Critical Study With a Collection of the Related Texts and Commentary:

Now we know that Speusippus did consider one to be the first odd number, whereas Aristotle thinks that two is the first number and explicitly denies that one is a number. [ … ]

Concerning the One, then, the differences between Speusippus and Aristotle amount to this: For the latter the One is not a number, nor a separately existing entity, but the principle of number because, each number being a plurality of abstract monads, the One is its measure.

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As Emerson wrote:

The world is young; the former great men call to us affectionately.

[ by Charles Cameron — my own three-way play, and a little goose ethology from Konrad Lorenz ]
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Konrad Lorenz, Paul Leyhausen, Motivation of human and animal behavior: an ethological view, p 129

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Returning to the topic of ternary logics and scissors paper stone, here’s another old post of mine (Dec 2000):

I’ve always thought it was a training in the complete frustration of the assumption that conflict could be decided, most of all by means of skill of any kind. I mean, if you want to decide on a random basis, toss a coin, and if you want to decide on a basis of power or skill, set up a contest in which superior power or skill succeeds…

In scissors paper stone you have a setup where (as in heads and tails) no choice is superior to any other as far as chance is concerned, but there’s a troubling “threeness” about the thing which means it’s not aligned with an “either/or” logic but with a subtler logic altogether.

Two other places where this kind of “intransitivity” relation can be found would be (a) the geese studied by Konrad Lorenz which had a pecking order “a > b > c > a” (ie of the three particular geese, one would always defer to the second, which would always defer to the third, which in turn would always defer to the first) — and this is a perfectly “natural” effect which Lorenz encountered in “real life” — and (b) the impossible triangle devised by L S and R Penrose, which is clearly and unambiguously paradoxical (though logically equivalent to the Lorenz geese as far as I can tell).

Anyhow, what I’m trying to suggest is that “scissors paper stone” can work a little like a koan, it can somehow challenge our usual binary asusmptions and train us in a more flexible and “lateral” way of thinking..

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Some thoughts about a game (real or agent-based) in which three players (or sides) compete, two teaming up against one in constantly different configurations of challenge and victory (June 2005):

The idea is simplicity itself, putting it into words unambiguously is difficult.

Yesterday I was at a hotel swimming pool where two sons of another guest and my own son Emlyn were playing around together, all aged around 10-12, with nobody else there, and I asked them to play a game where one of the three would be “top guy” and the other two would try to dunk and generally overthrow him, and as soon as it became clear that the top guy had been dunked and dethroned, there would be a new “top guy” (one of the two who had been doing the overthrowing and come out the obvious winner) and the other two would pounce on him…

They were not evenly matched, but any one of them was easily outmatched by the other two working together, and being “top guy” meant your head was above water and you were, so to speak, “comfortable” — so there was a real premium on being “top guy”, and the other two were (at any time) eager to collaborate to get the position.

And there was no tendency for the two brothers to gang up against my son, because the immediacy of two defeating one was more urgent and compelling than any ideas of teaming by kinship interests, minor differences in strength and skill, etc…

More:

Prisoners’ Dilemma deals with the essence of twoness, as do many win / lose games such as tennis or chess, and this game deals with the essence of threeness, as (in a very different mode) does paper scissors rock.

My sense from PSR, and reason for being particularly interested in threeness in games, is that PSR involves thinking in flagrant defiance of our usual binary logic as humans.

I suspect my threeness game could be paradigmatic for cooperation and competition, in that each player at any given moment is either “top guy” or “member of the opposition” — and thus plays either “sole defender” (competing without a trace of collaboration) or “team attacker” (cooperating to compete) at any give moment, but with a very rapid turnover between the two.

The kids seemed to enjoy the in-the-pool version yesterday, until it the water-play got a bit too rough after about forty minutes or an hour of enthusiastic splashing and dunking.

And finally:

As a game designer, I want to think through this mode of play, two against one with switching, in a number of media — water play, three-person tag, possible card-game instantiations, board games, a chess variant perhaps, a variant on my own HipBone Games, etc — and as a conceptual matrix for game-theorizing, modeling, understanding conflict and conflict resolution, etc.

I wonder what ideas and possible uses the basic idea might trigger in others…

[ by Charles Cameron — Adam Elkus, Umberto Eco, Chris Crawford and John Robb ]
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Rock Paper Scissors, diagram by Enzoklop via Wikimedia

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Adam Elkus talks about strategy and games, in the inaugural Center for International Maritime Security “Real Time Strategy” podcast. What delighted me was his commentary on rock paper scissors between the 9.55 and 11 minute marks:

I would say that if I was to pick a single game for people to play in a structured way to understand a lot about strategy. Here’s, actually I’ll probably surprise a lot of you people here, and say they can probably just do well with rock paper scissors, in a sense that a lot of games have representational issues of how realistic or generalizable they are, and at the core a lot of strategy amounts to making choices about what to do without knowing what your opponent will do, and the game that’s one of the most atomic and basic in the way it represents that is rock paper scissors. But not just a one off game, a finite game, if you play repeated games of rock paper scissors, the way people win is by detecting sequential dependencies in the various choices that their opponent makes – so learning about the opponent over time, particularly their choices of what they’re going to field, is a very useful heuristic, is a very useful educational gesture..

Adam has more to say about rock paper scissors at his Zenpundit post, Master and (Drone) Commander?

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A couple of additional quotes, from an earlier post of mine in a private venue:

Here’s Umberto Eco in his Search for the Perfect Language:

Recent studies have established that unlike western thought, based on a two-valued logic (either true or false), Aymara thought is based on a three-valued logic, and is, therefore, capable of expressing modal subtleties which other languages can only capture through complex circumlocutions…

And here is Chris Crawford, from his justly famous Art of Computer Game Design:

The advantage of asymmetric games lies in the ability to build nontransitive or triangular relationships into the game. Transitivity is a well-defined mathematical property. In the context of games it is best illustrated with the rock-scissors-paper game. Two players play this game; each secretly selects one of the three pieces; they simultaneously announce and compare their choices. If both made the same choice the result is a draw and the game is repeated. If they make different choices, then rock breaks scissors, scissors cut paper, and paper enfolds rock. This relationship, in which each component can defeat one other and can be defeated by one other, is a nontransitive relationship; the fact that rock beats scissors and scissors beat paper does not mean that rock beats paper. Notice that this particular nontransitive relationship only produces clean results with three components. This is because each component only relates to two other components; it beats one and loses to the other. A rock-scissors-paper game with binary outcomes (win or lose) cannot be made with more than three components. One could be made with multiple components if several levels of victory (using a point system, perhaps) were admitted.

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John Robb on The Future of Drone Warfare is worth conasidering here, too, and play nicely with more of Adam’s thoughts in the podcast.

See also my post, Of games III: Rock, Paper, Tank.

And I think I’d best stop here, and make a second post on rock-scissors-paper and threeness games in general.

[ by Charles Cameron — sometimes a DoubleQuote — or even a triple or quad — is not enough ]
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So here is the first in a new occasional series I’ll call Chain-links. I haven’t figured out a format for presenting these things yet, but something of that kind will probably emerge along the way. In the meanwhile, my first entry in the series is about silence.

You are invited to consider the series of quotes here as the flow of a single idea down a sequence of steps, fluid, shifting in emphasis..

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A Roman courtroom appearance:

And Jesus stood before the governor: and the governor asked him, saying, Art thou the King of the Jews? And Jesus said unto him, Thou sayest. And when he was accused of the chief priests and elders, he answered nothing. Then said Pilate unto him, Hearest thou not how many things they witness against thee? And he answered him to never a word; insomuch that the governor marvelled greatly.

                        Matthew 27. 11-14

A British courtroom, many centuries later:

Not so. Not so, Master Secretary. The maxim is “Qui tacet consentire”: the maxim of the law is “Silence gives consent”. If therefore you wish to construe what my silence betokened, you must construe that I consented, not that I denied.

                        

                        Thomas More, in A Man for All Seasons

Contemporary diplomatic protocol:

A proposal with strong support is deemed to have been agreed unless any member raises an objection to it before a precise deadline: silence signifies assent – or, at least, acquiescence.

                        GR Berridge, Diplomacy: Theory and Practice

Before a Congressional committee, under interrogation or in court:

On counsel’s advice, I invoke my right under the Fifth Amendment not to answer, on the grounds I may incriminate myself.

                        “Taking the Fifth”

When journos ask truth of power:

No comment.

                        Press secretaries and their bureaucrats everywhere.

And for good measure:

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How does Thomas More before Cromwell — or Christ before Pilate — compare with the American who takes the Fifth, the harried executive who won’t comment?

What kind of speech is silence?

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Water flowing down the steps in the Fort Worth Water Gardens: