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

Saturday, 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..

Rumsfeld and Churchill’s game, also..

Monday, January 25th, 2016

[ by Charles Cameron — two Churchill games suitable for militarily-inclined cigar mavens ]

First, because Rumsfeld here releases Churchill‘s own game in digital form, we have Churchill Solitaire:

And second, more interesting from my POV because it’s a variant on what I’ve called “threeness games” —


Two-sided nuke-rattling against the ISIS third?

Thursday, December 17th, 2015

[ by Charles Cameron — trying to catch up with posts here when working on book proposals ]

Consider these two statements made in recent days:


How does a war game — or game theory, for that matter — deal with the differenes, similarities, or continuum between threats and exercises on the one hand, and the actions they threaten or game on the other?


I have eagerly forgotten what temperature a nuclear strike inflicts on its human victims, and just how quickly they arrive there from room temperature. A sahih (trustworthy) hadith found in Tirmidhi tells us that the Prophet reserved the burning of infidels for God in the hereafter, and rejected its use by his followers in carrying out a death sentence:

That ‘Ali burnt some people who apostasized from Islam. This news reached Ibn ‘Abbas, so he said: “If it were me I would have killed them according to the statement of Messenger of Allah (saw). The Messenger of Allah (saw) said: ‘Whoever changes his religion then kill him.’ And I would not have burned them because the Messenger of Allah (saw) said: ‘Do not punish with the punishment of Allah.’ So this reached ‘Ali, and he said: “Ibn ‘Abbas has told the truth.”

I lasck specific knowledge of contemporary commentary on this hadith, but it occurs to me that in the time of the early Muslim community’s war for survival, apostasy would be equivalent to desertion. The US sentence for desertion in time of war, to this day, is described thus in the US Manual for Courts-Martial:

Any person found guilty of desertion or attempt to desert shall be punished, if the offense is committed in time of war, by death or such other punishment as a court-martial may direct,

The death penalty for desertion in time of war was last administered by US authorities in 1945.


Don’t we have something pretty close to a taboo on the use of nuclear weaponry?

Spectacularly non-obvious, 2: threeness games

Friday, October 30th, 2015

[ by Charles Cameron — my own three-way play, and a little goose ethology from Konrad Lorenz ]

lorenz goose geese gander pecking order from laws of the game
Konrad Lorenz, Paul Leyhausen, Motivation of human and animal behavior: an ethological view, p 129


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..


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…


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…

Trump as Cinderella’s Fairy Godmother

Monday, September 28th, 2015

[ by Charles Cameron — on finger-based decision theory ]

Surely this is the answer to Decision Theory and Human Behavior — don’t we all do it this way?

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