Alexander Cockburn in Beat the Devil

It's always a pleasure to read Cockburn in The Nation (and in Counterpunch, which I highly recommend), but this time he has outdone himself in amusing first paragraphs. This is from a column titled "The Triumph of Crackpot Realism" (August 14/21 issue, pg 10):

The frayed threads anchoring the American government to reality have finally snapped, just at the moment radiologists are reporting that Americans are getting too fat to be X-rayed or shoved into any existing MRI tube. The gamma rays can't get through the blubber, same way actual conditions in the outside world bounce off the impenetrable dome of imbecility sheltering America's political leadership. Twenty-three years after one of America's stupidest Presidents announced Star Wars, Reagan's dream has come true. Behind ramparts guarded by a coalition of liars extending from Rupert Murdoch to the New York Times, from Bill O'Reilly to PBS, America is totally shielded from truth.

Nontransitivity in partisan misere games

In continuing to mess around with misere partisan games, I just found that the three birthday-two-or-less games 0, {1|*}, and { | 0,-1} stand in the relations

Of course, one doesn't want an relation like "greater than" to be nontransitive. I'm actually glad to find pathology like this because it means that there's probably some interesting theory to be worked out for misere partisan games that doesn't just follow the path taken in Conway's On Numbers and Games.

In normal play, the recursive definition of a game's negative is

In introducing this notation, one expects that

will be true, and it is true, for arbitrary G, in normal play. The G+(-G)= equation already fails for *2 in misere play, since *2 would be its own "negative," yet *2+*2 is not indistinguishable from zero.

Nevertheless, I still held out some hope that order relations might be a useful concept in misere play, in particular for reduction to some (as yet, undetermined) notion of a misere canonical form via dominated options (and they still might be, somehow), even with this somewhat flawed version of the "negative" operator.

In normal play, one can say that G > H if G + (-H) is a win for Left, no matter who moves first. I wondered how this would behave in misere play, assuming that the definition of "minus" is as it is in normal play, and the definition of > is as it is normal play, and that's how I (more precisely: Mathematica and I) found the example.