Tag Archives: math

Impressions of “Biblical Games: Game Theory and the Hebrew Bible” by Steven J. Brams

biblical games steven j brams

Biblical Games is a fun book. Brams has written a basic introduction to game theory, designed to be a text used in a 400/500 level college class on the subject. But it’s also a fun introduction to the literature of the Hebrew Bible, and could be used as such in a theology class at a similar level. Plenty is missing and left out of both, but where else can you get such an unusual double-introduction?

Game theory is a way of mathematically modeling human interactions based on preferences. Game theory breaks down human behavior into a small number of games, such as the Battle of the Sexes game (trigger warning: assumes basic familiarity with human sexes).

Because the Hebrew Bible concerns human struggling in an incomprehensible world, there are plenty examples of these “games.” For example, in discussions the Battle of the Sexes game, Brams describes Samson and Delilah, David and Abigail, and Esther and Ahasuerus. While much is left out (the romantic comedy innuendo of the “golden scepter,” and the sadomasochistic subtext of Samson and Delilah, for instance), Brams treats his subjects seriously, which is far more than is done in most sermons and even much pop biblical criticism. No “dumb semite” theory here.


Biblical Games twice examines the Binding of Isaac, once presenting a preference schedule that might explains what happened in the Hebrew Bible (that Abraham did not believe his son would truly die), and another that explains an alternative set of actions (if Abraham had refused to bind Isaac).  But that each is equally convincing seems to be a problem.  If human interaction can be “formalized” — put into mathematical terms — so easily, in such contradictory ways, is not the “formalization” simply an obscurantic tautology?

Other biblical themes — such as the “fraught with background” nature of the Hebrew Bible (where much more is hinted at or assumed than is spoken) are hinted at, which makes Biblical Games a good teaser to the Old Testament. Likewise, Brams briefly describes how God almost seems to be a composite character, in some ways fully divine, in some ways a human being, in some ways proceeding from a different source…

My greatest disappointment in Biblical Games is that in discussing God, both the author’s mathematics and theology fail. In the final chapter, where Brams discusses the “theory of moves” (pdf description), he for the first time hints at the terrifying implications of “stopping power.” But otherwise God is presented as just another player, traveling in time at 60 minutes/hour with all the rest.

A time-bound God is problematic because a basic conception of God (explicitly rejected by Brams) is that He is hyper-dimensional, at least present at all possible points in time at once (which would at the very least make Him a four-dimensional being, as opposed to three-dimensional beings traveling along the axis of a fourth dimension). This would have been a neat way to introduce hyperspatial geometry, the idea that a higher-dimensional object can be “unfolded” or “shadowed” into lower-dimensional space. The shadow of the tesseract, or four-dimensional cube, can be drawn in this manner…


While the shadow of an unfolded tessaract on two-dimensional space looks like


One imagines a fuller description of God would have lead to an additional, interesting chapter, but such was more forthcoming. For “cursed is he who is hung on a tree” (Deuteronomy 21:23), as was the Son of David (2 Samuel 18:9). But such a chapter must be kept to our imagination.

Biblical Games is a fun book. It’s not the final or most convening word on either game theory or the Hebrew Bible, but its a very readable introduction to both.

Liberals v. Science

Science is unpopular. Many, especially among the uneducated branches of the religious right, reject evolution.

It is equally unpopular among many liberals, who reject what science says about sex differences.

As educated liberals have much more influence over the formation of national policy than uneducated religionists, I’m more concerned about liberals.

For instance, yet another study came out showing, once again, that males have a much greater variance in math achievement than females. That is, female scores tend to bunch together near the mean, while male scales are more likely to be way up or way down. While this leaves the average unchanged, it implies both more math PhDs and more special education students will be males. More of the typical ‘good students’ (but not overachievers) that teachers like are females.


Unsurprisingly, the New York Times reports the study as finding no sex differences. Other liberal publications, such as the Los Angeles Times, Scientific American, and The Chronicle of Higher Education toe the party line. This would be like a Jack Chick pamphlet describing modern biology as reporting no evidence for evolution.

Fortunately, the Wall Street Journal (owned by Rupert Murdoch, who supports science) gets it right.

Thanks to gnxp, Marginal Revolution, and Statistical Modeling, Causal Inference, and Social Science for helping to uncover this story.