March 1st, 2007

Biblical Games

Mathematics is no more than symbolism. But it is the only symbolism invented by the human mind which steadfastly resists the constant attempts of the mind to shift and smudge the meaning. (c) J. Bronowski and Bruce Mazlish, The Western Intellectual Tradition

Game theory, in my opinion, is a tool ideally suited for penetrating the complex decision-making situation often described in the Bible.
Although the idea that God and cast of human characters play games may seem bizarre if not preposterous, I shall try to show in a variety of biblical stories that this is not only a reasonable interpretation but also that the players in these games - including God - acted rationally.

The Imposition of Constraints

To decide whom to help and support, it would appear rational for God to impose constraints on human activities. The first constraint God imposed on man was not to eat from the tree of knowledge of good and bad in the Garden of Eden.
To demonstrate the value of constraints on, surprisingly, man as well as God, consider the outcome matrix (see figure).

God, depicted as the row player, has two strategies in this two-person game:

1. Impose constraints: I
2. Don't impose constraints: Ii

Like God, Adam and Eve have two strategies:

1. Adhere to constraints: A
2. Don't adhere to constraints: Aa

(x,y) = (God, Adam and Eve)
4 = best, 3 = next best, 2 = next worst, 1 = worst

One might ask what it means for God not to impose constraints and then for Adam and Eve to adhere to the (nonexistent) constraints. In this situation I assume that Adam and Eve are aware of God's preferences as to what constraints they might voluntarily observe. Similarly, God knows Adam and Eve preferences. A game in which each player knows the other player's preferences is called a game of complete information.
The consequences arising from the strategy choices of both players are summarized verbally in the outcome matrix. (The pairs of numbers associated with the different outcomes define the preferences of the players.)

(c) Steven Brams, Biblical Games: a strategic Analysis of stories in the Old Testament

The line between blasphemy and irony is very slight. But... it is one of the best mathematical theories :)
promo seagull_gull october 6, 2014 19:23 Leave a comment
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