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Monday, June 16, 2008

Monday June 16, 2008

Filed under: General,Geometry — m759 @ 9:00 PM
Bloomsday for Nash:
The Revelation Game

(American Mathematical Society Feb. 2008
review of Steven Brams’s Superior Beings:
If They Exist, How Would We Know?)

(pdf, 15 megabytes)

“Brams does not attempt to prove or disprove God. He uses elementary ideas from game theory to create situations between a Person (P) and God (Supreme Being, SB) and discusses how each reacts to the other in these model scenarios….

In the ‘Revelation Game,’ for example, the Person (P) has two options:
1) P can believe in SB’s existence
2) P can not believe in SB’s existence
The Supreme Being also has two options:
1) SB can reveal Himself
2) SB can not reveal Himself

Each player also has a primary and secondary goal. For the Person, the primary goal is to have his belief (or non-belief) confirmed by evidence (or lack thereof). The secondary goal is to ‘prefer to believe in SB’s existence.’ For the Supreme Being, the primary goal is to have P believe in His existence, while the secondary goal is to not reveal Himself. These goals allow us to rank all the outcomes for each player from best (4) to worst (1). We end up with a matrix as follows (the first number in the parentheses represents the SB’s ranking for that box; the second number represents P’s ranking):

Revelation Game payoff matrix

The question we must answer is: what is the Nash equilibrium in this case?”

Analogously:

Lotteries on
Bloomsday,
June 16,
2008
Pennsylvania
(No revelation)
New York
(Revelation)
Mid-day
(No belief)
418

The Exorcist

No belief,
no revelation

064

4x4x4 cube summarizing geometry of the I Ching

Revelation
without belief

Evening
(Belief)
709

Human Conflict Number Five album by The 10,000 Maniacs

Belief without
revelation

198

(A Cheap
Epiphany)

Black disc from end of Ch. 17 of Ulysses

Belief and
revelation

The holy image

Black disc from end of Ch. 17 of Ulysses

denoting belief and revelation
may be interpreted as
a black hole or as a
symbol by James Joyce:

When?

Going to dark bed there was a square round Sinbad the Sailor roc’s auk’s egg in the night of the bed of all the auks of the rocs of Darkinbad the Brightdayler.

Where?

Black disc from end of Ch. 17 in Ulysses

Ulysses, conclusion of Chapter 17

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