Re: virus: reverberant doubt
Fri, 6 Dec 1996 14:21:39 -0600 (CST)

On Wed, 27 Nov 1996, Duane Hewitt wrote:

> Reverberant doubt comes from a passage in Darwin's Dangerous Idea that is
> quoted from Hofstadter. He refers to it as "Wolf's Dilemma" in which a
> nondilemma is turned into a serious dilemma by nothing but the passage of
> time and the possibility of reverberant doubt.
> The quoted passage follows:
> Imagine that twenty people are selected from your high school graduation
> class, you among them. You don't know which others have been selected ...
> All you know is that they are all connected to a central computer. Each of
> you is in a little cubicle, seated on a chair and facing one button on an
> otherwise blank wall. You are given ten minutes to decide whether or not
> to push your button. At the end of that time, a light will go on for ten
> seconds, and while it is on, you may either push or refrain from pushing.
> All the responses will then go to the central computer and one minute
> later they will result in consequences. Fortunately, the consequences can
> only be good. If you pushed your button you will get $100, no strings
> attached ... If NOBODY pushed their button then EVERYBODY will get $1000.
> But if there was even a single button pusher, the refrainers will get
> nothing at all. [Hofstadter 1985, 752-53]{quoted from Dennett 1995,
> 507-508}
> Now this is a situation which at first glance the solution seems obvious.

WHAT???? At a first glance, the solution seems *inobvious* to me. See
below: problem setup is everything.

> But there is room for doubt regarding the rationality of your fellow
> classmates. It is suggested that "A bunch of amiable slowpokes" would
> arrive at a better outcome than "razor-sharp logicians who all think
> perversely recursively reverberantly".
> Any comments?

As a 20-player nonzero-sum game: the solution is inobvious, if it indeed
exists. The problem setup has wiped out the social context required to
allow easy access to the first solution suggested above [all 20 do not
press that button]. The problem starts with a 'model of mind' for the 19
others, and generally torments the Math Department.

As a 2-player zero-sum game: "Me against a hostile universe"

Me/19 others PRESS NoPress
PRESS $100 $100
NoPress $0 $1000

In a hostile universe [Murphy's Law, 2nd law of Thermodynamics[sic],
whatever], it is in "nature's" best interest to have at least 1 of the 19
PRESS the button, thus completely locking out 1 column of the diagram:

Me/19 others PRESS
PRESS $100
NoPress $0

So, in a hostile universe, the calculation is easy: "press the button".