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    Re: Still on LOP's
    From: Martin Gardner
    Date: 2002 Apr 20, 07:32 -0700

    My point, and I do have one...
    As this discussion continues, I think it drifts perilously from George's
    start, into muddy and shoal water:
    Here's where I stand -
    I have no reason to doubt probability ellipses, even if I can't calculate
    them.  I believe they tell us as much as we would want to know about where
    we are.
    What I wanted to do was follow George and see if a much simpler geometric
    analysis could  - just for the hell of it - give us a single number for the
    chances we were inside the hat.
    For me, taking simplified probability distributions, etc. goes the wrong
    way: I have the greatest confidence that these approaches, simulations,
    numerical methods, etc, will ultimately give us ellipses - the hard way.
    The scariest suggestion I have heard, and I can't recall who said it, was
    that perhaps there is no single number that defines our likelihood of being
    inside the hat in all cases.
    Somebody who does understand the ellipses might find an example where the
    90% ( or 85%, or 92%) ellipse lies entirely outside the hat, or entirely
    within it - that would convince me there's no single value for the odds of
    being inside the hat, and I could move on with my life.

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