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Re: Monty Hall Problem

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  • Jürgen Ahting
    Hi Victor, Hi Steve, the problem is not with intuition or rational thought alone but with a mismatch between their results. This mismatch is created by
    Message 1 of 2 , Apr 14, 2005
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      Hi Victor,
      Hi Steve,

      the problem is not with intuition or rational thought alone but with a
      mismatch between their results.

      This mismatch is created by tricking the person who has to choose with
      clever wording on a wrong trail.
      It's about choosing a door with the "price" and then "switching".

      The real story goes the other way round:
      - You choose one door you will /not/ open.
      - The host is forced to open one of the other doors with a goat.
      - Then you take the remaining third door.

      It is obvious that your 2/3 chance of initially picking a door with a
      goat directly translates into a 2/3 chance of finding the price behind
      the third door:
      - You never intended to pick the "price" door on your first try,
      - You don't do any "switching" because you always intended to select the
      third door.


      Or look at it an other way:

      If you are led into the room with three doors, one open showing a goat,
      your chance is 50%.
      It is the information you get you're told under which restrictions the
      host had to open the door with goat, i.e. which door he was not allowed
      to open, which shifts the chances to 2/3 in your favor.


      So the point is not that rational thought can lead to false conclusions.
      The point is how easy it is to trick us off the track of rational
      thought without letting us realize it.
      Our intuition tells us that we are still on the track of rational
      thought while we are in fact already stuck in quicksand.


      Jürgen

      --------
      Jürgen Ahting - AMECO GmbH

      If you give me six lines written by the most honest man, I will find
      something in them to hang him. -- Cardinal Richelieu


      Victor wrote:
      > > How is intuition relevant to this thread? Both the right answer
      > > and wrong answer are based on rational thought.
      >
      > All rational thought is ultimately based on intuition. For example,
      if you
      > think about the mathematical axioms, you'll see that they are designed to
      > reflect a certain intuition about the world. This becomes obvious
      when you
      > compare the motivation for the Euclidian geometry as compared with the
      > spherical geometry, like the concept of the shortest path between two
      > points.
      >
      > Rather than being incongruent, rational thought and intuition are
      > intertwined aspects of the same thought processes.
      >
      > Victor
      >
      > ===============================================
      >
      > ----- Original Message -----
      > From: "Steve Bate" <steve@t...>
      > To: <extremeprogramming@yahoogroups.com>
      > Sent: Thursday, April 14, 2005 9:11 AM
      > Subject: RE: [XP] Monty Hall Problem
      >
      >
      > >
      > > > From: Ron Jeffries [mailto:ronjeffries@X...]
      > > >
      > > > On Thursday, April 14, 2005, at 3:47:13 AM, Alain Ravet wrote:
      > > > > Intuitively, I would.
      > > > > But that's the point of this thread: being wrong, by intuition :)
      > > >
      > > > Perhaps. Or perhaps the lesson is that there is a way to look at
      > > > things such that intuition works for us instead of against. Because
      > > > this time, our intuition is helping us. Switching is the right thing
      > > > to do with p=2/3.
      > >
      > > How is intuition relevant to this thread? Both the right answer
      > > and wrong answer are based on rational thought. It seems to me
      > > the thread is showing the potential weakness of rational thought
      > > rather than saying anything about intuition (which is not based on
      > > reason). Are we more willing to admit our "intuition" is wrong than
      > > that our reasoning is wrong?
      > >
      > > It can be somewhat disheartening to be so certain we know something
      > > is true and be convinced that we can prove it rationally and then
      > > find out we were wrong. If we can be this certain and wrong on
      > > relatively simple topics, how can we be certain about our reasoning
      > > on more complex topics? I wonder if blaming the mistake on
      > > "intuition" is our way of escaping that question.
      > >
      > > Steve
    • Jürgen Ahting
      Hi William, ... - Being reasonable and being rational gets things done. - Playing to the intuition of your superiors might give you a pay rise. This matches
      Message 2 of 2 , Apr 14, 2005
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        Hi William,


        > 3. Being reasonable and being rational were apparently not
        > characteristics needed to be a successful software product
        > manager.

        - "Being reasonable and being rational" gets things done.
        - Playing to the intuition of your superiors might give you a pay rise.

        This matches what is often regarded as a "/successful/ software product
        manager" ;-)

        Jürgen

        --
        Jürgen Ahting - AMECO GmbH

        If you give me six lines written by the most honest man, I will find
        something in them to hang him. -- Cardinal Richelieu
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