From: "a_jakulin@"@hotmail.com   
      
   jonathan wrote:   
   > If 2 variables correlate we can't imply causality. It could be that   
   > the 1st variable cause the other. It could be the other way around.   
   > It could be that they both correlates with a third variable.   
      
   Generally, it's impossible to know if it was something causal or just   
   a coincidence. Statisticians mantain that causality can only be   
   verified through controlled experiments. If you have variables X and   
   Y, you confirm causality by wiggling X while keeping everything else   
   constant. If Y "feels" this wiggling, X causes Y. You can perform the   
   experiment in the other direction and wiggle Y. If wiggling Y doesn't   
   affect X, but wiggling X affects Y, we can state that X causes Y.   
      
   Most real phenomena, however, involve bidirectional interactions: the   
   Earth is tugging on the Moon as much as Moon is tugging on Earth.   
   Indiscriminate use of causality may be misleading here. Furthermore,   
   it is very hard to keep everything constant: how do you know?   
      
   > I've heard that if we know 3 variables, then we can imply causality.   
   > How in the earth the 3rd variable help us that?   
      
   The 3rd variable can invalidate a causal claim. For example, if I say   
   that X causes Y. I then observe the 3rd variable Z, and it turns out   
   that X and Y are independent in the context of Z. This can be written   
   information-theoretically as I(X;Y|Z)=0. Therefore, a better   
   explanation of the situation is that Z causes both X and Y. So,   
   interpret the 3rd variable as something that invalidates causal   
   claims, this is known as Simpson's paradox. This way, by postulating   
   causal claims when they cannot be falsified, is the basis for some   
   machine learning methods that seek to discover causality.   
      
   In brief:   
   * assert causality for empirical phenomena can only be done based on   
   controlled experiments   
   * the 3rd variable can be used to falsify a causal claim without   
   controlled experiments; but a 4th variable can falsify this   
   falsification, and so on.   
      
   This is a very simple take on things. This stuff is subject to active   
   debate in general. Others might want to fill in some more detail.   
   Also, see:   
   http://bayes.cs.ucla.edu/home.html   
   http://www.hss.cmu.edu/philosophy/people/directory/Peter_Spirtes.html   
   http://plato.stanford.edu/entries/causation-process/   
      
   Best regards,   
               Aleks   
   --   
   mag. Aleks Jakulin   
   http://www.ailab.si/aleks/   
   Artificial Intelligence Laboratory,   
   Faculty of Computer and Information Science,   
   University of Ljubljana, Slovenia.   
      
   [ comp.ai is moderated.  To submit, just post and be patient, or if ]   
   [ that fails mail your article to , and ]   
   [ ask your news administrator to fix the problems with your system. ]   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)