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1) How we determine whether the higher dimensions are Unstable or Unpredictable? Or on the basis of what assumption we make this prediction?

Dimensions

(Source of Image: Max Tegmark. See also this Wikipedia article.)

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The diagram is taken from the Max Tegmark reference in your linked wikipedia article. In it Tegmark explains how he came to those conclusions. – twistor59 Jan 1 '13 at 15:53
    
@twistor59: Thanks. Updated the question accordingly. – Qmechanic Jan 1 '13 at 16:02
    
Related: physics.stackexchange.com/q/10651/2451 – Qmechanic Jan 1 '13 at 16:03

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