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This question already has an answer here:

I have seen multiple times that physicists used a formula to find the number of vacua in string theory, What formula was used to calculate the number of vacua in string theory? How did they arrive at 10^500? This is somewhat different from the question of why string theory has such a large landscape; I am asking for the mathematical details of the situation not just the logic. I want to know what math led to this, not "because there are a lot of manifolds"

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marked as duplicate by John Rennie, Kyle Kanos, ACuriousMind, joshphysics, Brandon Enright Dec 12 '14 at 20:01

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ possible duplicate of Why does string theory have such a huge landscape? $\endgroup$ – John Rennie Dec 12 '14 at 15:22
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    $\begingroup$ Damon, the accepted answer to the question I've linked explains how the $10^{500}$ is calculated, though it's in a comment to the answer not the answer itself. The source article (also written by Urs Schreiber) is here, and the calculation is discussed in the section Models in type II string theory / F-theory. $\endgroup$ – John Rennie Dec 12 '14 at 15:33
  • $\begingroup$ The only answer that comes to my mind is that sometimes theorists who have encountered non-trivial problems calculating physically testable predictions will resort to calculating untestable intellectual nonsense. I think that many "predictions" by string theorists can be summarized under this rule of perfectly normal human behavior. Having said that, this doesn't take anything away from the necessity to work trough the depths of string theory, even if it will probably be for nothing else than to reject a non-trivial, albeit beautiful hypothesis. $\endgroup$ – CuriousOne Dec 13 '14 at 1:11