The weak anthropic principle and the landscape of string theory

We note that there is an exception to the general arguments that no falsifiable predictions can be made, on the basis of of presently available data, by applying the weak anthropic principle (WAP) to the landscape of string theory. If there are infinitely more vacua in the landscape for one sign of a parameter than the other, within an anthropicaly allowed range, then under very weak assumptions about the probability measure one gets a firm prediction favoring that sign of that parameter. It is interesting to note that while the understanding of the string landscape is evolving, present evidence on the nature of the landscape allows such an argument to be made, leading to the conclusion that the WAP favors a negative value for the cosmological constant, $\mathrm{\Lambda }$, in contradiction to the result of astronomical observations. The viability of applying the WAP to string theory then requires that either there are found an infinite discretum of anthropically allowed vacua for $\Lambda

0$,ortherecentlyfoundinfinitediscretumofsolutionsfor$\Lambda <0$ be reduced to a finite value.