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For two points X, Y in Teichmuller space, the Lipschitz distance L(X,Y) from X to Y was defined by Thurston to be the log of the minimal Lipschitz constant from X to Y. We define a symmetric version by taking S(X,Y)=max{ L(X,Y), L(Y,X) } and compare this with the Teichmuller distance T(X,Y) between X,Y. In particular, we give an example of points X,Y such that S(X,Y) is arbitrarily close to zero while T(X,Y) is arbitrarily large. We also show, however, that on the thick part of Teichmuller space, the two distances are equal up to a bounded error. Further analysis of the thin part will be mentioned if time permits. (Joint work with Kasra Rafi)