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The structural properties of the world are not sensitive to small local perturbations of many parameters about their actual values. However, nuclear physics would change drastically with even small changes in mu and md at the level of a few percent. Grand unification leaves these as independent parameters without relations fixed by symmetries, so we may conjecture that they remain so in more inclusive unified theories. This leaves just about enough freedom for a multiverse to find a world which has stable protons, produces carbon and oxygen, and still endows these atoms with a rich interactive chemistry.

The paradigm of a fixed, calculable, dimensionless quantity in physics is the anomalous magnetic moment of the electron (Hughes and Kinoshita 1999). In a display of spectacular experimental and theoretical technique, it is measured to be (Van Dyck, Schwinberg and Dehmelt 1987) a ident (g - 2) / 2 = 1,159,652,188.4 (4.3) x 10-12, a precision of 4 parts per billion; it is calculated to even better accuracy except for the uncertainty in the fine structure constant, which limits accuracy of the agreement to about 30 ppb. This agreement cannot be an accident - the precision tells us that we really understand the origin of this dimensionless number. The precision is exceptional because the dimensionless numbers can be measured so accurately and the theory is clean enough to calculate so accurately. It is hard to measure precisely because nothing in particular depends critically on what the exact final digits in the expansion are. We expect this to be so in such a case of a mathematically computable number. It would be disturbing if a different number in the ninth decimal place would make a big difference to (say) element production, because it would indicate a conspiracy at a level where we have no mechanism to explain it. On the other hand a fine tuning in an adjustable parameter is easy to live with because we have a physical way to arrange that. So, the attitude adopted here is that maybe we can find the adjustable parameters by looking for the places where fine tuning is needed. The clue is in the derivative DeltaWorld / Deltaparameter, how much the phenomena change as a result of a parameter change; we should look for the fundamental flexibilities in the fundamental theory where this derivative is large.

Grand Unification permits about enough freedom in Standard Model parameters to account for the apparent fine tunings by selection from an ensemble of possibilities. This is a useful lesson to bear in mind as unification theory forges ahead seeking to fix new predictions - contrary to the aspirations of many in the unification community, we should not expect to find more relationships among Standard Model parameters to be fixed by symmetry in the final theory than are fixed by the ideas we have in place already, at least not among the light fermion masses.

These considerations may help to guide us to the connections of superstrings to the low energy world. For example, Kane et al. (2000) have pointed out that the ideal superstring theory indeed predicts absolutely everything, including the light lepton mass ratios, seemingly allowing no room for tuning. However, even here there is the possibility that the exact predictions do not specify a unique universe at low energy but correspond to many discrete options - many minima in a vast superpotential. If the minima are numerous enough a close-to-optimal set of parameters can still be found. The fundamental theory might predict the properties of all the minima but the main choice may still be made by selection. String-motivated ideas for explaining the mass hierarchy outside of the context of standard GUTs (e.g. theories with extra dimensions - Arkani-Hamed et al. 1998, Dienes et al. 1998, 1999, Randall and Sundrum 1999) may offer similar options for optimizing the Yukawa couplings.

Anthropic arguments are often said to lack predictive power. However, within a theoretical framework specific predictions do emerge from the guesses made from anthropic clues, which could falsify a particular conjecture: for example, the conjecture that the deuteron and proton stability arise from selection of light quark masses from a continuous spectrum of possible values predicts that in fundamental theory, it will not be possible to mathematically derive from first principles the value of (md - mu) / mproton. At the very least this should be regarded as a challenge to a community which has so far been very successful in discovering ways to reduce the number of free parameters in various unification schemes. One is reminded of Darwin's theory, which is a powerful explanatory tool even though some question its predictive power. Anthropic arguments are vulnerable in the same way to ``just-so'' storytelling but may nevertheless form an important part of cosmological theory.


I am grateful for conversations with D. Brownlee, S. Ellis, G. Gonzalez, W. Haxton, G. Kane, M. Perry, J. Preskill, M. Rees, S. Sharpe, M. Tegmark, P. Ward, and L. Yaffe, and am particularly grateful for detailed comments by M. Fukugita. This work was supported by NASA and NSF at the University of Washington, by the Isaac Newton Institute for Mathematical Sciences, University of Cambridge, and by a Humboldt Research Award at the Max Planck Institute für Astrophysik, Garching.

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