  Constants of Nature that have nongeneric values pose a riddle often referred
to as the finetuning problem. The conspicuous values assumed by many physical
constants (e.g., the vanishing effective cosmological constant, the smallness
of the Higgs mass compared to the Planck scale, the finestructure constants,
$\Theta_{QCD}$) seem to coincide with values that are obtained if one assumes
that Nature in general seeks out multiple point values for intensive
parameters. Multiple point values would occur in the presence of many
coexisting phases. Such coexistence could be enforced by having fixed but not
finetuned amounts of extensive quantities. We show that universally fixed
amounts of extensive quantities is tantamount to having long range nonlocal
interactions of a special type: these interactions are identical between fields
at all pairs of spacetime points regardless of the spacetime distance between
them. Such omnipresent nonlocal interactions, which can be described by a very
general form of a reparameterization invariant action, would not be perceived
as ``action at a distance'' but rather most likely incorporated into our theory
as constants of Nature. Hence one can speculate that this mild form of
nonlocality is the underlying explanation of Nature's affinity for the multiple
point. We also speculate that nonlocal effects, described by fields depending
on two spacetime points, may be responsible for the replication of the fields
in three generations. Such a nonlocal mechanism would also triple the number of
boson fields, as in the antigrand unification model. We briefly review the
multiple point predictions for the three fine structure constants and the
resolution of the quark-lepton mass hierarchy problem in this antigrand unified
extension of the Standard Model.
