  Current numerical conformal bootstrap techniques carve out islands in theory
space by repeatedly checking whether points are allowed or excluded. We propose
a new method for searching theory space that replaces the binary information
"allowed"/"excluded" with a continuous "navigator" function that is negative in
the allowed region and positive in the excluded region. Such a navigator
function allows one to efficiently explore high-dimensional parameter spaces
and smoothly sail towards any islands they may contain. The specific functions
we introduce have several attractive features: they are everywhere
well-defined, can be computed with standard methods, and evaluation of their
gradient is immediate due to an SDP gradient formula that we provide. The
latter property allows for the use of efficient quasi-Newton optimization
methods, which we illustrate by navigating towards the 3d Ising island.
