  The point-to-set principle characterizes the Hausdorff dimension of a subset
$E\subseteq\R^n$ by the effective dimension of its individual points. This
characterization has been used to prove several results in classical, i.e.,
without any computability requirements, analysis. Recent work has shown that
algorithmic techniques can be fruitfully applied to Marstrand's projection
theorem, a fundamental result in fractal geometry.
  In this paper, we introduce an extension of point-to-set principle - the
notion of optimal oracles for subsets $E\subseteq\R^n$. One of the primary
motivations of this definition is that, if $E$ has optimal oracles, then the
conclusion of Marstrand's projection theorem holds for $E$. We show that every
analytic set has optimal oracles. We also prove that if the Hausdorff and
packing dimensions of $E$ agree, then $E$ has optimal oracles. Thus, the
existence of optimal oracles subsume the currently known sufficient conditions
for Marstrand's theorem to hold.
  Under certain assumptions, every set has optimal oracles. However, assuming
the axiom of choice and the continuum hypothesis, we construct sets which do
not have optimal oracles. This construction naturally leads to a new,
algorithmic, proof of Davies theorem on projections.
