  Between Snyder's quantized space-time model in de Sitter space of momenta and
the \dS special relativity on \dS-spacetime of radius $R$ with Beltrami
coordinates, there is a one-to-one dual correspondence supported by a minimum
uncertainty-like argument. Together with Planck length $\ell_P$, $R\simeq
(3/\Lambda)^{1/2}$ should be a fundamental constant. They lead to a
dimensionless constant $g{\sim\ell_PR^{-1}}=(G\hbar c^{-3}\Lambda/3)^{1/2}\sim
10^{-61}$. These indicate that physics at these two scales should be dual to
each other and there is in-between gravity of local \dS-invariance
characterized by $g$. A simple model of \dS-gravity with a gauge-like action on
umbilical manifolds may show these characters. It can pass the observation
tests and support the duality.
