  The astronomically observed value of the cosmological constant is small but
non-zero. This raises two questions together known as the cosmological constant
problem a) why is lambda so nearly zero? b) why is lambda not EXACTLY zero?
Sorkin has proposed that b) can be naturally explained as a one by square root
N fluctuation by invoking discreteness of spacetime at the Planck scale due to
quantum gravity. In this paper we shed light on these questions by developing
an analogy between the cosmological constant and the surface tension of
membranes. The ``cosmological constant problem'' has a natural analogue in the
membrane context: the vanishingly small surface tension of fluid membranes
provides an example where question a) above arises and is answered. We go on to
find a direct analogue of Sorkin's proposal for answering question b) in the
membrane context, where the discreteness of spacetime translates into the
molecular structure of matter. We propose analogue experiments to probe a small
and fluctuating surface tension in fluid membranes. A counterpart of
dimensional reduction a la Kaluza-Klein and large extra dimensions also appears
in the physics of fluid membranes.
