there is an idea in number theory that if two objects are congruent modulo a prime p, then the congruence can also be seen for the special values of l functions attached to the objects. here is a context explicating this idea: suppose f and f' are holomorphic cuspidal eigenforms of weight k and level n, and suppose f is congruent to f' modulo p; suppose g is another cuspidal eigenform of weight l; if the difference k - l is large then the rankin-selberg l function l(s, f x g) has enough critical points; same for l(s, f' x g); one expects then that there is a congruence modulo p between the algebraic parts of l(m, f x g) and l(m, f' x g) for any critical point m. in this talk, after elaborating on this idea, i will describe the results of some computational experiments where one sees such congruences for ratios of critical values for rankin-selberg l-functions. towards the end of my talk, time-permitting, i will sketch a framework involving eisenstein cohomology for gl(4) over q which will permit us to prove such congruences. this is joint work with my student p. narayanan.