My approach for initiating discussion  of "large data" visualizes "Data Assimilation": the numerical  blending of
(a) all Observations of a system with (b) "Ideas" (expressed as model simulations based on laws/theories)..

This results in optimal analysis of a system state, which can be used for
(a) diagnosing system  mechanics,
(b) providing  initial conditions for predictions into the future,
(c) identifying errors in observations or models,
(d) predicting  forecast chaotic uncertainty,
(e) understanding mechanisms of change (e.g. natural climate variability vs. human-induced change)
(f) clarifying statistical & mechanistic relationships (e.g., power law pdfs)

Future developments:

(a) Observations from a huge variety of sources, with increased spatial resolution
(b) Models
of higher resolution, with more precisely & complete algorithms