Some wags would say that many (most?) large scale, long term computer simulations fall into this category, although you might have a hard time getting their proponents to agree with this assessment. (You know what I'm talking about!) On the other hand, Chris Anderson's now-famous rant "The End of Theory: The Data Deluge Makes the Scientific Method Obsolete" argues that data trumps theory: http://www.wired.com/science/discoveries/magazine/16-07/pb_theory "All models are wrong, but some are useful." So proclaimed statistician George Box 30 years ago, and he was right. Peter Norvig, Google's research director, offered an update to George Box's maxim: "All models are wrong, and increasingly you can succeed without them." At 08:41 AM 7/2/2013, James Propp wrote:
For some thoughts about the enterprise of computing quantities one hasn't rigorously defined, see http://mathoverflow.net/questions/135536/procedure-based-as-opposed-to-defin... (which I hope will elicit interesting responses over the next few days).
Jim Propp