"They build models to match the observed data. When the models don't match new data they develop new theories and test them against the new data."

Thanks, an apt description of "Just So" models. Such models are mainly empirical, built on observed data plus some math and physics in an attempt to match what's observed or imagined by the model's creator. Time after time such models have failed to predict the surprises that nature has in store.

Another type of really heavily mathematical models are those self-deluding models designed by economics PhDs that were widely employed in financial risk assessments. They basicly told the customers (Financial Institutions, Bond Rating Firms, etc.) just what they wanted to hear, that their new financial products had acceptical risk. In this instance the wrong type of statistical tools were used, normal curve distribution oriented models that failed to match the cruel real world. A semi-technical and entertaining treatise on the folly of these seemingly analytical model builders can be found in mathemetician-financial analyist-engineer Nassim Nicholas Taleb's "The Black Swan". Money quote, "The government-sponsored institution Fannie Mae, when I look at its risks, seems to be sitting on a barrel of dynamite, vulnerable to the slightest hiccup. But not to worry: their large staff of scientists deem these events "unlikely"."

Contrast these flawed modeling attempts with Newtonian or realtivistic model predictions that are NOT empirical but are computational models based on the laws of physics and correctly applied mathematics. I know which types I believe in and which types I am skeptical of. Most folks don't distinguish between the approaches.