The predictions about artificial beaches involve obviously absurd models. The reason coastal engineers and geologists go through the futile exercise is that the federal government will not authorize the corps to build beaches without a calculation of the cost-benefit ratio, and that requires a prediction of the beaches’ durability. Although the model has no discernible basis in reality, it continues to be cited around the world because no other model even attempts to answer that important question. [...] In spite of the fact that qualitative models produce better results, our society as a whole remains overconfident about quantitative modeling. [...] We suggest applying the embarrassment test. If it would be embarrassing to state out loud a simplified version of a model’s parameters or processes, then the model cannot accurately portray the process. [...] A scientist who stated those assumptions in a public lecture would be hooted off the podium. But buried deep within a model, such absurdities are considered valid.
While the article is quite extreme in its derision of quantitative models, plugs the book the authors wrote, and employs easy rhetoric by providing only positive examples of a few failures and not negative examples of many successes, it is right that quantitative models are overrated in our society, especially in domains that involve complex systems. The myriad of unrealistic and often silly assumptions are hidden beneath layers of obtuse mathematics.
Statistics and probability were attempts to deal with failure of deterministic mathematical models, and Bayesian statistics is a further attempt to manage the uncertainty arising from not knowing what the right model is. Moreover, a vague posterior is a clear signal that you don’t have enough data to make predictions.
Someone once derided philosophers by saying that first they stir up the dust, and then they complain that they cannot see: they are taking too many things into consideration, and this prevents them from coming up with a working model that will predict anything. One does have to simplify to make any prediction, and philosophers are good at criticizing the simplifications. Finally, even false models are known to yield good results, as we are reminded by that old joke:
An engineer, a statistician, and a physicist went to the races one Saturday and laid their money down. Commiserating in the bar after the race, the engineer says, “I don’t understand why I lost all my money. I measured all the horses and calculated their strength and mechanical advantage and figured out how fast they could run. . . ”
The statistician interrupted him: “. . . but you didn’t take individual variations into account. I did a statistical analysis of their previous performances and bet on the horses with the highest probability of winning. . . ”
“. . . so if you’re so hot why are you broke?” asked the engineer. But before the argument can grow, the physicist takes out his pipe and they get a glimpse of his well-fattened wallet. Obviously here was a man who knows something about horses. They both demanded to know his secret.
“Well,” he says, between puffs on the pipe, “first I assumed all the horses were identical, spherical and in vacuum. . . ”