ape said:
I once came across the idea that the truth of our models is not what is important, but what is important is that our models allow us to make accurate predictions regardless of whether or not they are technically true.
Is this idea correct and is it shared by the physics community at large?
bapowell said:
I suppose it depends on the individual. If you are a statistician, then you probably only care whether the model makes accurate predictions. But as a physicist, I like to think that our current models are more than handy statistical representations. I would hope that they reveal something fundamental and true about what our universe is made of and how it has evolved.
I like this patient truthful commonsense answer. I'll perturb the discussion a little in the hope of contributing a different angle. It may sound a bit wacky:
what is important about a mathematical model?
Models inspire us with new concepts and ideas. We even add new words to our spoken language in an effort to understand models and how they work.
The human mind, its language, evolves. There are no prior fixed boundaries to thought.
One person can say "this model explains nothing, it merely fits the data and makes correct predictions, but it does not say anything true about nature".
He may not have the necessary concepts to recognize the truth which the model holds.
Another person, or the same person later, may tune into the model and be inspired by it.
Or he may be troubled by some puzzle and be forced to invent another model to cure an apparent paradox or conflict.
The human mind, and its ability to understand nature, evolves----as if walking forwards on two legs----the right foot is the mathematical model that fits the data and the left foot is the verbal understanding of what the model "means".
Sometimes one is ahead somethings the other. When we advance the model we do not care what it "means" (and we may not have words to translate what the model grasps for us) we care only that it fits the data. Then we step forward with the other foot and learn from the model a new idea, and then perhaps go ahead with new intuition.
Walking like this, with two legs, is better than trying to hop along on just one foot.
"Raffiniert ist der Herr Gott, aber boshaft ist er nicht."
This is a faith in the evolution of the human mind that goes on two feet. It is the faith that the mathematical models that we construct will not mislead us and fool us. The universe is not malicious although the mathematical regularities may be subtle and elegant, unintuitive at first. Yet the universe is ultimately understandable. The patterns of regularity are hot deceptive (though they might seem mystifying at first when we don't have the adequate words to say them).
http://math.furman.edu/~mwoodard/ascquote.html
This is to conjecture the idea that
what is important about our models is that they are part of a process of growth, of "living up" to the universe.