A man flying in a hot air balloon realizes he is lost. He reduces his altitude and spots a man in a field down below. He lowers the balloon further and shouts, “Excuse me, can you tell me where I am?” The man below says, “Yes, you’re in a hot air balloon, about 30 feet above this field.” “You must be an mathematician,” says the balloonist. “I am. How did you know?” “Everything you told me is technically correct, but it’s of no use to anyone.”
“Very clever! And you must be a manager,” says the guy in the field. “Amazing! How did you work it out?” asks the balloonist. “Well, there you are in your elevated position generating hot air, you have no idea where you are or what you’re doing, but somehow you’ve decided it’s my problem.”
It’s a funny joke but beside the point. Knowing that he is in a balloon about 30 feet above a field is actually very useful. It’s just useless to tell him what he clearly already knows.
Sorry I’m dense. What does this have to do with anything? It is true that the balloonist is in a hot air balloon 30 feet above a field. These are correct facts. Are you arguing for a concept of truth which would not qualify “Yes, you’re in a hot air balloon, about 30 feet above this field” to be a true statement?
I think Lumifer is suggesting that a model can correspond accurately to reality (e.g., representing the fact that X is in a hot air balloon 30 feet above Y’s current location) but none the less be useless (e.g., because all X wants to know is how to get to Vladivostok, and knowing he’s in a balloon 30 feet above Y doesn’t help with that). And that this is an example of how a model can be “bad” other than inaccurate correspondence with reality, which is what you were asking for a few comments upthread.
Recall an old joke:
“Very clever! And you must be a manager,” says the guy in the field. “Amazing! How did you work it out?” asks the balloonist. “Well, there you are in your elevated position generating hot air, you have no idea where you are or what you’re doing, but somehow you’ve decided it’s my problem.”
Yep. Moral of the story: never let the twain meet :-)
It’s a funny joke but beside the point. Knowing that he is in a balloon about 30 feet above a field is actually very useful. It’s just useless to tell him what he clearly already knows.
Sorry I’m dense. What does this have to do with anything? It is true that the balloonist is in a hot air balloon 30 feet above a field. These are correct facts. Are you arguing for a concept of truth which would not qualify “Yes, you’re in a hot air balloon, about 30 feet above this field” to be a true statement?
I think Lumifer is suggesting that a model can correspond accurately to reality (e.g., representing the fact that X is in a hot air balloon 30 feet above Y’s current location) but none the less be useless (e.g., because all X wants to know is how to get to Vladivostok, and knowing he’s in a balloon 30 feet above Y doesn’t help with that). And that this is an example of how a model can be “bad” other than inaccurate correspondence with reality, which is what you were asking for a few comments upthread.
Indeed they are. That is, actually, the point.
Recall your own question (emphasis mine): “in what ways can a model be useless that differ from it not corresponding to reality?”