A little knowledge can be more dangerous—and embarrassing—than complete ignorance.
Yes. As a math professor, I sort of agree and sort of disagree with this post. On the one hand, people have lots of misunderstandings about math, as people like John Allen Paulos have written. But on the other hand, it’s NOT true that everything has a simple mathematical model. Often mathematical models that might be useful in physics are not especially useful elsewhere, and even more often the most important thing is not the model’s predictions, but the errors.
Look at the Social Security model, for example. It’s incredibly unreliable, because it makes long-time predictions based on a single parameter (average growth of GNP) which is assumed to be constant over 40 years. And the difference in predictions by changing this widely varying number is on the order of 10-20 years.
But the problem is that a few people think they know the math here and think they understand the situation completely because of it. In fact they know a tiny bit of math (or trust that other people know the math), and end up doing incredibly stupid things because of it. If they actually knew more, they would be a lot more careful with things like personal accounts and such. Instead we trust a few political appointees, process a couple of the numbers involved, and base everything on that.
And if you disagree with me about personal accounts on Social Security or something, and just think I’m a liberal who shouldn’t be taken seriously, compare the Doomsday argument http://en.wikipedia.org/wiki/Doomsday_argument. It uses statistics (which most people don’t understand) to make a trivial prediction with absurd consequences that gets taken seriously. People with a little understanding of statistics will take it seriously, but people who actually understand the limitations of statistics will realize it’s ridiculous.
A little knowledge can be more dangerous—and embarrassing—than complete ignorance.
Yes. As a math professor, I sort of agree and sort of disagree with this post. On the one hand, people have lots of misunderstandings about math, as people like John Allen Paulos have written. But on the other hand, it’s NOT true that everything has a simple mathematical model. Often mathematical models that might be useful in physics are not especially useful elsewhere, and even more often the most important thing is not the model’s predictions, but the errors.
Look at the Social Security model, for example. It’s incredibly unreliable, because it makes long-time predictions based on a single parameter (average growth of GNP) which is assumed to be constant over 40 years. And the difference in predictions by changing this widely varying number is on the order of 10-20 years.
But the problem is that a few people think they know the math here and think they understand the situation completely because of it. In fact they know a tiny bit of math (or trust that other people know the math), and end up doing incredibly stupid things because of it. If they actually knew more, they would be a lot more careful with things like personal accounts and such. Instead we trust a few political appointees, process a couple of the numbers involved, and base everything on that.
And if you disagree with me about personal accounts on Social Security or something, and just think I’m a liberal who shouldn’t be taken seriously, compare the Doomsday argument http://en.wikipedia.org/wiki/Doomsday_argument. It uses statistics (which most people don’t understand) to make a trivial prediction with absurd consequences that gets taken seriously. People with a little understanding of statistics will take it seriously, but people who actually understand the limitations of statistics will realize it’s ridiculous.