More bad math journalism
The New York Times Science section had an article today on free will and consciousness. Overall a decent article, but its discussion of Godel's incompleteness theorem made me want to drive a nail into someone's head. There are just way too many things wrong with it, so I'll just reproduce the whole section here, bolding the most inane parts:
According to deep mathematical principles, they say, even machines can become too complicated to predict their own behavior and would labor under the delusion of free will.
If by free will we mean the ability to choose, even a simple laptop computer has some kind of free will, said Seth Lloyd, an expert on quantum computing and professor of mechanical engineering at the Massachusetts Institute of Technology.
Every time you click on an icon, he explained, the computer’s operating system decides how to allocate memory space, based on some deterministic instructions. But, Dr. Lloyd said, “If I ask how long will it take to boot up five minutes from now, the operating system will say ‘I don’t know, wait and see, and I’ll make decisions and let you know.’ ”
Why can’t computers say what they’re going to do? In 1930, the Austrian philosopher Kurt Gödel proved that in any formal system of logic, which includes mathematics and a kind of idealized computer called a Turing machine, there are statements that cannot be proven either true or false. Among them are self-referential statements like the famous paradox stated by the Cretan philosopher Epimenides, who said that all Cretans are liars: if he is telling the truth, then, as a Cretan, he is lying.
One implication is that no system can contain a complete representation of itself, or as Janna Levin, a cosmologist at Barnard College of Columbia University and author of the 2006 novel about Gödel, “A Madman Dreams of Turing Machines,” said: “Gödel says you can’t program intelligence as complex as yourself. But you can let it evolve. A complex machine would still suffer from the illusion of free will.”
Another implication is there is no algorithm, or recipe for computation, to determine when or if any given computer program will finish some calculation. The only way to find out is to set it computing and see what happens. Any way to find out would be tantamount to doing the calculation itself.
“There are no shortcuts in computation,” Dr. Lloyd said.
That means that the more reasonably you try to act, the more unpredictable you are, at least to yourself, Dr. Lloyd said. Even if your wife knows you will order the chile rellenos, you have to live your life to find out.
To him that sounds like free will of a sort, for machines as well as for us. Our actions are determined, but so what? We still don’t know what they will be until the waiter brings the tray.
That works for me, because I am comfortable with so-called physicalist reasoning, and I’m always happy to leverage concepts of higher mathematics to cut through philosophical knots.
Why do people so often assume that purely abstract mathematical results about infinite structures are the right explanation for trivial, completely finitistic everyday facts? And since when is Janna Levin, a physicist who wrote a novel about Godel, an expert on logic and philosophy of mathematics?
The article also talks about people who believe that quantum mechanics gives evidence for the existence of free will. I didn't know that anyone actually seriously believed that.
According to deep mathematical principles, they say, even machines can become too complicated to predict their own behavior and would labor under the delusion of free will.
If by free will we mean the ability to choose, even a simple laptop computer has some kind of free will, said Seth Lloyd, an expert on quantum computing and professor of mechanical engineering at the Massachusetts Institute of Technology.
Every time you click on an icon, he explained, the computer’s operating system decides how to allocate memory space, based on some deterministic instructions. But, Dr. Lloyd said, “If I ask how long will it take to boot up five minutes from now, the operating system will say ‘I don’t know, wait and see, and I’ll make decisions and let you know.’ ”
Why can’t computers say what they’re going to do? In 1930, the Austrian philosopher Kurt Gödel proved that in any formal system of logic, which includes mathematics and a kind of idealized computer called a Turing machine, there are statements that cannot be proven either true or false. Among them are self-referential statements like the famous paradox stated by the Cretan philosopher Epimenides, who said that all Cretans are liars: if he is telling the truth, then, as a Cretan, he is lying.
One implication is that no system can contain a complete representation of itself, or as Janna Levin, a cosmologist at Barnard College of Columbia University and author of the 2006 novel about Gödel, “A Madman Dreams of Turing Machines,” said: “Gödel says you can’t program intelligence as complex as yourself. But you can let it evolve. A complex machine would still suffer from the illusion of free will.”
Another implication is there is no algorithm, or recipe for computation, to determine when or if any given computer program will finish some calculation. The only way to find out is to set it computing and see what happens. Any way to find out would be tantamount to doing the calculation itself.
“There are no shortcuts in computation,” Dr. Lloyd said.
That means that the more reasonably you try to act, the more unpredictable you are, at least to yourself, Dr. Lloyd said. Even if your wife knows you will order the chile rellenos, you have to live your life to find out.
To him that sounds like free will of a sort, for machines as well as for us. Our actions are determined, but so what? We still don’t know what they will be until the waiter brings the tray.
That works for me, because I am comfortable with so-called physicalist reasoning, and I’m always happy to leverage concepts of higher mathematics to cut through philosophical knots.
Why do people so often assume that purely abstract mathematical results about infinite structures are the right explanation for trivial, completely finitistic everyday facts? And since when is Janna Levin, a physicist who wrote a novel about Godel, an expert on logic and philosophy of mathematics?
The article also talks about people who believe that quantum mechanics gives evidence for the existence of free will. I didn't know that anyone actually seriously believed that.