“Obviously, you can’t rewrite the laws of math with C. But a C program can produce obviously incorrect statements, such as “2 + 2 = 5″. There is, on average, one bug in every ten lines of C code.”
That, of course, is a completely different statement. But then you are suggesting that Bayes-Language is incapable of representing a false statement—which is an obvious lie.
Yup. I see it. It’s begging the point that I’m arguing—that the model is the universe.
“Then, of course, it is no longer Bayes-language. You cannot simply redefine math- every theorem is tangled up with every other theorem to produce a coherent system, which will give you exactly one correct answer to every question. See http://lesswrong.com/lw/nz/arguing_by_definition/.”
Yes, it is Bayes-language. Mathematics does NOT describe the universe, it describes mathematics—it is the variables which you input INTO the mathematics which make it describe a particular real-world situation. Mathematics is a modeling language no different from any other save in precision.
“It’s perfectly possible to write a C program that inputs all the right data and generates garbage. You cannot write a Bayes program that inputs all the right data and generates garbage.”
You’re begging the point, and yes, you can. Others have put this eloquently enough, however.
“Every prediction that the laws of physics make has been tested over and over again (often to ten decimal places or more).”
You missed the point—we can’t predict what the next law of physics we’ll discover will be.
“The laws of physics do not require a coordinate system of any sort to function, although this admittedly requires some pretty fancy math to get at (see Gravitation, by Meisner, Wheeler and Thorne).”
That’s very good, if not entirely accurate. All variables are variables on some coordinate system or another, after all, if not a spacial one. The coordinate systems are particular mathematical models.
“If I wrote a version of GR that made gravity repulsive instead of attractive (a perfectly valid thing to do, mathematically), it would not be accurate in describing the universe, as this universe does not make things fall up.”
You didn’t perform the appropriate transformations. They get quite nasty in this case, as your coordinate system would have to warp quite considerably in some fashion or another, but it can be done. As a very simple example, suppose a two-particle system, with the perspective as one of the particles; you then merely need to change the behavior of your measuring concept—say, light—to arrive in a time T inversely proportional to the distance. More complex systems with more complex variables would require exponentially more complex transformations to describe related concepts.
Tom -
“Obviously, you can’t rewrite the laws of math with C. But a C program can produce obviously incorrect statements, such as “2 + 2 = 5″. There is, on average, one bug in every ten lines of C code.”
That, of course, is a completely different statement. But then you are suggesting that Bayes-Language is incapable of representing a false statement—which is an obvious lie.
“See http://lesswrong.com/lw/ms/is_reality_ugly/.”
Yup. I see it. It’s begging the point that I’m arguing—that the model is the universe.
“Then, of course, it is no longer Bayes-language. You cannot simply redefine math- every theorem is tangled up with every other theorem to produce a coherent system, which will give you exactly one correct answer to every question. See http://lesswrong.com/lw/nz/arguing_by_definition/.”
Yes, it is Bayes-language. Mathematics does NOT describe the universe, it describes mathematics—it is the variables which you input INTO the mathematics which make it describe a particular real-world situation. Mathematics is a modeling language no different from any other save in precision.
“It’s perfectly possible to write a C program that inputs all the right data and generates garbage. You cannot write a Bayes program that inputs all the right data and generates garbage.”
You’re begging the point, and yes, you can. Others have put this eloquently enough, however.
“Every prediction that the laws of physics make has been tested over and over again (often to ten decimal places or more).”
You missed the point—we can’t predict what the next law of physics we’ll discover will be.
“The laws of physics do not require a coordinate system of any sort to function, although this admittedly requires some pretty fancy math to get at (see Gravitation, by Meisner, Wheeler and Thorne).”
That’s very good, if not entirely accurate. All variables are variables on some coordinate system or another, after all, if not a spacial one. The coordinate systems are particular mathematical models.
“If I wrote a version of GR that made gravity repulsive instead of attractive (a perfectly valid thing to do, mathematically), it would not be accurate in describing the universe, as this universe does not make things fall up.”
You didn’t perform the appropriate transformations. They get quite nasty in this case, as your coordinate system would have to warp quite considerably in some fashion or another, but it can be done. As a very simple example, suppose a two-particle system, with the perspective as one of the particles; you then merely need to change the behavior of your measuring concept—say, light—to arrive in a time T inversely proportional to the distance. More complex systems with more complex variables would require exponentially more complex transformations to describe related concepts.