“Tom—you can’t write a C program that adds 2 and 2 and gets 5.”
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.
“And you’re adding in an additional layer of model, besides—remember that 2 means absolutely nothing in the universe.”
“Bayes-language can describe a universe completely contradictory to the one we live in, simply by using different definitions.”
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/.
“This is no different from what you do in C.”
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.
“as we have no way to assign probability that we have a significant enough subset of those laws to be able to produce meaningful predictions of the laws of physics we don’t yet know.”
Every prediction that the laws of physics make has been tested over and over again (often to ten decimal places or more).
“And second, the laws of physics are equivalent to multiple contradictory coordinate systems.”
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).
“Any model can be, with the correct translations and transformations and definitions, accurate in describing the universe.”
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.
“Tom—you can’t write a C program that adds 2 and 2 and gets 5.”
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.
“And you’re adding in an additional layer of model, besides—remember that 2 means absolutely nothing in the universe.”
See http://lesswrong.com/lw/ms/is_reality_ugly/.
“Bayes-language can describe a universe completely contradictory to the one we live in, simply by using different definitions.”
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/.
“This is no different from what you do in C.”
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.
“as we have no way to assign probability that we have a significant enough subset of those laws to be able to produce meaningful predictions of the laws of physics we don’t yet know.”
Every prediction that the laws of physics make has been tested over and over again (often to ten decimal places or more).
“And second, the laws of physics are equivalent to multiple contradictory coordinate systems.”
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).
“Any model can be, with the correct translations and transformations and definitions, accurate in describing the universe.”
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.