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.

Tom - you can't write a C program that adds 2 and 2 and gets 5. You can write a C program that takes two and two, and produces five - through an entirely different algorithm than addition. And you're adding in an additional layer of model, besides - remember that 2 means absolutely nothing in the universe. "Two" is a concept within a particular mathematical model. You can choose the axioms for your model pretty much at will - the only question is how you have to twist the model to make it describe the universe.

And yes, I can write a program in Bayes-language that assigns a 1% probability to the Sun rising - simply by changing the definitions for these things, as you did when you wrote that you could write a C program that added 2 and 2 to get 5. It is the definitions - a form of axiom in themselves - that give meaning to the modeling language. Bayes-language can describe a universe completely contradictory to the one we live in, simply by using different definitions.

Bayes-language doesn't naturally describe the probability of the Sun rising, after all - you can't derive that probability from Bayes-language itself. You have to code in every meaningful variable, and their relationships to one another. This is no different from what you do in C.

And first, no, the laws of physics are provably no such thing - 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. And second, the laws of physics are equivalent to multiple contradictory coordinate systems. Any model can be, with the correct translations and transformations and definitions, accurate in describing the universe. That the universe behaves as a model might expect it to, therefore, says nothing about the universe, only about the model - and only as a model.

Eliezer - Bayesian theory is a model. It isn't the universe. This is where you will be losing most of your readers - yes, you can express anything in Bayesian terms. You can express anything in C, too - this doesn't mean the universe is a program, and it doesn't provide any fundamental insight into how the universe works.

Ayn Rand was wrong in many regards - and her epistemology came after the definition for her philosophy, and should certainly be discounted as rationalization and little more - but any half-rational Objectivist will recognize that the philosophy should be regarded objectively, and her quite subjective views of personal values should be taken with a grain of salt.

Incidentally, if you're interested in her as a character, you may want to read We The Living (Which she herself described as a philosophical autobiography) - there are several hints scattered throughout it that she always had a love affair with power, that it was not merely something that she developed later in her life.

I've believed this was so for a long time, after reading about the Klu Klux Klan. Which, it is weird to think, was once a (for the time) moderate and respected political institution. After the Grand Dragon got caught in a sex scandal, membership dwindled rapidly, leaving a core of fanatics - with results that I think we're all quite familiar with.

I think the schism in Objectivism ended differently - because I don't think on the one hand you have the fanatics, but rather simply two groups, each of which ended up defining Objectivism differently. One treats Objectivism as a complete value set, by which every aspect of their lives can be defined. I don't think they're fanatics, but, rather individuals who already lived in agreement with that value set. And on the other hand are those whose value system has a different set of values, who treat Objectivism as an approach to thinking rather than the definition of it. The latter definition is best expressed in Atlas Shrugged and We The Living; the former is best expressed in The Fountainhead and her philosophical essays. It's a distinction in definition. I am, incidentally, of the latter persuasion - I consider myself an Objectivist, but disagree with Ayn Rand on the matter of values. (I, for example, reverse her logic - life is important because it is necessary to reason, rather than the other way around.)

I didn't mean specifically, I meant on average. My apologies for the poor phrasing. Yes, any individual formula's odds of being correct can vary. (To deny this would be to deny Bayesian reasoning, and I think I might get mugged here if I tried that.)

the fact that their agreement-about-observations was predictable in advance doesn't make it any less an agreement. (And if you're talking only about the parts of those theories that are "theories about the reasons why", bracketing all the agreements about what's observed and how to calculate it, then I don't think you are entitled to call the things that disagree completely "models for modern theoretical physics".)

- It renders that agreement meaningless. If you curve-fit seven points, and come up with a thousand different formulas, the fact that each of these thousand formulas includes each of those seven points produces exactly no additional information. The fact of the matter is that we have discarded every formula which DIDN'T describe those points - that the remaining formulas do describe them tells us absolutely nothing about either the points or the relative value of the formulas with respect to one another.

At best, out of N formulas, each has a 1/N chance of being correct. (At worst, none of the formulas is correct.)

Nick - that proof works fine for any of the neorealist models, in which Everett's model is, variably, placed. The problem is in interpretation. Remember that there is great disagreement in the Copenhagen models about where, exactly, waveform collapse happens - after all, if one treats the quantum measurement device itself as being in a quantum state, then 100% correlation may be acceptable. (Because the waveform state of the computer wasn't collapsed until the first and third measurements were examined together.)

The real problem here is that the Copenhagen models are effectively unscientific, since it is fundamentally impossible to disprove the concept that anything that is unmeasured is in an uncertain/undefined state. It's an intellectual parlour trick, and shouldn't be taken seriously.

They agree about observations - but we already have the observations, so that doesn't mean much. Any theory worth thinking about isn't going to disagree about those observations, which, after all, they are created to explain. They disagree in every way it is meaningful that they, theories about the reason why, MAY disagree - in the reasons why. And extreme verificationists can go take a leap off a logical cliff when it comes to discussing differences in the reasons why something may be.

Notably, regarding theoretical physics, there are at least nine models for modern theoretical physics, all of which can perfectly explain the empirical observations, and all of which are completely and totally contradictory to one another. (Okay, almost all of which. There are a few compatibilities scattered amongst them. Neorealism can work fine with the multiverse model, and there are a small handful of models which are derived from Bohr's interpretations and are semicompatible with one another.)