Haven’t read the book, so I looked at some reviews, and… it seems to me that there two different questions:
a) Are there universal laws in math and physics? (Yes.)
b) Are the consequences of such laws trivial? (No.)
So we seem to have two groups of people talking past each other, when one group says “there is a unifying principle behind this all, it’s not just an arbitrary hodgepodge of tricks all the way down”, and the other group says “but calculating everything from the first principles is difficult, often impossible, and my tricks work, so what’s your problem”.
To simplify it a lot, it’s like one person saying “multiplying by 10 is really simple, you just add a zero to the end” and another person says “the laws of multiplication are the same for all numbers, 10 is not a separate magisterium”. Both of them are right. It is very useful to be able to multiply by 10 quickly. But if your students start to believe that multiplication by 10 follows separate laws of math, something is seriously wrong. (Especially if they sometimes happen to apply the rule like this: “2.0 × 10 = 2.00”. At that moment you should realize they were just following the motions, even if they got their previous 999 calculations right.) Using tricks is okay, if you understand why they work. Believing it is arbitrary tricks all the way down is not.
Bayesians don’t say “the frequentist tricks don’t work”. They say “they work, because they are simplifications of a more general principle, and by the way these are their unstated assumptions, so of course if you apply two tricks using different assumptions, you might get two different results”. But that doesn’t mean one shouldn’t know or shouldn’t use the tricks.
Also, looking at another review...
She strongly objects, for example, to the idea that consciousness is somehow intimately involved in the measurement process
...yeah, of course. Classical Less Wrong topic.
Each law thus comes with a ceteris paribus (all else being equal) clause attached. So, for example, the ideal gas law tells us how pressure, volume, and temperature are related, but it is reliable only for closed systems. When she says that such laws are not very useful she means something quite specific, namely, that such a law is, by itself, almost useless for understanding p-t-v relationships in open systems, like the Earth’s atmosphere, where all else is NOT equal. Such laws are extremely useful as foundational concepts in our abstract understanding of how the universe works, but it can take years, or decades, or even centuries after the discovery of a law for engineers and technologists to figure out how to cash out all of the “all else being equal” clauses in the real situations where the laws operate. For example, the central laws governing fusion in plasma are pretty well understood, but turning that understanding into an operating fusion generator is proving extremely difficult.
the “law of gravity” is a great example: No two bodies REALLY interact SOLELY in accordance with the “law of gravity.” In the real world, electromagnetic forces, inertia, gravitation from other bodies, and a host of other forces are at play—and you must “correct” for those other forces, Luc, if you want to land safely on Mars.
I see absolutely no problem with this. The laws may be simple, their consequences complex.
To be more precise—although this comment is already too long—it would make sense to distinguish two kinds of “laws”. I don’t know if there is already a name for this. Some laws are simply “generalizations of observations”. You observe thousand white sheep, you conclude “all sheep are white”. Then you see a black sheep. Oops! But there is another approach, which goes something like “imagine that this world is a simulation; what would be the rules of the simulation so that they would produce the kind of outcomes we observe”. Simulation here is only a metaphor; Einstein would use the metaphor of understanding God’s mind, etc. The idea is to think which underlying principles could be responsible for what we see, as opposed to merely noticing the trends in what we see.
And yes, it works differently in math and in physics; physics tries to describe a given existing universe, math is kinda its own map and territory at the same time. But in both cases, there is this idea of looking for the underlying principles, whether those are universal laws in physics or axioms in math, as opposed to merely collecting stamps (which is also a useful thing to do).
Are there universal laws in math and physics? (Yes.)
No.
The argument against universal laws in physics is based on the fact that they use ceteris paribus clauses. You said it was ridiculous for different laws to hold outside the laboratory, but CP is only guaranteed inside the laboratory: the first rule of experimentation is to change only one thing per experiment, thus enforcing CP artificially.
As for maths, there are disputes about proof by contradiction (intuitionism) , the axiom of choice and so.
There is a difference between “the law applies randomly” and “multiple laws apply, you need to sum their effects”.
If you say “if one apple costs 10 cents, then three apples cost 30 cents”, the rule is not refuted by saying “but I bought three apples and a cola, and I paid 80 cents”. The law of gravity does not stop being universal just because the ball stops falling downwards after I kick it.
To simplify it a lot, it’s like one person saying “multiplying by 10 is really simple, you just add a zero to the end” and another person says “the laws of multiplication are the same for all numbers, 10 is not a separate magisterium”. Both of them are right. It is very useful to be able to multiply by 10 quickly.
But it’s worse than that. There’s a difference between being able use shortcuts, and having to. And there’s a difference between the shortcut resulting in the same answer, and the shortcut being an approximation.
Since Bayes is uncomputable in the general case, cognitively limited agents have to use heuristic replacements instead. That means Bayes isn’t important in practice, unless you forget about the maths and focus on non-
fquantitative maxims, as has happened.
Cognitively limited agents include AIs. At one time, lesswrong believed that Bayes underpinned decision theory, decision theory underpinned rationality,
and some combination of decision theory and Bayes could be used to predict the behaviour of ASIs.
Edit:
(Which to is to say that they disbelieved in the simple argument that agents cannot predict more complex agents, in general). But if an agent is using heuristics to overcome it’s computational limitations, you can’t predict it using pure Bayes, even assuming you somehow don’t have computation limitations, because heuristics give different and worse answers. That is, you can’t predict it as a black box and would need to know it’s code.
So Bayes isn’t useful for the two things it was believed to be useful for, so whats left is basically a philosophical claim ,that Bayes subsumes frequentism, so that frequentism is not really rivalrous. But Bayes itself is subsumed by radical probabilism, which is more general still!
Haven’t read the book, so I looked at some reviews, and… it seems to me that there two different questions:
a) Are there universal laws in math and physics? (Yes.)
b) Are the consequences of such laws trivial? (No.)
So we seem to have two groups of people talking past each other, when one group says “there is a unifying principle behind this all, it’s not just an arbitrary hodgepodge of tricks all the way down”, and the other group says “but calculating everything from the first principles is difficult, often impossible, and my tricks work, so what’s your problem”.
To simplify it a lot, it’s like one person saying “multiplying by 10 is really simple, you just add a zero to the end” and another person says “the laws of multiplication are the same for all numbers, 10 is not a separate magisterium”. Both of them are right. It is very useful to be able to multiply by 10 quickly. But if your students start to believe that multiplication by 10 follows separate laws of math, something is seriously wrong. (Especially if they sometimes happen to apply the rule like this: “2.0 × 10 = 2.00”. At that moment you should realize they were just following the motions, even if they got their previous 999 calculations right.) Using tricks is okay, if you understand why they work. Believing it is arbitrary tricks all the way down is not.
Bayesians don’t say “the frequentist tricks don’t work”. They say “they work, because they are simplifications of a more general principle, and by the way these are their unstated assumptions, so of course if you apply two tricks using different assumptions, you might get two different results”. But that doesn’t mean one shouldn’t know or shouldn’t use the tricks.
Also, looking at another review...
...yeah, of course. Classical Less Wrong topic.
I see absolutely no problem with this. The laws may be simple, their consequences complex.
To be more precise—although this comment is already too long—it would make sense to distinguish two kinds of “laws”. I don’t know if there is already a name for this. Some laws are simply “generalizations of observations”. You observe thousand white sheep, you conclude “all sheep are white”. Then you see a black sheep. Oops! But there is another approach, which goes something like “imagine that this world is a simulation; what would be the rules of the simulation so that they would produce the kind of outcomes we observe”. Simulation here is only a metaphor; Einstein would use the metaphor of understanding God’s mind, etc. The idea is to think which underlying principles could be responsible for what we see, as opposed to merely noticing the trends in what we see.
And yes, it works differently in math and in physics; physics tries to describe a given existing universe, math is kinda its own map and territory at the same time. But in both cases, there is this idea of looking for the underlying principles, whether those are universal laws in physics or axioms in math, as opposed to merely collecting stamps (which is also a useful thing to do).
No.
The argument against universal laws in physics is based on the fact that they use ceteris paribus clauses. You said it was ridiculous for different laws to hold outside the laboratory, but CP is only guaranteed inside the laboratory: the first rule of experimentation is to change only one thing per experiment, thus enforcing CP artificially.
As for maths, there are disputes about proof by contradiction (intuitionism) , the axiom of choice and so.
There is a difference between “the law applies randomly” and “multiple laws apply, you need to sum their effects”.
If you say “if one apple costs 10 cents, then three apples cost 30 cents”, the rule is not refuted by saying “but I bought three apples and a cola, and I paid 80 cents”. The law of gravity does not stop being universal just because the ball stops falling downwards after I kick it.
The way “laws” combine is much more complex than simple summation. If it were that simple, we would already have a TOE.
But it’s worse than that. There’s a difference between being able use shortcuts, and having to. And there’s a difference between the shortcut resulting in the same answer, and the shortcut being an approximation.
Since Bayes is uncomputable in the general case, cognitively limited agents have to use heuristic replacements instead. That means Bayes isn’t important in practice, unless you forget about the maths and focus on non- fquantitative maxims, as has happened.
Cognitively limited agents include AIs. At one time, lesswrong believed that Bayes underpinned decision theory, decision theory underpinned rationality, and some combination of decision theory and Bayes could be used to predict the behaviour of ASIs.
Edit:
(Which to is to say that they disbelieved in the simple argument that agents cannot predict more complex agents, in general). But if an agent is using heuristics to overcome it’s computational limitations, you can’t predict it using pure Bayes, even assuming you somehow don’t have computation limitations, because heuristics give different and worse answers. That is, you can’t predict it as a black box and would need to know it’s code.
So Bayes isn’t useful for the two things it was believed to be useful for, so whats left is basically a philosophical claim ,that Bayes subsumes frequentism, so that frequentism is not really rivalrous. But Bayes itself is subsumed by radical probabilism, which is more general still!