I think that ‘read the Sequences’ is our polite way of telling people that there is a certain body of ideas that forms a common background for the discussions here, and that it does not serve either the newcomer or the community, to post here before being at least somewhat familiar with that background.
No, just no. I wouldn’t wish “read the quantum mechanics sequence” on anyone.
May I ask why? It might be worth rewriting those sequences to make them more accessible—you don’t need to see the exact math to be taught most of this stuff, after all, and I think that sequence probably does too much “teach Quantum Mechanics” and too little “teach the lessons from QM that are relevant” (mind you, I absolutely love that sequence because I want to learn QM, not just lessons-from-QM, but I can also follow the math ^^)
For both “Amplitude Configurations” and “Joint Configurations”, you summarised it just fine without mentioning complex numbers (except to note that this is the formal notation used). This would be an example of “being able to teach the lessons/concepts of QM, without teaching the math”—you can leave out the complex numbers entirely, and just present the ideas.
I’m only about halfway finished, but it hasn’t shown any signs of getting particularly more mathematical.
Mind you, I absolutely love that Eliezer is teaching the math, because it’s something I want to learn. But the basic idea of “drop apple, it falls” and even “falling objects fall faster over time” can be taught without resorting to calculus. I think that same level of abstraction could be applied to the QM sequence to make it MUCH more approachable. (Heck, if people were interested, I’d be game for writing it :))
You misunderstood the purpose—these are my comments on the sequence, not a summary. I seriously doubt anyone could actually learn anything from my notes alone.
I absolutely love that Eliezer is teaching the math
Let me try to figure out where our disagreement is: I believe you can learn the basics of “how gravity works” without knowing the calculus that was used to derive it. You can learn the basics of “how gravity works” without even knowing g = 9.8m/s^2, or the algebra necessary to solve that equation. You can teach the basic concepts of “things fall”, “heavy things fall as fast as light things”, and probably even “things fall faster the longer they’ve been falling” to a 5 year old.
Do you agree that a child can learn something useful about the way the world works from these non-mathematical lessons in gravity?
The difference between gravity and quantum physics is that by the time someone is ready to learn about gravity, they’ve lived gravity and experienced it their whole life.
Yes, they’ve “experienced” quantum physics too, but their intuitions about it will (almost certainly) turn out to be mostly wrong; therefore, mathematics is required.
The difference between gravity and quantum physics is that by the time someone is ready to learn about gravity, they’ve lived gravity and experienced it their whole life.
People seriously thought the Earth was the center of the universe. They thought that light objects fell slower than heavy ones. My intuitive experience of the world is that it’s flat and the sky is a hemisphere enclosing me. I can still teach the reality of gravity to a five year old, despite it being unintuitive. You don’t have to have everyday experience to learn something.
I’m confused why “experimental evidence” is less convincing than mathematics. I’ve taught the first half of the sequence to others without even mentioning complex numbers, so my anecdotal experience is that no, people do not need mathematics to correct their intuitions.
You’re conflating experimental evidence (by which I imagine you mean the two-slit experiment and etc., correct me if I’m wrong) with everyday experience. The latter contains virtually no useful information about quantum physics. It entices us to think that matter is made up of particles, that observables take fixed values after being measured, and so on...
Unfortunately it’s also sort of misguided in purpose; the cosmological interpretation of quantum mechanics is the normality that quantum mechanics adds up to and doesn’t need to be justified with nearly as much appeal to the secret powers of Bayes. I remember thinking this a few years ago; I remember thinking that people not immediately seeing it was evidence that compartmentalization was stronger than I thought amongst humans… I think I had a higher opinion of humans back then. Luckily Tegmark actually wrote up some math and has high status so I have someone to back me up for once.
That paper is dubious and confused. Their arguments revolve around infinite product states, representing an infinite number of causally disconnected copies of some physical entity. The whole argument is (i) in such states, the observable states of an individual entity appear as infinitely repeated factors with asymptotic frequencies equal to Born probabilities (ii) the basis decomposition of such infinite product states produces other infinite product states with the same property. From (ii), they wish to argue that the very notion of a cosmic superposition is redundant, and so there is no need for many worlds in the Everett sense. Or at least, they claim that there is no difference between the notion of one Everett world and many Everett worlds.
The first thing to note is that their whole construction really needs to be placed in a bigger context. The universe does not just consist of infinitely many causally disconnected copies of the same thing. Each copy is interacting with its environment, which (supposing the inflationary cosmology that they also assume) is in turn entangled with the degrees of freedom of its cosmological environment, all the way back to the beginning of inflation. There is no mention of entanglement prior to inflation, whether that is an issue, and how it could not be an issue if it is real. This lack of a larger framework makes it difficult to sensibly discuss what they have written. But their infinite product states really need to be embedded in some larger thing, the wavefunction of the universe, which is not a product state. The paper is dubious because it does not address this point.
The second thing to note is the total confusion regarding what the actual message of the paper is. Their technical argument is that a superposition of their special infinite product states is itself just another infinite product state. From this mathematical fact they conclude (page 9) that they don’t know if it’s a superposition any more. This isn’t “adding up to normality”; this is like spinning on one spot so fast that you lose all sense of direction, and then concluding that all directions are the same direction, because you can no longer tell the difference between them.
To really take apart a paper like this one, it’s not enough to show that it contains nonsensical statements; you have to figure out the philosophical genesis of the authors’ mistake, and then show how they employed the formalism in the service of their mistake. In such a diagnosis, first you establish explicitly what constitutes valid reasoning about the aspect of the theory that they propose to address, then you show how they spin mathematically valid manipulations into wrong, tendentious, or meaningless statements about physical reality. This is a tiresome thing to do and I hope to avoid doing it in full for this paper. But meanwhile, I am quite confident that it belongs in the rogues’ gallery of papers which falsely assert that they are now, finally, really-truly, solving the problems of MWI.
No, just no. I wouldn’t wish “read the quantum mechanics sequence” on anyone.
May I ask why? It might be worth rewriting those sequences to make them more accessible—you don’t need to see the exact math to be taught most of this stuff, after all, and I think that sequence probably does too much “teach Quantum Mechanics” and too little “teach the lessons from QM that are relevant” (mind you, I absolutely love that sequence because I want to learn QM, not just lessons-from-QM, but I can also follow the math ^^)
I disagree extraordinarily strongly with the statement
and the implication that one can learn “relevant lessons of QM” without actually learning QM.
Here are my comments on the QM sequence, which summarize my current stance. I welcome objections or corrections.
For both “Amplitude Configurations” and “Joint Configurations”, you summarised it just fine without mentioning complex numbers (except to note that this is the formal notation used). This would be an example of “being able to teach the lessons/concepts of QM, without teaching the math”—you can leave out the complex numbers entirely, and just present the ideas.
I’m only about halfway finished, but it hasn’t shown any signs of getting particularly more mathematical.
Mind you, I absolutely love that Eliezer is teaching the math, because it’s something I want to learn. But the basic idea of “drop apple, it falls” and even “falling objects fall faster over time” can be taught without resorting to calculus. I think that same level of abstraction could be applied to the QM sequence to make it MUCH more approachable. (Heck, if people were interested, I’d be game for writing it :))
You misunderstood the purpose—these are my comments on the sequence, not a summary. I seriously doubt anyone could actually learn anything from my notes alone.
What.
Let me try to figure out where our disagreement is: I believe you can learn the basics of “how gravity works” without knowing the calculus that was used to derive it. You can learn the basics of “how gravity works” without even knowing g = 9.8m/s^2, or the algebra necessary to solve that equation. You can teach the basic concepts of “things fall”, “heavy things fall as fast as light things”, and probably even “things fall faster the longer they’ve been falling” to a 5 year old.
Do you agree that a child can learn something useful about the way the world works from these non-mathematical lessons in gravity?
The difference between gravity and quantum physics is that by the time someone is ready to learn about gravity, they’ve lived gravity and experienced it their whole life.
Yes, they’ve “experienced” quantum physics too, but their intuitions about it will (almost certainly) turn out to be mostly wrong; therefore, mathematics is required.
People seriously thought the Earth was the center of the universe. They thought that light objects fell slower than heavy ones. My intuitive experience of the world is that it’s flat and the sky is a hemisphere enclosing me. I can still teach the reality of gravity to a five year old, despite it being unintuitive. You don’t have to have everyday experience to learn something.
I’m confused why “experimental evidence” is less convincing than mathematics. I’ve taught the first half of the sequence to others without even mentioning complex numbers, so my anecdotal experience is that no, people do not need mathematics to correct their intuitions.
You’re conflating experimental evidence (by which I imagine you mean the two-slit experiment and etc., correct me if I’m wrong) with everyday experience. The latter contains virtually no useful information about quantum physics. It entices us to think that matter is made up of particles, that observables take fixed values after being measured, and so on...
Well, I would argue that that’s the least relevant sequence.
Really.
This comment caused me to read the entire QM sequence. Thank you.
Unfortunately it’s also sort of misguided in purpose; the cosmological interpretation of quantum mechanics is the normality that quantum mechanics adds up to and doesn’t need to be justified with nearly as much appeal to the secret powers of Bayes. I remember thinking this a few years ago; I remember thinking that people not immediately seeing it was evidence that compartmentalization was stronger than I thought amongst humans… I think I had a higher opinion of humans back then. Luckily Tegmark actually wrote up some math and has high status so I have someone to back me up for once.
That paper is dubious and confused. Their arguments revolve around infinite product states, representing an infinite number of causally disconnected copies of some physical entity. The whole argument is (i) in such states, the observable states of an individual entity appear as infinitely repeated factors with asymptotic frequencies equal to Born probabilities (ii) the basis decomposition of such infinite product states produces other infinite product states with the same property. From (ii), they wish to argue that the very notion of a cosmic superposition is redundant, and so there is no need for many worlds in the Everett sense. Or at least, they claim that there is no difference between the notion of one Everett world and many Everett worlds.
The first thing to note is that their whole construction really needs to be placed in a bigger context. The universe does not just consist of infinitely many causally disconnected copies of the same thing. Each copy is interacting with its environment, which (supposing the inflationary cosmology that they also assume) is in turn entangled with the degrees of freedom of its cosmological environment, all the way back to the beginning of inflation. There is no mention of entanglement prior to inflation, whether that is an issue, and how it could not be an issue if it is real. This lack of a larger framework makes it difficult to sensibly discuss what they have written. But their infinite product states really need to be embedded in some larger thing, the wavefunction of the universe, which is not a product state. The paper is dubious because it does not address this point.
The second thing to note is the total confusion regarding what the actual message of the paper is. Their technical argument is that a superposition of their special infinite product states is itself just another infinite product state. From this mathematical fact they conclude (page 9) that they don’t know if it’s a superposition any more. This isn’t “adding up to normality”; this is like spinning on one spot so fast that you lose all sense of direction, and then concluding that all directions are the same direction, because you can no longer tell the difference between them.
To really take apart a paper like this one, it’s not enough to show that it contains nonsensical statements; you have to figure out the philosophical genesis of the authors’ mistake, and then show how they employed the formalism in the service of their mistake. In such a diagnosis, first you establish explicitly what constitutes valid reasoning about the aspect of the theory that they propose to address, then you show how they spin mathematically valid manipulations into wrong, tendentious, or meaningless statements about physical reality. This is a tiresome thing to do and I hope to avoid doing it in full for this paper. But meanwhile, I am quite confident that it belongs in the rogues’ gallery of papers which falsely assert that they are now, finally, really-truly, solving the problems of MWI.
Noted; I will lower my confidence in its ultimate sense-making-ness.