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...
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...