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The author of this piece says he was struggling to understand complex conjugates. If you don't understand what that is, please read the wikipedia, so you can co

The author of this piece says he was struggling to understand complex conjugates. If you don't understand what that is, please read the wikipedia, so you can contextualize his level of familiarity with the material he speaks about. I don't think the author is being dishonest. But that admission is extremely striking to me. [edit: Can some admin give me guidance on how to make the point I'm clearly trying to make? I'm not sure how to make this point without being discourteous.]

kowlo 6y ago
> [edit: Can some admin give me guidance on how to make the point I'm clearly trying to make? I'm not sure how to make this point without being discourteous.] not an admin, but seems like you made your point
ajkjk 6y ago
I mean.. if their problem is not understanding the math of conjugation at all, then yes, they're pretty elementary and are going to have trouble with QM. But if their problem is not being able to stomach the "just-because" explanations that every QM resigns to using to explain wtf complex conjugation has to do with reality, then I completely, totally sympathize. Learning QM consists of learning to silence your objections to the fact that none of the things you're being asked to believe make any sense. It gets somewhat more scrutable when you deal with relativistic QM, where, at least, the terms in Schrodinger equation start to make intuitive sense (it's the first couple terms in the Taylor expansion of E psi = sqrt(p^2 + m^2) psi = m sqrt(p^2/m^2 + 1) psi = (m + 1/2 p^2/m)psi ), but then spinors enter the picture and all intuition goes out the window again.
- groby_b 6y ago
  I'd maybe swallow this explanation for complex conjugates as applied to QM. (They're still extremely useful for e.g. circuit analysis, as a practical application) But it's not just complex conjugates, but eigenvectors as well. Also spectacular: "the square root of a negative number, which by definition does not exist" Uh. That's a complete lack of connection to anything beyond 10th grade math. Maybe not the ideal foundation for criticizing QM. And yes, I get the complaint that QM comes with a lot of "if you just hold your nose and accept this", and intuition doesn't really work for it - but that's hardly a valid criticism by itself, outside of saying "well, this is hard to understand". And the idea that a mathematical model isn't perfect and as a result of that can't be true really just betrays a complete misunderstanding how models work. This piece boils down to "I don't understand it, and so it can't be correct".
- pdonis 6y ago
  > Learning QM consists of learning to silence your objections to the fact that none of the things you're being asked to believe make any sense. Yes, but the reason you're learning those things is that that is the way reality actually works. That's what happens when you actually do experiments. Richard Feynman once remarked: "quantum mechanics was not wished upon us by theorists". We have QM because physicists were dragged to it kicking and screaming by actual experiments that showed them that reality does not work the way classical physics describes. And the reason all those difficult mathematical tools have to be taught is that that's the only way physicists know how to build models that make correct predictions about what happens when you do those experiments. In other words, yes, you can say QM doesn't make sense, but that's because reality doesn't make sense--at least not if "make sense" means "works the way my human intuitions, which never evolved to deal with quantum phenomena, say it should". Yes, reality doesn't work the way our human intuitions say it should. That means we have to retrain our intuitions--which is what a lot of learning QM is really about.
  - ajkjk 6y ago
    Agreed, to an extent. But some of the parts of QM seem like things reality demands (double slit experiments) and other parts seem like horrible mathematical artifacts that in enough years we'll come to regret (like the Schrödinger equation). But of course that's not a stance I can defend unless we figure out a better mathematical model for it. Just a hunch.
  - drran 6y ago
    Sufficiently complex math is able to synthesize speech and draw pictures. Yes, complex math is able to predict the behavior of the quantum world. So what? OpenGL is also able to predict realistic pictures. Is knowledge in OpenGL mechanics will improve our knowledge in the physics? My teacher told me, that I will really know physics when I will be able to derive my own equations. I extended this definition to "I will really know physics when I will be able to create the physical model of a physical thing, to be able to watch it with my own eyes".
- BeetleB 6y ago
  > But if their problem is not being able to stomach the "just-because" explanations that every QM resigns to using to explain wtf complex conjugation has to do with reality Having studied both engineering and physics, I can tell you that there is nothing observable in the universe that requires complex arithmetic/algebra/theory. We use it because it makes the math a lot more convenient. BTW, the use of complex math for real world applications goes way beyond QM, and predates it significantly. Engineers use it all the time: AC Circuit theory is full of it. As is electromagnetics. As is power (motors, etc). As is anything involving Fourier or Laplace Transforms (i.e. almost all engineering). You can come up with purely real mathematics to describe all of the above, but it would be tedious.
  - thisrod 6y ago
    The mathematicians have a saying: the shortest path between two facts about real numbers often passes through the complex plane.
whatshisface 6y ago
All of the philosophical complexity the author finds here can also be found in Newtonian mechanics. Papers are still being published today about the philosophy of Newtonian mechanics, using it as a gateway and simple test piece for the philosophy of physics or science overall. A common mistake among, I guess you could call them "rookie philosophers of science," is to look for the grandest examples of the problems they study, and overlook the simplest places where the problem is exhibited. The best philosophy deals with the simplest materials possible, no more than is required to build the case being made.
floxy 6y ago
>complex conjugates I wonder if there would be less objection by the author if he was exposed to geometric algebra, to help with difficulties encountered by sqrt(-1) philosophical issues.
john-shaffer 6y ago
You did fine. There's just a lot of down-voting for poor reasons. I've had comments down-voted about three seconds after posting them.
mellosouls 6y ago
John Horgan is a long established and excellent science writer, and given that he's commenting on philosophical issues here as much as anything, I don't agree his difficulty with some mathematical elements of the subject - which he's gracious enough to commit to learning, and humble enough to admit to struggling with - affects his point, which isn't without merit. But can you call a theory true if no one understands it? A century after inventing quantum mechanics, physicists still squabble over what, exactly, it tells us about reality. I think his question is a little loaded - it's a cliché that "nobody understands it", and I'm sure there are physicists who would bridle a little at that being true. His following claim (disputes over what it tells us) - while true - is not quite the same thing, so the argument is flawed in that regard, but not because of a problem learning maths.
- thisrod 6y ago
  > But can you call a theory true if no one understands it? I understand non-relativistic quantum mechanics, i.e. the Schrodinger equation, so close to perfectly as makes no difference. So do thousands of other physicists. We don't all understand it in the same way. The atomic scale is removed from the human scale by an order of magnitude of orders of magnitude, they do things differently there, so humans can't appeal to their experience to say that one self-consistent description of atomic phenomena is real and another isn't. But the way I understand quantum mechanics is self-consistent, so is the way any the next physicist understands it, and we'll all agree what result it predicts for any experiment you can imagine. If you want more than that, science can't help you.
thechao 6y ago
I also find it disingenuous that he dismisses the square-root of negative one as "imaginary" (not real), but doesn't appear to have a problem with algebraic numbers, negative numbers, or fractions (all of which are also extensions of the base ring). I'm trying to imagine how he'd feel about incomputable normal numbers...

kowlo 6y ago

> [edit: Can some admin give me guidance on how to make the point I'm clearly trying to make? I'm not sure how to make this point without being discourteous.] not an admin, but seems like you made your point

ajkjk 6y ago

I mean.. if their problem is not understanding the math of conjugation at all, then yes, they're pretty elementary and are going to have trouble with QM. But if their problem is not being able to stomach the "just-because" explanations that every QM resigns to using to explain wtf complex conjugation has to do with reality, then I completely, totally sympathize. Learning QM consists of learning to silence your objections to the fact that none of the things you're being asked to believe make any sense. It gets somewhat more scrutable when you deal with relativistic QM, where, at least, the terms in Schrodinger equation start to make intuitive sense (it's the first couple terms in the Taylor expansion of E psi = sqrt(p^2 + m^2) psi = m sqrt(p^2/m^2 + 1) psi = (m + 1/2 p^2/m)psi ), but then spinors enter the picture and all intuition goes out the window again.

groby_b 6y ago
I'd maybe swallow this explanation for complex conjugates as applied to QM. (They're still extremely useful for e.g. circuit analysis, as a practical application) But it's not just complex conjugates, but eigenvectors as well. Also spectacular: "the square root of a negative number, which by definition does not exist" Uh. That's a complete lack of connection to anything beyond 10th grade math. Maybe not the ideal foundation for criticizing QM. And yes, I get the complaint that QM comes with a lot of "if you just hold your nose and accept this", and intuition doesn't really work for it - but that's hardly a valid criticism by itself, outside of saying "well, this is hard to understand". And the idea that a mathematical model isn't perfect and as a result of that can't be true really just betrays a complete misunderstanding how models work. This piece boils down to "I don't understand it, and so it can't be correct".
pdonis 6y ago
> Learning QM consists of learning to silence your objections to the fact that none of the things you're being asked to believe make any sense. Yes, but the reason you're learning those things is that that is the way reality actually works. That's what happens when you actually do experiments. Richard Feynman once remarked: "quantum mechanics was not wished upon us by theorists". We have QM because physicists were dragged to it kicking and screaming by actual experiments that showed them that reality does not work the way classical physics describes. And the reason all those difficult mathematical tools have to be taught is that that's the only way physicists know how to build models that make correct predictions about what happens when you do those experiments. In other words, yes, you can say QM doesn't make sense, but that's because reality doesn't make sense--at least not if "make sense" means "works the way my human intuitions, which never evolved to deal with quantum phenomena, say it should". Yes, reality doesn't work the way our human intuitions say it should. That means we have to retrain our intuitions--which is what a lot of learning QM is really about.
- ajkjk 6y ago
  Agreed, to an extent. But some of the parts of QM seem like things reality demands (double slit experiments) and other parts seem like horrible mathematical artifacts that in enough years we'll come to regret (like the Schrödinger equation). But of course that's not a stance I can defend unless we figure out a better mathematical model for it. Just a hunch.
- drran 6y ago
  Sufficiently complex math is able to synthesize speech and draw pictures. Yes, complex math is able to predict the behavior of the quantum world. So what? OpenGL is also able to predict realistic pictures. Is knowledge in OpenGL mechanics will improve our knowledge in the physics? My teacher told me, that I will really know physics when I will be able to derive my own equations. I extended this definition to "I will really know physics when I will be able to create the physical model of a physical thing, to be able to watch it with my own eyes".
BeetleB 6y ago
> But if their problem is not being able to stomach the "just-because" explanations that every QM resigns to using to explain wtf complex conjugation has to do with reality Having studied both engineering and physics, I can tell you that there is nothing observable in the universe that requires complex arithmetic/algebra/theory. We use it because it makes the math a lot more convenient. BTW, the use of complex math for real world applications goes way beyond QM, and predates it significantly. Engineers use it all the time: AC Circuit theory is full of it. As is electromagnetics. As is power (motors, etc). As is anything involving Fourier or Laplace Transforms (i.e. almost all engineering). You can come up with purely real mathematics to describe all of the above, but it would be tedious.
- thisrod 6y ago
  The mathematicians have a saying: the shortest path between two facts about real numbers often passes through the complex plane.

whatshisface 6y ago

All of the philosophical complexity the author finds here can also be found in Newtonian mechanics. Papers are still being published today about the philosophy of Newtonian mechanics, using it as a gateway and simple test piece for the philosophy of physics or science overall. A common mistake among, I guess you could call them "rookie philosophers of science," is to look for the grandest examples of the problems they study, and overlook the simplest places where the problem is exhibited. The best philosophy deals with the simplest materials possible, no more than is required to build the case being made.

floxy 6y ago

>complex conjugates I wonder if there would be less objection by the author if he was exposed to geometric algebra, to help with difficulties encountered by sqrt(-1) philosophical issues.

john-shaffer 6y ago

You did fine. There's just a lot of down-voting for poor reasons. I've had comments down-voted about three seconds after posting them.

mellosouls 6y ago

John Horgan is a long established and excellent science writer, and given that he's commenting on philosophical issues here as much as anything, I don't agree his difficulty with some mathematical elements of the subject - which he's gracious enough to commit to learning, and humble enough to admit to struggling with - affects his point, which isn't without merit. But can you call a theory true if no one understands it? A century after inventing quantum mechanics, physicists still squabble over what, exactly, it tells us about reality. I think his question is a little loaded - it's a cliché that "nobody understands it", and I'm sure there are physicists who would bridle a little at that being true. His following claim (disputes over what it tells us) - while true - is not quite the same thing, so the argument is flawed in that regard, but not because of a problem learning maths.

thisrod 6y ago
> But can you call a theory true if no one understands it? I understand non-relativistic quantum mechanics, i.e. the Schrodinger equation, so close to perfectly as makes no difference. So do thousands of other physicists. We don't all understand it in the same way. The atomic scale is removed from the human scale by an order of magnitude of orders of magnitude, they do things differently there, so humans can't appeal to their experience to say that one self-consistent description of atomic phenomena is real and another isn't. But the way I understand quantum mechanics is self-consistent, so is the way any the next physicist understands it, and we'll all agree what result it predicts for any experiment you can imagine. If you want more than that, science can't help you.

thechao 6y ago

I also find it disingenuous that he dismisses the square-root of negative one as "imaginary" (not real), but doesn't appear to have a problem with algebraic numbers, negative numbers, or fractions (all of which are also extensions of the base ring). I'm trying to imagine how he'd feel about incomputable normal numbers...