if you have no independent knowledge of these areas as a solid foundation for your opinions about them, it is reasonable to conclude that you have let your enthusiasm for the underlying philosophy of these sequences lead you to an illusory “understanding” that is in reality sheer rationalization.
I haven’t read the quantum physics sequence on Less Wrong. I got my physics from lots of other sources.
if you really believe you understand them in some “non-mathematical” way, you are fooling yourself… it seems inconceivable that someone could gain such understanding in a “non-mathematical” way
Are we just disagreeing about the meaning of “understand” or something? Are you using the word “understanding” in an unusual way, such that there is no such thing as non-mathematical understanding?
Also, at one point you seem to say that I can’t have evidence about whether Copenhagen is correct or incorrect without understanding all the equations involved? That seems too obviously false; I assume I’m misunderstanding you?
For what it’s worth, I agree with Vladimir_M. Eliezer has a nice post about this. One way to test your understanding of physics would be to google for problem sets on special relativity, or something, and see how many problems you can solve.
About what in particular? Just the vibe of “How dare you? Get off my lawn!” or is there something in the comment you are actually replying to which you would dispute? If the latter then I must affirm the observation “That seem too obviously false” and, like Luke, apply the benefit of the doubt. That would mean assuming that you aren’t really responding to the grandparent at all and more just chiming in with a general sentiment.
One way to test your understanding of physics would be to google for problem sets on special relativity, or something, and see how many problems you can solve.
That does sound like fun. It’s been too long!
Linking this back to the question of verbal and conceptual vs mathematical understanding I note that some of these could (and probably should) be verbal problems. Of the kind that use a broad basic understanding of the physics principles and not just the juggling about of numbers and manipulating some memorized equations. Because that really is useful knowledge (as well).
Alice is running very fast holding a long pole. The pole is held parallel to the direction in which she is running. She’s running into a barn with an open door. When the pole is stationary relative to the barn, it does not fit inside it completely. A tiny bit sticks out, preventing the door from being shut. However, since the pole is now in motion, Bob, who is standing by the barn door, sees its length contracted, allowing it to fit completely inside the barn. This means that Bob can wait for Alice to enter the barn and then shut the door. Let’s say he shuts the door as soon as the leading edge of the pole makes contact with the barn wall opposite the door. But from Alice’s perspective, it is the barn’s length that has contracted, not the pole’s. From her perspective, how do you account for the fact that she is able to run the pole completely into the barn so that Bob can shut the barn door?
The usual response to the twin paradox is that the twins’ situation is not symmetrical because the one who leaves Earth must undergo non-inertial motion in order to turn around and return. However, it is possible to reproduce the twin paradox without either twin accelerating, and without moving to curved spacetimes. Can you think of how one might construct this situation?
We all know that according to special relativity it is impossible for a massive object to accelerate until it catches up with a photon. However, it is possible for a massive object to accelerate so that, in its rest frame, its distance from a photon always remains the same. What would the word-line of such an object look like?
We have two spaceships A and B, initially flying at the same uniform velocity. A is flying behind B, and there is a taut string connecting the nose of A to the tail of B. The spaceships both accelerate so that an observer who starts out at rest relative to them will measure the distance between them as unchanging throughout the acceleration. When the ships stop accelerating they are moving relative to the observer. This means the observer should see the string as Lorentz contracted, but, by hypothesis, the distance between the spaceships unchanged. Does this mean the string breaks? Describe what happens from the perspective of the space-ships.
Sbe Nyvpr, gur cbyr’f raq uvggvat gur onpx jnyy naq Obo pybfvat gur qbbe jvyy abg or fvzhygnarbhf. Jura gur cbyr uvgf gur onpx raq bs gur jnyy, fbzr bs vg jvyy fgvyy or fgvpxvat bhg bs gur onea. Ohg gung ovg jvyy pbagvahr zbivat vagb gur onea, orpnhfr vg unf abg lrg unq gvzr gb erprvir gur vasbezngvba gung gur bgure raq bs gur cbyr unf uvg n jnyy. Gung vasbezngvba pnaabg cebcntngr snfgre guna gur fcrrq bs yvtug. Guvf zrnaf gurer jvyy or n crevbq qhevat juvpu gur onpx raq bs gur cbyr pbagvahrf gb zbir nybat jvgu Nyvpr juvyr gur sebag raq unf orra fgbccrq ol gur jnyy. Gur cbyr qrsbezf, nyybjvat vg gb svg vagb gur onea ol gur gvzr Obo fuhgf gur qbbe.
Bar cbffvovyvgl vf gb unir n plyvaqevpny fcnprgvzr, jurer fcnpr vf xvaq bs yvxr Cnpzna. N crefba geniryyvat ng havsbez irybpvgl va nal qverpgvba jvyy neevir onpx gb jurer fur fgnegrq sebz. Guvf vf n syng fcnprgvzr. Va guvf pnfr, bar gjva pna sbyybj na varegvny cngu gung jvaqf nebhaq gur plyvaqre, juvyr gur bgure gjva sbyybjf n cngu gung tbrf fgenvtug hc gur plyvaqre. Gur nflzzrgel vf qhr gb gbcbybtvpny qvssreraprf orgjrra gur cnguf, abg nppryrengvba.
Gur jbeqyvar bs guvf bowrpg jvyy or n ulcreobyn jvgu gur cubgba’f cngu nf nflzcgbgr.
Gur fgevat jvyy oernx. Sebz gur crefcrpgvir bs gur fcnprfuvcf, gur qvfgnapr orgjrra gurz vapernfrf nf gurl nppryrengr, pnhfvat gur fgevat gb oernx. Vs gur qvfgnapr orgjrra gur fuvcf va gur erfg senzr fgnlf gur fnzr rira gubhtu gur fcnprfuvcf ner nppryrengvat, guvf zrnaf gur qvfgnapr orgjrra gur fuvcf va gurve bja senzr zhfg or vapernfvat (gb pbhagrenpg Yberagm pbagenpgvba). Guvf vf Oryy’f fcnprfuvc cnenqbk, qvfphffrq va terngre qrgnvy urer.
Gubfr gjb cnguf ner vaqrrq flzzrgevp, naq gubfr gjvaf jvyy or gur fnzr ntr jura gurl zrrg. Gur fcnprgvzr vagreiny gurl genirefr jvyy or rknpgyl gur fnzr.
The math of special relativity helps not one whit in solving problems 1, 2 and 4. Problem 3 of course can be answered qualitatively without math, but to indicate with any specificity you will need math.
Moreover, you can be quite proficient with the math of SR and be floored by these. I knew an undergrad who could do acceleration problems yet couldn’t work his way through problem 1, because the course had focused on gamma and neglected spacetime diagrams.
Spacetime diagrams are the math of special relativity. Doing algebra with gammas without insight on how it relates to the Minkowski spacetime is like the proverbial blind men grasping various parts of the elephant. (Why such godawful approaches are still foisted upon students is a mystery to me.)
Just the vibe of “How dare you? Get off my lawn!” or is there something in the comment you are actually replying to which you would dispute?
Why on Earth do you think it’s “my lawn” in any sense? I have readily and repeatedly pointed out that I’m a complete amateur in physics, and I claim no status whatsoever as a physicist. I am making a purely negative and reactive point that pop-physics is about fake explanations perpetuated mostly for status-related reasons.
Pardon me. I mean “Get off my neighbor’s lawn! You kids these days need to learn respect!”
(In case my message is insufficiently overt I am suggesting you have the ‘status-related reasons’ approximately backward.)
pop-physics is about fake explanations
Nonsense. Or, again, you are talking about an entirely different thing. Sources with bullshit fake explanations can be found and so can sources that give solid explanations with only limited mathematical detail, summaries and take home findings that have been worked out by others. It is the latter that lukeprog is referring to.
Pardon me. I mean “Get off my neighbor’s lawn! You kids these days need to learn respect!”
Your speculations about my motives here are stupendously wrongheaded. If you look at my previous LW comments, you’ll see that one of my recurring themes, on which I hammer incessantly, is that in many fields, people who get officially credentialed as experts under the present system are in fact naked emperors whose supposed expertise couldn’t withstand scrutiny by a smart amateur who tries to make honest sense of it. (And also that excessive faith in credentialed expertise is a widespread and under-appreciated bias even among many LW contributors.) Assuming that I would act as a self-appointed guardian of a credentialist intellectual monopoly is absurd given the views I have expressed loudly and repeatedly.
In fact, if we’re going to discuss the workings of the present system, the mainstream respectable view is that as an amateur, one should pay homage to credentialed experts in physics for their pop-science writings, extol these writings as a great source of enlightenment, and raise one’s own status by being an owner and reader of such books. So rather than looking at my claims as upholding the intellectual monopoly of credentialed experts, you can view them as attacking the way these experts abuse their position for monetary and status gain by getting into these enterprises in pop-science. Such enterprises are supposedly educational and enlightening, but in fact entirely obscurantist and subservient to upholding the existing credentialist and bureaucratic hierarchy. (This even aside from the purely venal interest involved.)
I think Vladimir is saying physics is like that. Because when you take away the math, you are no longer able to explain what is really going on.
Is that the right link? Because the that post, “Guessing the Teacher’s Password”, gives a purely verbal description of a object getting heated up and turned around. Explicit mathematics doesn’t come into it either on the part of the successful student or the reader of the document. Basically it provides yet another example which reduces Vladimir’s claims to absurdity.
When I was young, I read popular physics books such as Richard Feynman’s QED: The Strange Theory of Light and Matter. I knew that light was waves, sound was waves, matter was waves. I took pride in my scientific literacy, when I was nine years old.
When I was older, and I began to read the Feynman Lectures on Physics, I ran across a gem called “the wave equation”. I could follow the equation’s derivation, but, looking back, I couldn’t see its truth at a glance. So I thought about the wave equation for three days, on and off, until I saw that it was embarrassingly obvious. And when I finally understood, I realized that the whole time I had accepted the honest assurance of physicists that light was waves, sound was waves, matter was waves, I had not had the vaguest idea of what the word “wave” meant to a physicist.
Are we just disagreeing about the meaning of “understand” or something? Are you using the word “understanding” in an unusual way, such that there is no such thing as non-mathematical understanding?
No. Some things can be understood without mathematics, and some can’t. I’m just claiming that QM and relativity (including the basic intuitive understanding of these fields) fall into the latter category, and by extension also various fields of modern physics that have them as prerequisites.
Also, at one point you seem to say that I can’t have evidence about whether Copenhagen is correct or incorrect without understanding all the equations involved? That seems too obviously false; I assume I’m misunderstanding you?
I have no idea what you mean by “all the equations involved”; I certainly never mentioned any such thing. There are many different ways in which Copenhagen might be formulated, which may involve different mathematical concepts and equations used to express them—but any formulation that rises above fuzzy and obscurantist fake-explanation talk must necessarily have a mathematical basis. I mean, if you’re going to talk about “collapse of the wave function,” you’d better have a solid understanding of what a “wave function” is and what exactly it collapses into.
I haven’t read the quantum physics sequence on Less Wrong. I got my physics from lots of other sources.
Are we just disagreeing about the meaning of “understand” or something? Are you using the word “understanding” in an unusual way, such that there is no such thing as non-mathematical understanding?
Also, at one point you seem to say that I can’t have evidence about whether Copenhagen is correct or incorrect without understanding all the equations involved? That seems too obviously false; I assume I’m misunderstanding you?
For what it’s worth, I agree with Vladimir_M. Eliezer has a nice post about this. One way to test your understanding of physics would be to google for problem sets on special relativity, or something, and see how many problems you can solve.
About what in particular? Just the vibe of “How dare you? Get off my lawn!” or is there something in the comment you are actually replying to which you would dispute? If the latter then I must affirm the observation “That seem too obviously false” and, like Luke, apply the benefit of the doubt. That would mean assuming that you aren’t really responding to the grandparent at all and more just chiming in with a general sentiment.
That does sound like fun. It’s been too long!
Linking this back to the question of verbal and conceptual vs mathematical understanding I note that some of these could (and probably should) be verbal problems. Of the kind that use a broad basic understanding of the physics principles and not just the juggling about of numbers and manipulating some memorized equations. Because that really is useful knowledge (as well).
Some verbal problems on special relativity:
Alice is running very fast holding a long pole. The pole is held parallel to the direction in which she is running. She’s running into a barn with an open door. When the pole is stationary relative to the barn, it does not fit inside it completely. A tiny bit sticks out, preventing the door from being shut. However, since the pole is now in motion, Bob, who is standing by the barn door, sees its length contracted, allowing it to fit completely inside the barn. This means that Bob can wait for Alice to enter the barn and then shut the door. Let’s say he shuts the door as soon as the leading edge of the pole makes contact with the barn wall opposite the door. But from Alice’s perspective, it is the barn’s length that has contracted, not the pole’s. From her perspective, how do you account for the fact that she is able to run the pole completely into the barn so that Bob can shut the barn door?
The usual response to the twin paradox is that the twins’ situation is not symmetrical because the one who leaves Earth must undergo non-inertial motion in order to turn around and return. However, it is possible to reproduce the twin paradox without either twin accelerating, and without moving to curved spacetimes. Can you think of how one might construct this situation?
We all know that according to special relativity it is impossible for a massive object to accelerate until it catches up with a photon. However, it is possible for a massive object to accelerate so that, in its rest frame, its distance from a photon always remains the same. What would the word-line of such an object look like?
We have two spaceships A and B, initially flying at the same uniform velocity. A is flying behind B, and there is a taut string connecting the nose of A to the tail of B. The spaceships both accelerate so that an observer who starts out at rest relative to them will measure the distance between them as unchanging throughout the acceleration. When the ships stop accelerating they are moving relative to the observer. This means the observer should see the string as Lorentz contracted, but, by hypothesis, the distance between the spaceships unchanged. Does this mean the string breaks? Describe what happens from the perspective of the space-ships.
EDIT: Solutions here.
Solutions, or at least sketches of solutions:
Sbe Nyvpr, gur cbyr’f raq uvggvat gur onpx jnyy naq Obo pybfvat gur qbbe jvyy abg or fvzhygnarbhf. Jura gur cbyr uvgf gur onpx raq bs gur jnyy, fbzr bs vg jvyy fgvyy or fgvpxvat bhg bs gur onea. Ohg gung ovg jvyy pbagvahr zbivat vagb gur onea, orpnhfr vg unf abg lrg unq gvzr gb erprvir gur vasbezngvba gung gur bgure raq bs gur cbyr unf uvg n jnyy. Gung vasbezngvba pnaabg cebcntngr snfgre guna gur fcrrq bs yvtug. Guvf zrnaf gurer jvyy or n crevbq qhevat juvpu gur onpx raq bs gur cbyr pbagvahrf gb zbir nybat jvgu Nyvpr juvyr gur sebag raq unf orra fgbccrq ol gur jnyy. Gur cbyr qrsbezf, nyybjvat vg gb svg vagb gur onea ol gur gvzr Obo fuhgf gur qbbe.
Bar cbffvovyvgl vf gb unir n plyvaqevpny fcnprgvzr, jurer fcnpr vf xvaq bs yvxr Cnpzna. N crefba geniryyvat ng havsbez irybpvgl va nal qverpgvba jvyy neevir onpx gb jurer fur fgnegrq sebz. Guvf vf n syng fcnprgvzr. Va guvf pnfr, bar gjva pna sbyybj na varegvny cngu gung jvaqf nebhaq gur plyvaqre, juvyr gur bgure gjva sbyybjf n cngu gung tbrf fgenvtug hc gur plyvaqre. Gur nflzzrgel vf qhr gb gbcbybtvpny qvssreraprf orgjrra gur cnguf, abg nppryrengvba.
Gur jbeqyvar bs guvf bowrpg jvyy or n ulcreobyn jvgu gur cubgba’f cngu nf nflzcgbgr.
Gur fgevat jvyy oernx. Sebz gur crefcrpgvir bs gur fcnprfuvcf, gur qvfgnapr orgjrra gurz vapernfrf nf gurl nppryrengr, pnhfvat gur fgevat gb oernx. Vs gur qvfgnapr orgjrra gur fuvcf va gur erfg senzr fgnlf gur fnzr rira gubhtu gur fcnprfuvcf ner nppryrengvat, guvf zrnaf gur qvfgnapr orgjrra gur fuvcf va gurve bja senzr zhfg or vapernfvat (gb pbhagrenpg Yberagm pbagenpgvba). Guvf vf Oryy’f fcnprfuvc cnenqbk, qvfphffrq va terngre qrgnvy urer.
Jung vs gur gjvaf ner zbivat nebhaq gur plyvaqre ng gur fnzr fcrrq va bccbfvgr qverpgvbaf? Gung’f flzzrgevp.
Gubfr gjb cnguf ner vaqrrq flzzrgevp, naq gubfr gjvaf jvyy or gur fnzr ntr jura gurl zrrg. Gur fcnprgvzr vagreiny gurl genirefr jvyy or rknpgyl gur fnzr.
This is exactly what I need about when I’m starting to need it. Thank you.
The math of special relativity helps not one whit in solving problems 1, 2 and 4. Problem 3 of course can be answered qualitatively without math, but to indicate with any specificity you will need math.
Moreover, you can be quite proficient with the math of SR and be floored by these. I knew an undergrad who could do acceleration problems yet couldn’t work his way through problem 1, because the course had focused on gamma and neglected spacetime diagrams.
I think someone without a detailed grasp of spacetime diagrams should be able to answer problem 1, as long as they know the following principles:
Gur eryngvivgl bs fvzhygnarvgl
Ab fhcreyhzvany fvtanyvat
Spacetime diagrams are the math of special relativity. Doing algebra with gammas without insight on how it relates to the Minkowski spacetime is like the proverbial blind men grasping various parts of the elephant. (Why such godawful approaches are still foisted upon students is a mystery to me.)
Why on Earth do you think it’s “my lawn” in any sense? I have readily and repeatedly pointed out that I’m a complete amateur in physics, and I claim no status whatsoever as a physicist. I am making a purely negative and reactive point that pop-physics is about fake explanations perpetuated mostly for status-related reasons.
Pardon me. I mean “Get off my neighbor’s lawn! You kids these days need to learn respect!”
(In case my message is insufficiently overt I am suggesting you have the ‘status-related reasons’ approximately backward.)
Nonsense. Or, again, you are talking about an entirely different thing. Sources with bullshit fake explanations can be found and so can sources that give solid explanations with only limited mathematical detail, summaries and take home findings that have been worked out by others. It is the latter that lukeprog is referring to.
Your speculations about my motives here are stupendously wrongheaded. If you look at my previous LW comments, you’ll see that one of my recurring themes, on which I hammer incessantly, is that in many fields, people who get officially credentialed as experts under the present system are in fact naked emperors whose supposed expertise couldn’t withstand scrutiny by a smart amateur who tries to make honest sense of it. (And also that excessive faith in credentialed expertise is a widespread and under-appreciated bias even among many LW contributors.) Assuming that I would act as a self-appointed guardian of a credentialist intellectual monopoly is absurd given the views I have expressed loudly and repeatedly.
In fact, if we’re going to discuss the workings of the present system, the mainstream respectable view is that as an amateur, one should pay homage to credentialed experts in physics for their pop-science writings, extol these writings as a great source of enlightenment, and raise one’s own status by being an owner and reader of such books. So rather than looking at my claims as upholding the intellectual monopoly of credentialed experts, you can view them as attacking the way these experts abuse their position for monetary and status gain by getting into these enterprises in pop-science. Such enterprises are supposedly educational and enlightening, but in fact entirely obscurantist and subservient to upholding the existing credentialist and bureaucratic hierarchy. (This even aside from the purely venal interest involved.)
Luke, do you agree there is no such thing as a non-mathy understanding of graph theory?
I think Vladimir is saying physics is like that. Because when you take away the math, you are no longer able to explain what is really going on.
Can such an explanation really be called “great”?
Is that the right link? Because the that post, “Guessing the Teacher’s Password”, gives a purely verbal description of a object getting heated up and turned around. Explicit mathematics doesn’t come into it either on the part of the successful student or the reader of the document. Basically it provides yet another example which reduces Vladimir’s claims to absurdity.
No. Some things can be understood without mathematics, and some can’t. I’m just claiming that QM and relativity (including the basic intuitive understanding of these fields) fall into the latter category, and by extension also various fields of modern physics that have them as prerequisites.
I have no idea what you mean by “all the equations involved”; I certainly never mentioned any such thing. There are many different ways in which Copenhagen might be formulated, which may involve different mathematical concepts and equations used to express them—but any formulation that rises above fuzzy and obscurantist fake-explanation talk must necessarily have a mathematical basis. I mean, if you’re going to talk about “collapse of the wave function,” you’d better have a solid understanding of what a “wave function” is and what exactly it collapses into.