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Vladimir_M comments on Great Explanations - Less Wrong
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I see that the physics list consists of math-free pop-science books. I don't see how these can possibly count as "great explanations," since it's impossible to gain any real understanding of physics from such materials.
For example, a good explanation of relativity would first present the concepts of Minkowski spacetime and proper time, and then show how all those "relativistic effects" follow from these reasonably simple concepts. (This as opposed to a bad explanation of the traditional sort that confuses the reader with various "effects" and "paradoxes.") Then it would explain how a curved metric with a Minkowski signature can make the geodesic lines look like the free fall curves of Newtonian gravity, thus providing an intuitive grasp of the whole "gravity is geometry" business. Beyond that, you just have to get into the hairy tensor stuff, and even this minimum requires a solid knowledge of algebra, analytic geometry, and basic calculus. Anything less than that is just rambling that may have a lot of entertainment and signaling value, but won't move you one millimeter closer to any real insight.
Agreed. A good elementary exposition of relativity along these lines is Bob Geroch's General Relativity from A to B.
EDIT: Actually, I realize I'm only in partial agreement with Vladimir. While I do think that many pop-sci explanations of theoretical physics are fairly worthless and often actively misleading, I do not think that it is impossible to gain real insight into (say) the general theory of relativity without mastering differential geometry. Geroch's book presupposes only high school mathematics, but it provides a genuinely deep insight into relativity.
I described the requirements as algebra, analytic geometry, and basic calculus, which is more or less within advanced high-school math. (Without calculus, I don't see how you could explain integrals along the world line, which are the very heart of the matter.)
However, note that just high-school algebra is already worlds apart from purely prose-based, general-audience pop-science. I would guess that for an average reader (let alone owner) of pop-science books, following a text using algebra would be far harder than it would be to figure out tensors for a reasonably math-savvy twelfth grade student.
I agree, and I wonder how much more widely it applies than the mathematically based subjects. Just because something is expressed in words rather than formally manipulable symbols does not, I suspect, make it any easier to arrive at sound understanding based on sound assessment of evidence and argument. However, it does make it easier to mistakenly think that you have done so.
It is easy to just go with the narrative flow, nodding along to it without asking "is this true?", "is this cherry-picked evidence?", "is the writer working to a hidden bottom line?", and so on, and even if one does, it's a lot more work to answer these questions in a subject such as history than in mathematics, where you can and should work out the proofs yourself, or in physics, where a short trip to Google will turn up reliable sources about the red shift of stars.
I agree -- that's why I sometimes point out that for people who imagine themselves to be so much more rational than average, a real test would be to try and make some sense of such fuzzy and controversial topics.
Also, in subjects outside of hard sciences, the danger isn't just that you may fall in with the flow of a well-written bad argument, but also that a valid argument might have such bad ideological or signaling implications that you'll desperately grasp for any excuse to reject it without due consideration.
Speaking as someone who has read a few popular treatments and none of the proper textbooks ... yeah, I agree. I have no insight into general relativity at all, and precious little into special relativity.
Vladimir,
Our discussion has been long. Let me reply to you here, and leave the tangents of our discussion hanging so I can return to the origin.
You say "it's impossible to gain any real understanding of physics from such materials [e.g. pop-sci books]."
I'm still not sure what you mean by "real understanding," but all I'm trying to claim in the post above is that readable but non-technical explanations of scientific concepts and theories from people like Brian Greene and Richard Dawkins can be helpful. They have helped me, for one. They have improved not just my ability to guess the teacher's password, but also my ability to have more accurate anticipations in ways that help me achieve my goals. Is that something you actually think is "impossible"?
If so, what is your response to the examples wedrifid and I gave?
If not, what is it that you do mean?
My original point was only about physics, not about evolution, and I have already written that there is an important difference between the accessibility of these two for lay readers. So by dragging evolution into the discussion again, you are obscuring the issue.
Yes, I do think that math-free popular books about modern physics (by which I mean QM, relativity, and the more advanced fields that use them) cannot give the reader any such ability.
A physicist with good writing skills could easily write a book full of completely nonsensical pop-scientific "explanations" of relativity and QM (let alone cosmology etc.), and there would be no way for non-expert readers to notice that something's wrong (unless they noticed that it's explicitly contradicting something they previously read elsewhere). In contrast, someone who studies with full understanding from a real textbook will notice the errors of the author purely from internal evidence, since these errors will stick out blatantly in the otherwise smooth and clear logical flow of exposition. There we see the fundamental difference between real explanations and fake explanations.
Some of these examples are about using classical physics to improve on folk-physical intuitions or gain insight that can be based on folk physics or simple Newtonian physics. Such insights can indeed be gained without much (or even any) math, so I admit my claims should be qualified to exempt such cases. Note however that the original context was about advanced non-classical fields of physics, which are the subject of the overwhelming majority of pop-scientific texts, some of which you originally cited as supposedly "great explanations."
As for the example of the limited speed of light, it's a completely isolated rule that stands outside of any systematic understanding. It's as if you claimed that you can understand Maxwell's electromagnetic theory without knowing vector calculus, and then supported it by arguing that your non-mathematical understanding enables you to predict that bad things will happen if you touch uninsulated high-voltage lines. Yes, it is a correct rule that makes correct and practically useful predictions, but it's completely isolated and learned by heart -- and there is no way to connect it with some more general framework for understanding physical phenomena without learning real (i.e mathy) physics. [*] Similarly, unless you have real mathy knowledge of relativity, your knowledge of this particular fact about the limited speed of light is just an isolated fact, which is not integrated with any broader and deeper understanding of physics.
[*] -- Edit: Thinking about this a bit more, I would say that there are in fact such ways. Some people manage to develop amazing intuitive understanding of electromagnetic phenomena without any math or formalism at all, and sometimes their intuitions will be more accurate than the products of laborious number-crunching by experts. However, such understanding is about hands-on technical practice, and it's radically different from anything that can result from reading pop-science.
Huh? I didn't bring up evolution again. I mentioned Richard Dawkins, but not evolution, and the 'great explanation' from Dawkins that I list above is in physics (rainbows), not biology.
BTW, are the physics ones the only ones you object to? Are you still mostly on board with the project of tracking down good, engaging explanations of, say, biological and psychological concepts and theories?
You've offered enough exemptions now for your claim (speed of light, classical physics, and probably others) that I now understand that we agree more than initially seemed to be the case. Still, I think there are examples of math-free popular explanations of modern physics that can give readers like me the ability to have more accurate anticipations in ways that help us achieve our goals.
I gave a few examples but you didn't accept them.
I'm tempted to drop the discussion for now — unless you strongly object?
My mistake -- I didn't realize you were alluding to Dawkins talking about physics.
I think I have already explained clearly enough that it depends on the concrete topic in question. Some technical and scientific topics can be explained in a non-mathematical way that increases the understanding of smart lay readers. Others however can't, and attempts to do so will end up as sheer confusion and fake explanations. Modern physics just happens to be in the latter category.
Then you understand wrongly. I haven't budged one millimeter about the worthlessness of pop-scientific "explanations" of modern physics of the sort you cited initially. There is a fundamental difference between, on one hand, direct improvements on folk-physical intuition and simple facts memorized in isolation, and on the other hand, real understanding of complex and non-intuitive theories of modern physics.
I have no problem with that. I think what I've said so far should be clear enough.
What in the above comment is worth downvoting? All I say here is: "Here's what I'm still confused about; could you clarify?"
Luke. Do you realize for what kind of trivial stuff EY gets downvoted down to like below -10?
People adjust their expectations accordingly in order to, the charitable explanation goes, preserve the signalling value of karma as a low investment form of feedback for your comments, or as the less charitable goes, raise their expectations to an insane level.
You have the third highest karma score on the site. You acquired this position very rapidly and are very prolific, probably everyone knows your user handle, while for example I still didn't know most of the people on the top 10 list for like a year after I started reading.
Take it as a compliment.
Sit down and pour yourself a glass of your favourite beverage and smile when something that gets most people a 0 or 1 gets you a -1 and something that gets others a -1 or -2 will get you -5. Also remember it is bad signalling to ask "why am I donwovted?" when you have several 10k karma, it dosen't make sense, but people respond better at that point if you ask basically the same thing without using the word "vote" and its variants or "karma". :)
Karma isn't the point. As you've said, I'm not lacking in karma. The point is to improve the success of my communication by learning in detail what kinds of things set some people off.
Which, now that I think about it, is something I could have included in my original comment asking why the comment above it was downvoted.
Vladimir,
I gave four criteria to explain what I meant by a "great explanation" and your example fails criterion #3 and probably #4. We're talking about different kinds of "great explanations."
My post is meant as a list of great explanations intended for a general audience. The explanations you describe are mathematical explanations like you would find in textbooks written for people who will do advanced work in that field. I don't need to be able to prove Aumann's agreement theorem for me to understand how it should inform my Bayesian updates, and I don't need to be a physics graduate to understand why many worlds has advantages over the Copenhagen interpretation. Eliezer's relatively non-technical explanation of Occam's razor does move people more than "one millimeter closer" to understanding many things.
As you note, some things are impossible to explain to an average 13-year-old. By the same principle, some things are impossible to explain while remaining at the "general audience" level. You can produce confusion or fake explanations -- pop-science typically offers some mixture of these two -- but nothing even close to real explanations, let alone actual "clicks."
No, these explanations are far short of what one needs to do actual work in that field. Even the hairy tensor stuff I mentioned is just the beginning.
I wrote this based on my own experience trying to make some sense of relativity. What I sketched is the barest minimum that enabled me to gain anything resembling real insight instead of just confusion and fake explanations.
What I'm trying to say is this.
I do not have a technical understanding of biological evolution. I haven't looked up the equations in population genetics and elsewhere. But even a good pop-sci explanation of evolution from Richard Dawkins does make a positive impact in my understanding of the world. My non-technical understanding of evolution allows me to make more accurate predictions about the world than I would have otherwise. The trick is in making sure I do not over-estimate how well I understand evolution.
Do you actually disagree with this?
Edit: Also, just in case anybody is confused... the meaning of "explanation" in my post "great explanations" differs from the meaning of "explanation" in the phrase "fake explanations." They are two different words that happens to have the same spelling. A "great explanation" is a presentation of a topic that helps readers understand it. The word "explanation" in the sense of "fake explanation" refers to the type of explanation also used in the phrase "scientific explanation."
A good understanding of evolution can be had without any math, unlike physics. There is no math in The Origin of Species, but it's impossible to rewrite any major work of physics since Galileo without math while preserving its essential points.
In any case, what exactly are these more accurate predictions about the world that pop-physics enables you to make? I would be very curious to hear some examples.
My comment about fake explanations applies to any reasonable definition of "explanation." In fact, the points from the "Fake Explanations" article apply perfectly here. If the material from some prominent pop-science book were rearranged into something written in a similar style but in fact completely wrong and nonsensical and signed by an equally high-status author, how many readers of these books would realize that something's wrong?
I will never get a ping time to American servers from my home here in Melbourne of less than the distance times two divided by c.
If I drop a really heavy rock and a somewhat lighter rock from a moderate height there will be only a slight difference in how long they take to fall to the ground.
If I find some stuff that is really, really heavy and leave it in my pocket I will probably die of cancer.
Cars traveling towards me will sound slightly higher in pitch than after they go past me.
If I buy bullets that are designed to travel slower than sound they will probably make less noise than the bullets that go faster than the speed of sound.
If you give me some charts that show how much light of various wavelengths there is coming from two different stars and it so happens that they look really, really similar except that one is kind of 'stretched out' over the 'wavelength' axis I can tell you that the stretched out one is farther away from us.
And, the critical one:
You might believe that my lack of status as a mathematical physicist doesn't give me the right to make claims about Quantum Mechanics implications but the universe doesn't care. I can apply basic principles of rational thinking to filter large swathes of evidence from those who popularize physics and, particularly, the verbal, non-mathematical claims of physicists in order to work out whether or not a specific claim is likely to be correct.
Fair enough. There are indeed many ways in which the folk physics intuition can be improved by internalizing a rule that's simple enough to explain without math. I admit that my question was too aggressive and snarky.
However, I don't think any such simple insights will move you any close to understanding either QM or relativity (let alone more advanced topics such as cosmology or the controversies over QM interpretations), which was the topic of the original dispute. I must also point out that your rules are either from classical physics (and thus reasonably close to the relevant folk physics intuitions) or in the form of entirely opaque rules for which you can't find any justification except for appeal to authority. And I'm certainly not saying that as someone who has "status as a mathematical physicist"; I'm a complete amateur in physics, as I pointed out in an earlier comment. (Also, if you've read my earlier comments on LW, you'll know that I don't put much inherent weight on the official credentials of expertise bestowed by the present academic system.)
Also, regarding the trends in the Copenhagen vs. MW debate, how much of your opinion is based on understanding of the issues involved, and how much on mere perception of the social dynamics in the field?
Then, like Luke, I must observe that your definition of 'understanding' is completely incompatible with mine. Actually, no. I think we've moved beyond that now. You are just wrong.
Look at the first example for a start. That claim is based on understanding of (part of) relativity. But that example was only included coincidentally. May I remind you that the examples you demanded were for physics in general (and, for that matter, that the demand was in response to professed understanding of evolution.)? Space considerations stopped me before I also threw in predictions about "two really good clocks, one of which you fly around really fast!", the fellow who gets into a rocket and outlives his great grandchildren and what happens when you shoot not very many very small things through very small slits.
As I pointed out in my reply to Luke, knowledge of that fact constitutes "understanding of relativity" to the same extent that knowledge of the fact that you can get hurt by sticking your fingers into electrical installations constitutes understanding of electromagnetic theory. It's just a single fact you know in complete isolation, not a fact that is a part of some broader framework for understanding the world.
To build on this particular example, consider that some things like shadows, reflections, etc., can indeed move faster than light. Or, if you just spin on an office chair, in your rest frame the celestial objects are spinning around you way faster than c. Unless you can explain why such motions are consistent with the "no faster than light" principle, you have nothing more than a literally memorized fact that if it might be useful if something could move faster than c, it can't happen. It's a true fact, to be sure, and even a potentially useful one, but still.
The context was about the pop-scientific treatments of modern physics. If you insist on full precision, I will gladly admit that my wording about physics in general was imprecise, since there are indeed simple topics in classical physics where insight can be gained without math, building only on a folk-physics intuition. So please read my statements in their original context.
We aren't talking about the memorization of a simple fact about pings. We are talking about all the understanding you can have about relativity without having memorized a mathematical equation. This can be used to make the prediction that ping times will never be lower than the aforementioned limit.
You asked for examples of predictions about the world that can be made based on understanding physics minus the math. It would be disingenuous in the extreme to then dismiss all examples of predictions about the world given because they are, in fact, mere predictions about the world and therefore could have been memorized without real understanding.
My first prediction: If you (who I believe professed understanding of at least this much understanding of math) and lukeprog were locked in rooms disconnected from the outside world and given the task of answering this question not only would Luke be able to give an explanation, his explanation would be better than yours. You both know enough about physics to answer and Luke is better at explaining things.
My second prediction: There are many students who, in their physics exams, get all the questions that require mathematics correct and who, when encountering a question like this one, can't give an answer. Because not only is knowing the math not strictly necessary to answer this question, it isn't even sufficient.
Additional claim: It has been too long since I studied physics for me to remember all of the mathematics of special relativity. Yet when I did the aforementioned study I also gained a solid grasp of the fundamental principles. With that understanding I could recreate the interesting mathematics from first principles. I am confident of this because I've done it before, just for kicks. Because memorizing the math wasn't enough for me and I wanted to really grasp the science in depth. The way you do that is by knowing the concepts well enough that you could work out the equations for yourself. Because just memorizing them is detail work. (I haven't got a chance in hell of doing this with GR.)
In the various responses you have been given your claim that you can't have any understanding of physics without math has been overwhelmingly refuted. All you are left with is "But that understanding isn't true understanding, true understanding means you remember the math!" To that I reply "No, not all Scotsmen like haggis. You can only tell a true Scotsman by the kilt they are wearing!"
It is time to retreat from a complete rejection of all non-mathematical understanding so that you can express an actually tenable position regarding the limits of how much you can know about physics sans math. Because there really are such limits and I would love to be able to support you in declaring them. But right now you've gone overboard and tried to reject even that understanding which can exist. And that brings you to the realm of the absurd and I just can't support a position which is just obviously factually incorrect.
Question: If the world were wiped out tomorrow leaving a few people and you were the only survivor with any minimal scientific training, could you on your own reconstruct special relativity? If the answer to this is "no" then you don't understand it.
Note that by this standard I don't understand QM and I really don't understand GR and I'm a math grad student. It is ok to say that one doesn't understand things.
Yes. I already declared this, in a comment you replied to no less.
Funny you should mention that. I spent years working in IT, and this knowledge was actually useful once. I tried to ping a DNS router in Europe (I forget where) from California, and it came back in 1ms and I thought "Ummmmmm... no. You lie." It turned out one of the smart switches on the local network was fucked up and was somehow returning all pings itself.
Behold! Even a pop-sci understanding of physics controlled my anticipations in a way that was useful for accomplishing goals in the world.
That is pretty awesome, but I also don't think it's necessary to think about light speed to solve that problem. Anyone who spends a lot of time debugging networking problems knows that 1ms is unreasonably fast for any communication with a machine more than a couple router hops away, even if it's physically nearby.
I see that this is getting upvoted, but your example sounds like someone who realizes that a device doesn't work because it's not plugged in, and then makes a self-satisfied comment that his knowledge of electromagnetic theory usefully controlled his anticipations in this situation.
In other words, it's about simple conventional nuts-and-bolts technical knowledge, not an improvement on such knowledge brought by more advanced understanding of anything. There's no way someone who works in network administration wouldn't know that a "<1ms" ping coming from around the world is anomalous.
Actually, yes: I think this is correct.
But, I think I would have noticed something was wrong even if I hadn't worked in IT before. But I'm not certain of that.
This great story is related.
Typically, when someone's car breaks, they don't bring it to church, they bring it to a mechanic. In the distant past, people probably brought the equivalent of their cars (when broken) to the equivalent of church. This is progress. I could be wrong, but I think Luke wants more of this, in more domains. I personally think this is less a question of the right explanation, and more a question of daily necessity. If you need physics every day, you'll have fewer wrong ideas about it. But who needs physics every day? Almost no one.
(And yes, some people probably still bring their broken cars to church.)
EDIT: Not everybody wants to be or has the talent to be a "mechanic," but that doesn't matter. What matters is that people associate "broken car" either with "person who can fix broken car" or "reliable knowledge about how cars work" instead of "sky father."