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 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.
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.
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.
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"?
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 some...
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". :)
My post is meant as a list of great explanations intended for a general audience.
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."
The explanations you describe are mathematical explanations like you would find in textbooks written for people who will do advanced work in that field.
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.
My non-technical understanding of evolution allows me to make more accurate predictions about the world than I would have otherwise.
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.
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."
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?
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.
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:
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.
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.
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?
I don't know how much actual understanding you have about these issues, but if you really believe you understand them in some "non-mathematical" way, you are fooling yourself. Considering that all these are prominent recurring themes from the LW sequences, 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.
Now, I don't think one could even state a workable definition of the Copenhagen interpretation without a sizable mathematical background, so that your self-confident assertion that you "understand" that it's "probably incorrect" strikes me as absurd -- let alone your claim that your "non-mathematical understanding of contemporary physics allows [you] to see how the majority of scientists can be wrong" about these issues. (They may well be wrong, to be sure, but I don't think you have any real evidence either way.) And what are the "predictions about the world" that the supposed ...
As for your assertion about the implications of QM on the questions of personal identity, this looks even more as a belief that you've taken on faith, backed by sheer rationalizations. (Again, regardless of its actual merits when the real arguments are considered -- I'm not saying that it's incorrect, merely that you don't have any good reason to believe either way if your grasp of the issue is entirely non-mathematical.)
Leaving aside for now the question of understanding of Copenhagen validity but as for the specific claim about knowing enough contemporary physics to understand the implications to personal identity your rejection is just nonsense. You most certainly can gain enough knowledge to make conclusions about personal identity without knowing math.
Ask an impressive physicist:
"Dude are, like, atoms and combinations thereof in any way uniquely identified?"
He says "nah".
You say "kk"
From there you have some utterly trivial philosophizing to do to reject ideas of "same atoms for personal identity". This is a trivial question and basically relies on not being philosophically incompetent while also checking with a physicist just in case some relevant, surprising and bizarre phenomenon has appeared recently at incomprehensibly high levels of physics.
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 withou
Yvain's Parable of the Heartstone is by far the best explanation of metaethics that I have read. (I am actually surprised how much better I find it than other explanations. Does anyone know of something of similar quality that addresses the same things?)
I don't think Eliezer's Introduction to Bayes's Theorem should be on here. I seriously don't think it's that good. It labors its points, and after I read the whole thing I still didn't get that you could use it to judge between different hypotheses, which is pretty much the most amazing thing I've learned this year, incidentally.
However, his new version, which he's working on and I got to read when I volunteered as an illustrator briefly, is absolutely amazing. When he gets that one finished, it will deserve its place on this list.
Lazy Functional Programming: Learn You a Haskell for Great Good by Miran Lipovača
It's a bit long to qualify under requirement #2, so in particular I'd like to highlight chapters 11-13 as a great explanation of functors and monads. (Albeit one that requires you already grok haskell, hence the recommendation for the whole book).
Hi, thank you for creating this great list!
Aumann’s agreement theorem: Landsburg, The Big Questions, chapter 8.
This link is broken, and I was not able to find this chapter separately anywhere. I would appreciate if someone would be able to update the link or re-upload the document (or recommend another good article on this topic). Thank you.
Okay, I don't mean to be annoying, but I'm curious if anyone else ever thinks this way.
Right after I read this: "Those who do it well are rare and valuable", this is what I automatically thought: 'Okay, so he's setting himself up to, in the future, pursue a career in explaining, and this sentence/article functions as a tool of justification by making the value of the endeavor "objective" through writing it here'
That is, some part of me sometimes leaps away from the normal way of reading--which sees things as from the writer to yourself-...
FORTH is one of the most interesting programming languages, seeing as an implementation can be built in an afternoon of coding, in somehting as low level as assembly language. FORTH is home to many interesting ideas of metaprogramming, and serves as a worthy counterpart to LISP, albiet in the other end of the abstraction scale.
If you are familiar with assembly languages in general, the GNU Assembler's syntax or the Intel x86 platform, you might want to give Jonesforth a read. It is a well written Literal Programming style implementation of a FORTH for the x86 platform.
Does anyone know of a great explanation of the very early universe, preferably from the past 5 years?
Pretty much any chapter of Mermin's It's About Time is the best explanation I've ever read of its content matter, and he is not shy of giving you the maths to back up the intuition (or even to motivate it in some cases). If I had to pick one chapter, it would, perhaps oddly, probably be the first one, which explains Galilean relativity extraordinarily well.
General applicability of Bayesian inference: Judea Pearl, "Probabilistic Reasoning in Intelligent Systems", chapter 2. (Definitely not an explanation suitable for a teenager, but for a college student interested in the topic it is very good, I think.)
The first chapter of Tim Maudlin's Quantum Non-Locality and Relativity is a great explanation of Bell's theorem.
I don't have it at hand, but I recall the explanation of entropy, temperature, and the Boltzmann factor presented in the first chapter of "Thermal Physics" by Kittel and Kroemer being particularly clear, elegant, and direct.
More recently I enjoyed "Probability: a Survey of the Mathematical Theory" by John Lamperti. It is great for understanding things like Kolmogorov's 0-1 Law.
I recommend Spacetime Physics by Taylor and Wheeler for special relativity. This is a mathematical textbook however it only requires basic algebra and is accessible to highschool students.
For Physics I have to add in "The Road to Reality" by Roger Penrose. Much, much more engaging than an equivalent amount of information in textbook form!
For an overview of the evidence for evolution and why it is true (but not how evolution itself works), I really like the first chapter of Neil Shubin's Your Inner Fish [PDF].
Explaining is a difficult art. You can explain something so that your reader understands the words; [I try to] explain something so that the reader feels it in the marrow of his bones.
Richard Dawkins
My private school taught biology from the infamous creationist textbook Biology for Christian Schools, so my early understanding of evolution was a bit... confused. Lacking the curiosity to, say, check Altavista for a biologist’s explanation (faith is a virtue, don’t ya know), I remained confused about evolution for years.
Eventually I stumbled across an eloquent explanation of the fact that natural selection follows necessarily from heritability, variation, and selection.
Click. I got it.
Explaining is hard. Explainers need to pierce shields of misinformation (creationism), bridge vast inferential distances (probability theory), and cause readers to feel the truth of foreign concepts (quantum entanglement) in their bones. That isn’t easy. Those who do it well are rare and valuable.
Textbook writers are often skilled at explaining complex fields. That’s why I called on my fellow Less Wrongers to name their favorite textbooks (if they had read at least two other textbooks on those subjects). The Best Textbooks on Every Subject now gives 22 textbook recommendations, for fields as diverse as scientific self-help and representation theory.
Now I want to jump down a few levels in granularity. Let’s pool our knowledge to find great explanations for each important idea (in math, science, philosophy, etc.), whether or not there is equal value in the rest of the book or article in which each explanation is found.
Great explanations, in my meaning, have four traits:
A great explanation does more than report facts; it uses analogy and rhetoric and other tools to make readers feel the target idea in their bones.
A great explanation is not a single analogy nor a giant book. It is, roughly, between 2 and 100 pages in length.
A great explanation is comprehensible at best to a young teenager, or at least to a 75th percentile college graduate. (There may be no way to seriously explain string theory to an average 13-year-old.)
A great explanation is exciting to read.
By sharing great explanations we can more often experience that magical click.
I’ve barely begun to assemble the list below. Please comment with your own additions!
(The list below is exclusive to written explanations, but feel free to share your favorite explanations from other media. My favorite explanation of BASIC programming is a piece of software from Interplay called Learn to Program BASIC, and of course many people love Khan Academy’s videos and The Teaching Company’s audio courses.)
Epistemology
Aumann’s agreement theorem: Landsburg, The Big Questions, chapter 8.
Occam’s razor: Yudkowsky, Occam’s razor.
Math and Logic
Physics
Special relativity: Wolfson, Simply Einstein, chapters 2–12.
General relativity: Hawking, The Universe in a Nutshell, chapters 1–2.
Infinite, flat universe: Greene, The Hidden Reality, chapters 1–3.
Timeless reality / block universe: Greene, The Fabric of Reality, chapter 5.
Inflationary cosmology: Greene, The Hidden Reality, chapter 3.
Rainbows: Dawkins, The Magic of Reality, chapter 7.
Biology
Psychology
Anchoring: Kahneman, Thinking, Fast and Slow, chapter 11.
Availability heuristic: Kahneman, Thinking, Fast and Slow, chapters 12–13.
Prospect theory: Kahneman, Thinking, Fast and Slow, chapters 25–26.
Modularity of mind: Kurzban, Why Everyone (Else) is a Hypocrite, chapters 1–4.
Economics
