Looking At Liquids - Parts List: Fill & Download for Free

You arrive at lecture and sit perched on the edge of your seat, notebook open to a clean page and freshly-sharpened pencil in hand. You follow every word the professor says. Well, maybe you zone out a few times in the middle, but who doesn't? Besides, you're copying everything down and can review it later.That weekend, you diligently read the textbook. Maybe you skip a few parts since it's a busy week, but you definitely study the chapter summary and read all the examples. You do the homework problems, even starting three days early. When you're stuck, you go to office hours and ask the TA for help until they show you how to do it.Before the exam, you study your notes and the published homework solutions. You try the practice exam, and it seems the pieces are finally falling into place. You can solve most of the problems and remember most of the formulas and derivations! At last you take the final, referencing the single allowed sheet of notes you prepared at length the night before. You get almost every question right, or at least partial credit, and take home a well-deserved A.Three months later, you can hardly remember what the class was all about. What's going on? Why did you forget so much? Are you the only one? Should you have memorized more and worked even harder?The answer is no. A student who memorizes the entire physics curriculum is no more a physicist than one who memorizes the dictionary is a writer. Studying physics is about building skills, specifically the skills of modeling novel situations and solving difficult problems. The results in your textbook are just the raw material. You're a builder. Don't spend all your time collecting more materials. Collect a few, then build things. Here's how.The Cathedral and the StonesWhile delivering his famous set of freshman lectures on physics, Richard Feynman held a few special review sessions. In the first of these, he discussed the problem of trying to memorize all the physics you've learned:It will not do to memorize the formulas, and to say to yourself, "I know all the formulas; all I gotta do is figure out how to put 'em in the problem!"Now, you may succeed with this for a while, and the more you work on memorizing the formulas, the longer you'll go on with this method - but it doesn't work in the end.You might say, "I'm not gonna believe him, because I've always been successful: that's the way I've always done it; I'm always gonna do it that way."You are not always going to do it that way: you're going to flunk - not this year, not next year, but eventually, when you get your job, or something - you're going to lose along the line somewhere, because physics is an enormously extended thing: there are millions of formulas! It's impossible to remember all the formulas - it's impossible!And the great thing that you're ignoring, the powerful machine that you're not using, is this: suppose Figure 1 - 19 is a map of all the physics formulas, all the relations in physics. (It should have more than two dimensions, but let's suppose it's like that.)Now, suppose that something happened to your mind, that somehow all the material in some region was erased, and there was a little spot of missing goo in there. The relations of nature are so nice that it is possible, by logic, to "triangulate" from what is known to what's in the hole. (See Fig. 1-20.)And you can re-create the things that you've forgotten perpetually - if you don't forget too much, and if you know enough. In other words, there comes a time - which you haven't quite got to, yet - where you'll know so many things that as you forget them, you can reconstruct them from the pieces that you can still remember. It is therefore of first-rate importance that you know how to "triangulate" - that is, to know how to figure something out from what you already know. It is absolutely necessary. You might say, "Ah, I don't care; I'm a good memorizer! In fact, I took a course in memory!"That still doesn't work! Because the real utility of physicists - both to discover new laws of nature, and to develop new things in industry, and so on - is not to talk about what's already known, but to do something new - and so they triangulate out from the known things: they make a "triangulation" that no one has ever made before. (See Fig. 1-21.)In order to learn how to do that, you've got to forget the memorizing of formulas, and to try to learn to understand the interrelationships of nature. That's very much more difficult at the beginning, but it's the only successful way.Feynman's advice is a common theme in learning. Beginners want to memorize the details, while experts want to communicate a gestalt.Foreign language students talk about how many words they've memorized, but teachers see this as the most trivial component of fluency. Novice musicians try to get the notes and rhythms right, while experts want to find their own interpretation of the piece's aesthetic. Math students want to memorize theorems while mathematicians seek a way of thinking instead. History students see lists of dates and facts while professors see personality, context, and narrative. In each case, the beginner is too overwhelmed by details to see the whole. They look at a cathedral and see a pile of 100,000 stones.One particularly clear description of the difference between the experts' and beginners' minds comes from George Miller's 1956 study "The magical number seven, plus or minus two." Miller presented chess boards to both master-level chess players and to novices. He found that the masters could memorize an entire board in just five seconds, whereas the novices were hopeless, getting just a few pieces. However, this was only true when the participants were memorizing positions from real chess games. When Miller instead scattered the pieces at random, he found the masters' advantage disappeared. They, like the novices, could only remember a small portion of what they'd seen.The reason is that master-level chess players have "chunked" chess information. They no longer have to remember where each pawn is; they can instead remember where the weak point in the structure lies. Once they know that, the rest is inevitable and easily reconstructed.I played some chess in high school, never making it to a high level. At a tournament, I met a master who told me about how every square on the chess board was meaningful to him. Whereas, when writing down my move, I would have to count the rows and columns to figure out where I had put my knight ("A-B-C, 1-2-3-4, knight to C4") he would know instantaneously because the target square felt like C4, with all the attendant chess knowledge about control of the center or protection of the king that a knight on C4 entails.To see this same principle working in yourself right now, memorize the following. You have two seconds:首先放花生酱，然后果冻Easy, right? Well, it would be if you were literate in Chinese. Then you’d know it’s the important maxim, “first the peanut butter, then the jelly”.You can remember the equivalent English phrase no problem, but probably don't remember the Chinese characters at all (unless you know Chinese, of course). This is because you automatically process English to an extreme level. Your brain transforms the various loops and lines and spaces displayed on your screen into letters, then words, then a familiar sandwich-related maxim, all without any effort. It's only this highest-level abstraction that you remember. Using it, you could reproduce the detail of the phrase "first the peanut butter, then the jelly" fairly accurately, but you would likely forget something like whether I capitalized the first letter or whether the font had serifs.Remembering an equally-long list of randomly-chosen English words would be harder, a random list of letters harder still, and the seemingly-random characters of Chinese almost impossible without great effort. At each step, we lose more and more ability to abstract the raw data with our installed cognitive firmware, and this makes it harder and harder to extract meaning.That is why you have such a hard time memorizing equations and derivations from your physics classes. They aren't yet meaningful to you. They don't fit into a grand framework you've constructed. So after you turn in the final, they all start slipping away.Don't worry. Those details will become more memorable with time. In tutoring beginning students, I used to be surprised at how bad their memories were. We would work a problem in basic physics over the course of 20 minutes. The next time we met, I'd ask them about it as review. Personally, I could remember what the problem was, what the answer was, how to solve it, and even details such as the minor mistakes the student made along the way and the similar problems to which we'd compared it last week. Often, I found that the student remembered none of this - not even what the problem was asking! What had happened was, while I had been thinking about how this problem fit into their understanding of physics and wondering what their mistakes told me about which concepts they were still shaky on, they had been stressed out by what the sine of thirty degrees is and the difference between "centrifugal" and "centripetal".Imagine an athlete trying to play soccer, but just yesterday they learned about things like "running" and "kicking". They'd be so distracted by making sure they moved their legs in the right order that they'd have no concept of making a feint, much less things like how the movement pattern of their midfielder was opening a hole in the opponent's defense. The result is that the player does poorly and the coach gets frustrated.Much of a technical education works this way. You are trying to understand continuum mechanics when Newton's Laws are still not cemented in your mind, or quantum mechanics when you still haven't grasped linear algebra. Inevitably, you'll need to learn subjects more than once - the first time to grapple with the details, the second to see through to what's going on beyond.Once you start to see the big picture, you'll find the details become meaningful and you'll manipulate and remember them more easily. Randall Knight's Five Easy Lessons describes research on expert vs. novice problem solvers. Both groups were given the same physics problems and asked to narrate their thoughts aloud in stream-of-consciousness while they solved them (or failed to do so). Knight cites the following summary from Reif and Heller (1982)Observations by Larkin and Reif and ourselves indicate that experts rapidly redescribe the problems presented to them, often use qualitative arguments to plan solutions before elaborating them in greater mathematical detail, and make many decisions by first exploring their consequences. Furthermore, the underlying knowledge of such experts appears to be tightly structured in hierarchical fashion.By contrast, novice students commonly encounter difficulties because they fail to describe problems adequately. They usually do little prior planning or qualitative description. Instead of proceeding by successive refinements, they try to assemble solutions by stringing together miscellaneous mathematical formulas from their repertoire. Furthermore, their underlying knowledge consists largely of a loosely connected collection of such formulas.Experts see the cathedral first, then the stones. Novices grab desperately at every stone in sight and hope one of them is worth at least partial credit.In another experiment, subjects were given a bunch of physics problems and asked to invent categories for the problems, then put the problems in whatever category they belonged. Knight writes:Experts sort the problems into relatively few categories, such as "Problems that can be solved by using Newton's second law" or "Problems that can be solved using conservation of energy." Novices, on the other hand, make a much larger number of categories, such as "inclined plane problems" and "pulley problems" and "collision problems." That is, novices see primarily surface features of a problem, not the underlying physical principles.The "Aha!" FeelingIt is clear that your job as a student is to slowly build up the mental structures that experts have. As you do, details will get easier. Eventually, many details will become effortless. But how do you get there?In the Mathoverflow question I linked about memorizing theorems, Timothy Gowers wroteAs far as possible, you should turn yourself into the kind of person who does not have to remember the theorem in question. To get to that stage, the best way I know is simply to attempt to prove the theorem yourself. If you've tried sufficiently hard at that and got stuck, then have a quick look at the proof -- just enough to find out what the point is that you are missing. That should give you an Aha! feeling that will make the step far easier to remember in the future than if you had just passively read it.Feynman approached the same questionThe problem of how to deduce new things from old, and how to solve problems, is really very difficult to teach, and I don't really know how to do it. I don't know how to tell you something that will transform you from a person who can't analyze new situations or solve problems, to a person who can. In the case of the mathematics, I can transform you from somebody who can't differentiate to somebody who can, by giving you all the rules. But in the case of the physics, I can't transform you from somebody who can't to somebody who can, so I don't know what to do.Because I intuitively understand what's going on physically, I find it difficult to communicate: I can only do it by showing you examples. Therefore, the rest of this lecture, as well as the next one, will consist of doing a whole lot of little examples - of applications, of phenomena in the physical world or in the industrial world, of applications of physics in different places - to show you how what you already know will permit you to understand or to analyze what's going on. Only from examples will you be able to catch on.This sounds horribly inefficient to me. Feynman and Gowers both reached the highest level of achievement in their domains, and both are renowned as superb communicators. Despite this, neither has any better advice than "do it a lot and eventually expertise will just sort of happen." Mathematicians and physicists talk about the qualities of "mathematical maturity" and "physical insight". They're essential to moving past the most basic level, but it seems that no one knows quite where they come from.Circular ReasoningThere are certainly attempts to be more systematic than Feynman or Gowers, but before we get to that, let's take a case study. I recall that as a college freshman, I knew that the formula for the acceleration of a ball orbiting in a circle was [math]a = v^2/r[/math]. I wanted to know why, so I drew a picture:I imagined a small ball starting on the right side of the circle, heading upwards where the blue velocity vector [math]v_1[/math] is drawn. The ball moves around the circle, goes counter-clockwise over the top and then heads downwards on the left hand side, where the red velocity [math]v_2[/math] is. The ball's velocity changed, which means it accelerated. The acceleration is[math]a = \frac{\Delta v}{\Delta t}[/math][math]\[/math][math]Delta[/math][math] v[/math] is clearly [math]2v[/math], and [math]\[/math][math]Delta[/math][math] t[/math] is the time it takes to go half way around the circle, which is [math]\frac{\text{distance}}{\text{speed}} = \frac{\pi r}{v}[/math]. Hence, the acceleration is[math]a = \frac{2v}{\pi r/v} = \frac{2 v^2}{\pi r} \approx 0.64 \frac{v^2}{r}[/math]This isn't quite right. The answer is supposed to be [math]v^2/r[/math]. Somehow there is an extra factor of [math]2/\pi[/math] floating around.If you already understand calculus, this is a silly and obvious mistake. But for me it took quite some time - weeks, I think - until I understood that I had found the average acceleration, but the formula I was trying to derive was the instantaneous acceleration.The way I broke out of this mental rut was to think about the case where the ball has gone one quarter of the way around, like this:Then the same approach gives[math] a = \frac{\Delta v}{\Delta t} = \frac{2\sqrt{2}v^2}{\pi r} \approx 0.90 \frac{v^2}{r}[/math],which is closer to the right value. If you try it when the ball goes 1/8 the way around, you get[math]a = \frac{4 \sqrt{2 [/math][math]-[/math][math] \sqrt{2}}v^2}{\pi r} \approx 0.97 \frac{v^2}{r}[/math]and you're getting the idea that what you have to do is take the limit as the ball goes an infinitesimal fraction of the way around. (By the way, if I had been clever, maybe I'd have discovered Viète's formula this way, or something like it. I only recognized this now because I remembered encountering Viete's formula. So memory certainly has its place in allowing you to make connections. It's just not as central as beginners typically believe.)How do you do that "infinitesimal fraction of the way around" thing? Well, if the ball travels an angle [math]\theta[/math] around the circle, we can draw the before and after velocities asand[math] \[/math][math]Delta[/math][math] v = 2 \sin (\theta/2) v[/math]which in the limit [math]\theta \to 0[/math] becomes[math] \[/math][math]Delta[/math][math] v = \theta v[/math]and[math] a = \frac{\Delta v}{\Delta t} = \frac{\theta v}{\theta r/v} = \frac{v^2}{r}[/math]But all of this took a long time to come together in my mind, assembling gradually, but in discrete chunks with each small epiphany. As I walk through it now, I can see there are many concepts involved, and in fact if you're a beginning student it's likely that the argument isn't clear because I skipped some steps.The main idea in that argument is calculus - we're looking at an infinitesimal displacement of the ball. To understand the entire argument, though, we also need to do a fair amount of geometry, develop the idea of sliding velocity vectors around in space so they originate at the same point, introduce the concept of an arbitrary angle of rotation [math]\theta[/math], find the time it takes to rotate by that angle for a given [math]r[/math] and [math]v[/math], use the small-angle approximation of the sine function, and maybe a couple other things I'm not seeing.That's a lot of mental exercise. It's no wonder that working all this out for yourself is both harder and more effective than reading it in the book. Just reading it, you'll skip over or fail to appreciate how much goes into the derivation. The next time you try to understand something, you want those previously-mastered ideas about geometry and calculus already there in your mind, ready to be called up. They won't be if you let a book do all the work.Today, I can solve this problem in other ways. For example, I could write down the rectangular coordinates and differentiate, describe the motion in the complex plane as [math]r e^{i\omega t}[/math] and differentiate that, or transform to a rotating reference frame and note the centrifugal force on the stationary ball and conclude it must be accelerating in an inertial frame. A cute one is to write down the position and velocity vectors by intuition, and notice that going from position to velocity you rotate 90 degrees and multiply the length by [math]v/r[/math]. To go from velocity to acceleration is mathematically identical, so rotating another 90 degrees and multiply by [math]v/r[/math] again we obtain the answer.I can argue from dimensional analysis that the only way to get something with units of acceleration is [math]v^2/r[/math], or heuristically point out that if you increase the velocity, the velocity vectors get bigger, but we also go from one to the next in less time, so the acceleration ought to scale with [math]v^2[/math], etc.I also see aspects of the problem that I didn't back then, such as that this isn't really a physics problem. There are no physical laws involved. It would become a physics problem if we included that the ball is circling due to gravitational forces and used Newton's gravitational law, for example, but as it stands this problem is just a little math.So yes, I can easily memorize this result and provide a derivation for it. I can do that for most of the undergrad physics curriculum, including the pendulum and Doppler formulas you mentioned, and I think I could ace, or at least beat the class average, on the final in any undergraduate physics course at my university without extra preparation. But I can do that because I built up a general understanding of physics, not because I remember huge lists of equations and techniques.How to Chunk ItI can do these things now because of years' of accumulated experience. Somehow, my mind built chunks for thinking about elementary physics the same way chess players do for chess. I've taught classes, worked advanced problems, listened to people, discussed with people, tutored, written about physics on the internet, etc. It's a hodgepodge of activities and approaches, and there's no way for me to tease from my own experience what was most important to the learning process. Fortunately, people from various fields have made contributions to understanding how we create the cognitive machinery of expertise. Here is a quick hit list.George Pólya's How to Solve It examines the problem-solving process as a series of stages, and suggests the student ask themselves specific questions like, "Is it clear that there enough information to solve the problem?"Scott H Young, Cal Newport, and many others give specific advice on study skills: how to take notes, how to diagram out the connections between ideas, how to test your knowledge, how to fit what you're learning into the larger scheme of things, etc.When you do need to memorize things, spaced repetition software like Anki takes an algorithmic, research-backed approach to helping you remember facts with the minimum of time and effort.K. Anders Ericsson has tried to find the key factors that make some forms of practice better than others - things like getting feedback as you go and having clear goals. He refined these into the concept of Deliberate Practice. He also believes there is no shortcut. Even if you practice effectively, it usually takes around 10,000 hours of hard work to reach the highest levels in complex fields like physics or music.Chunking and assigning meaning are your mind's ways of dealing with the information overload of the minutiae that inevitably pop up in any field. Another approach, though, is to try to expand your mind's ability to handle those minutiae. If you can push your "magical number" from seven to ten, you'll be able to remember and understand more of your physics work because it takes a bit longer to fill your cognitive buffer. Dual N-Back exercises are the most popular method of working on this. Nootropic drugs may also provide benefits to some people. Low-hanging fruit first, though. If you aren't sleeping 8-9 hours a day, getting a few hours of exercise a week, and eating healthy food for most meals, you're probably giving up some of your mind's potential power already. (There is individual variation, though.)Howard Gardner is one champion of the idea of multiple intelligences, or different learning types. When working on electric fields, for example, Gardner might advise you to study Maxwell's equations, draw pictures of vector fields and intuit their curls, get up and use your body, pointing your arms around to indicate electric field vectors, write or speak about what you're studying, learn with a friend or tutor, or maybe even create musical mnemonics to help you study, depending on where your personal strengths lie. Certainly, all students should build facility with drawing sketches, plotting functions, manipulating equations, visualizing dynamics, and writing and speaking about the material.Psychologist Carol Dweck's research studies the effect of your attitude towards learning on how much you learn, finding, for example, that children praised for their hard work are likely to press on further and learn more when given tough problems, whereas children praised for their intelligence are more likely to give up.Productivity guru David Allen helps people organize their lives and defeat procrastination with specific techniques, such as dividing complicated tasks into small, specific "next actions" and deciding when to do them, then organizing them in a planner system.Mihály Csíkszentmihályi believes that people operate best in a state of "flow", where they are so focused on the task they find it enjoyable and engrossing to the point they're innately motivated to continue. He emphasizes, for example, that the task needs to be the right level of difficulty - not too hard and not too easy - to find the flow state. (Some people think this state doesn't jibe with deliberate practice; others contend it's possible to achieve both simultaneously.)Taken together, this yields enough practical advice to chew on for months or years. To summarize, when you are learning something new:Try to figure it out for yourselfIf you get stuck, take a peek at your textbook to get the main ideaTeach the idea to someone elseOnce you've learned something, repeat the entire reasoning behind it for yourself, working through each detailAsk yourself Pólya's questions when you're stuckUse Young and Newport's techniques to map out the ideas of your class and relate them to your prior knowledgeMake Anki decks and review them a few minutes a day to retain what you've learnedMake sure your study sessions include all the principles of deliberate practice, especially feedback, challenge, and attentionBuild an image of yourself as someone motivated by learning and proud of having worked hard and effectively rather than as someone proud of being smart or renowned.Find a organizational system that lets you handle all the details of life smoothly and efficiently.Search for the flow state, notice when you enter it, and put yourself in position to find flow more and more often.Work on different subjects, reviewing both advanced and basic material. They will eventually all form together in your mind, and you're likely to have to take at least two passes at any subject before you understand it well.Take care of your physical health.This list does not include reading every page of the textbook or solving every problem at the end of the chapter. Those things aren't necessarily bad, but they can easily become rote. Building the material up for yourself while dipping into reference materials for hints is likely to be more effective and more engaging, once you learn to do it. It is a slow, difficult process. It can be frustrating, sitting there wracking your brain and feeling incredibly stupid for not understanding something you know you're supposed to have down. And strangely, once you have it figured out, it will probably seem completely obvious! That's your reward. Once the thing is obvious, you've chunked it, and you can move on. (Though you still need to review with spaced repetition.) This is the opposite of the usual pattern of sitting in lectures and feeling you understand everything quite clearly, only to find it all evaporated the next day, or acing a final only to find your knowledge is all gone the next month.That, I believe, summarizes the practical knowledge and advice about the learning process. Memorizing equations and derivations is difficult and ineffective because they are just the details. You can only handle a few details before your mind gets swamped. To cope, train yourself to the point where you process equations and physical reasoning automatically. This will free your conscious effort up to take in the big picture and see what the subject is all about.It Just Gets In The Way, You SeeSomehow, I've developed a "this is calculus" instinct, so that if I see the problem about acceleration in circular motion, or any other problem about rates of change, I know that it's talking about a limit of some kind. Where does this instinct exist in my brain? What form does it take? How does it get called up at the right time?George Lakoff believes that almost everything we understand is via metaphor. Any sort of abstract concept is understood by linking it to concrete concepts we've previously understood. For example, in Where Mathematics Comes From, Lakoff and coauthor Rafael Nuñez argue that we think of the mathematical concept of a "set" as a sort of box or container with things stacked in it. We reason about sets using our intuition about boxes, then later go back and support our conclusions with the technical details. Learning to reason about sets, then, is learning to think about the box metaphor and translate it back and forth into the formal language of axioms and theorems. This seems to fit with the introspective reports of many mathematicians, who say they build intuitive or visual models of their mathematics when finding results, then add in the deltas and epsilons at the end.This may be why we so often see beginning students asking things like, "but what is the electron, really?" If they were told it is just a tiny little ball, that would work, because it's a very easy metaphor. But instead, they're told it's not a ball, not a particle, not a wave, not spinning even though it has spin, etc. In fact, they're told to dismiss all prior concepts entirely! This is something Lakoff believes is simply impossible. No wonder students are bobbing in an ocean of confused thought bubbles, with nothing but mixed metaphors to grasp at until the last straw evaporates, across the board.Linguists like Steven Pinker believe that the language we use tells us how our mind works. Physicists certainly do have a specialized lexicon, and the ability to use it correctly correlates pretty well to general physics intuition, in my experience. In his review of Pinker's The Stuff of Thought, Douglas Hofstadter summarizes:Pinker shows, for example, how subtle features of English verbs reveal hidden operations of the human mind. Consider such contrasting sentences as "The farmer loaded hay into the wagon" and "The farmer loaded the wagon with hay." In this pair, the verb "load" has two different kinds of objects: the stuff that gets moved and the place it goes. Also, in the first sentence, the destination is the object of one preposition; in the second, the stuff is the object of another. Pinker sees these "alternations" as constituting a "microclass" of verbs acting this way, such as "spray" ("spray water on the roses" versus "spray the roses with water"). Where does this observation lead him? To the idea that we sometimes frame events in terms of motion in physical space (moving hay; moving water) and sometimes in terms of motion in state-space (wagon becoming full; roses becoming wet).Moreover, there are verbs that refuse such alternations: for instance, "pour." We can say "I poured water into the glass" but not "I poured the glass with water." What accounts for this curious difference between "load" and "pour"? Pinker claims that pouring merely lets a liquid move under gravity's influence, whereas loading is motion determined by the human agent. "Pour" and "load" thus belong to different microclasses, and these microclasses reveal how we construe events. "[W]e have discovered a new layer of concepts that the mind uses to organize mundane experience: concepts about substance, space, time, and force," Pinker writes. " . . . [S]ome philosophers consider [these concepts] to be the very scaffolding that organizes mental life. . . . But we've stumbled upon these great categories of cognition . . . by trying to make sense of a small phenomenon in language acquisition."If correct, then in order to think about physics the way an expert does, we should learn to speak the way experts do. If we try to solve physics problems using the words "load" and "pour", we may be carrying around a bunch of distracting anthropocentric baggage. If we don't recognize that, we'll get stuck, saying the problem "doesn't make sense", when really it's our linguistically-instilled expectations that are wrong. To combat this, it may be just as helpful to gain facility with the language of physics as with its equations.Five Easy Lessons provides a clear example of such difficulties: the case study of "force". As I type this, my laptop is sitting on a desk which exerts an upward force on it. Few beginning students believe this is really a force, even after they've been browbeaten into drawing arrows for the "normal force" on exam diagrams.The problem is in the way we use "force":"The robber forced the door open.""Your apology sounded forced.""...the force of the explosion...""...the force of righteousness...""I'm being forced to take physics even though I'll never use it."Literally or figuratively, we think of "force" as implying not only motion, but intent or purpose, and also control. Force is for people pushing on things, or maybe for cars and projectiles. These things are using energy and will run down if left alone. But the desk under my laptop? It's just sitting there, totally passive. How could it be "exerting a force" when it doesn't even get tired? Needing some sort of rationalization for why the laptop doesn't fall, beginners say that it's not that the desk exerts a force on the laptop, the desk just provides something for the laptop to sit on. Or if something falls on the desk, the desk didn't exert a force to stop it. It just got in the way is all. Why doesn't the professor understand this obvious difference? A desk exerting a force? Come on...Five Easy Lessons describes how students only overcome this difficulty after seeing a classroom demonstration where, using a laser pointer and a mirror laid on the desk top, the professor demonstrates how when a heavy cinder block is laid on the desk, the surface responds by bending out of its natural shape, exerting force on the cinder block like a compressed spring would.You may need to find many such visualizations before you can reconcile your colloquial use of words with their use in physics. But this might also be dangerous, because although finding a way to make physics obey your idea about what a word means works decently in this case, in other instances it's your expectations for the word that ought to change. (Relativity, with words like "contraction", "slowing down", etc. is a good example.)Mythologist Joseph Campbell believes that we understand the world primarily through story. Perhaps we understand derivations, experimental evidence, and the logic behind physical conclusions as a sort of story, and it's in building this story that our cognitive chunks are formed.Mind The Neural Gap JunctionsYou are the pattern of neural activity in your brain. When a part of you changes, building a new memory, installing a new habit, or constructing a tool to approach a class of problems, that change must be reflected somewhere in your brain.Lesswrong user kalla724 describes this process in "Attention control is critical for changing/increasing/altering motivation"First thing to keep in mind is the plasticity of cortical maps. In essence, particular functional areas of our brain can expand or shrink based on how often (and how intensely) they are used. A small amount of this growth is physical, as new axons grow, expanding the white matter; most of it happens by repurposing any less-used circuitry in the vicinity of the active area. For example, our sense of sight is processed by our visual cortex, which turns signals from our eyes into lines, shapes, colors and movement. In blind people, however, this part of the brain becomes invaded by other senses, and begins to process sensations like touch and hearing, such that they become significantly more sensitive than in sighted people. Similarly, in deaf people, auditory cortex (part of the brain that processes sounds) becomes adapted to process visual information and gather language clues by sight.But, they caution, these neural changes occur primarily to those parts of our minds to which we pay conscious attention:A man is sitting in his living room, in front of a chessboard. Classical music plays in the background. The man is focused, thinking about the next move, about his chess strategy, and about the future possibilities of the game. His neural networks are optimizing, making him a better chess player.A man is sitting in his living room, in front of a chessboard. Classical music plays in the background. The man is focused, thinking about the music he hears, listening to the chords and anticipating the sounds still to come. His neural networks are optimizing, making him better at understanding music and hearing subtleties within a melody.A man is sitting in his living room, in front of a chessboard. Classical music plays in the background. The man is focused, gritting his teeth as another flash of pain comes from his bad back. His neural networks are optimizing, making the pain more intense, easier to feel, harder to ignore.You need to pay attention not just to doing physics, but to the right parts of doing physics - the parts most related to intuition.James Nearing gave his advice on how to do this in Mathematical Tools for PhysicistsHow do you learn intuition?When you've finished a problem and your answer agrees with the back of the book or with your friends or even a teacher, you're not done. The way do get an intuitive understanding of the mathematics and of the physics is to analyze your solution thoroughly. Does it make sense? There are almost always several parameters that enter the problem, so what happens to your solution when you push these parameters to their limits? In a mechanics problem, what if one mass is much larger than another? Does your solution do the right thing? In electromagnetism, if you make a couple of parameters equal to each other does it reduce everything to a simple, special case? When you're doing a surface integral should the answer be positive or negative and does your answer agree?When you address these questions to every problem you ever solve, you do several things. First, you'll find your own mistakes before someone else does. Second, you acquire an intuition about how the equations ought to behave and how the world that they describe ought to behave. Third, It makes all your later efforts easier because you will then have some clue about why the equations work the way they do. It reifies the algebra.Does it take extra time? Of course. It will however be some of the most valuable extra time you can spend.Is it only the students in my classes, or is it a widespread phenomenon that no one is willing to sketch a graph? (\Pulling teeth" is the cliche that comes to mind.) Maybe you've never been taught that there are a few basic methods that work, so look at section 1.8. And keep referring to it. This is one of those basic tools that is far more important than you've ever been told. It is astounding how many problems become simpler after you've sketched a graph. Also, until you've sketched some graphsof functions you really don't know how they behave.(To see the advice on graphs, along with a detailed step-by-step example, see his book, free online)Brown Big SpidersOne of the difficulties with chunks is that they're mostly subconscious. We may ultimately know of their existence, as did the chess master who told me he knew how each square of the chess board felt, but their precise nature and the process of their creation are almost immune to introspection. The study methods I've talked about above are empirically useful in creating chunks, so we have guidelines for how to make new chunks in general, but we usually don't know which ones we are creating.Lesswrong user Yvain comments on the essay Being a teacherI used to teach English as a second language. It was a mind trip.I remember one of my students saying something like "I saw a brown big spider". I responded "No, it should be 'big brown spider'". He asked why. Not only did I not know the rule involved, I had never even imagined that anyone would ever say it the other way until that moment.Such experiences were pretty much daily occurrences.In other words, the chunkiest cognitive process we have - language - develops largely without our awareness. (In retelling this story, I've met a surprising number of people who actually did know about adjective order in English, but most of them either learned English as a second language or had studied it in psychology or linguistics course.)This makes it incredibly difficult for physics teachers or textbook writers to communicate with beginners. It's inevitable that beginners will say that a certain lecturer or book just doesn't explain it clearly enough, or needs to give more examples. Meanwhile, the lecturer has no idea why what they said wasn't already perfectly clear and thinks the example was completely explicit. Neither party can articulate the problem, the student because they can't see the incorrect assumption they're making, the professor because they don't realize they've already made such an assumption.For example, once I was proctoring a test in a physics class for biology majors. A question on the test described a certain situation with light going through a prism and asked, "What is the sign of the phase shift?" A student came up to ask for clarification, and it wasn't until they'd asked their question three times that I finally got it. They thought they were supposed to find the "sign" as in a signpost, or marker. There would be some sort of observable behavior that would indicate that a phase shift had occurred, and that was the "sign of the phase shift." Until then, I was only able to think of "sign" as meaning positive or negative - did the wave get advanced or retarded?If you want to learn a language with all those rules you don't even know about, you need to immerse yourself. Endless drills and exercises from a book won't be enough, as millions of Americans a decade out of high school straining to remember, "Dondé esta el baño?" can attest. You need to read, speak, see, and hear that language all around you before it takes.To learn physics, then, read, speak, and hear it all around you. Attend colloquia. Read papers. Solve problems. Read books. Talk to professors and TA's, and expose yourself to all the patterns of thought that are the native language of the field.As you learn, you will build the right chunks to think about physics without realizing what they are. But there's a flip side to this problem, which is that when you're not doing physics, you can build the wrong chunks. They can get in the way, and again you don't realize it.In Drawing on the Right Side of the Brain, Betty Edwards discusses an exercise she gave her art students:One day, on impulse, I asked the students to copy a Picasso drawing upside down. That small experiment, more than anything else I had tried, showed that something very different is going on during the act of drawing. To my surprise, and to the students' surprise, the finished drawings were so extremely well done that I asked the class, "How come you can draw upside down when you can't draw right-side up?" The students responded, "Upside down, we didn't know what we were drawing."When we see a recognizable image, unconscious chunking immediately gets to work, interpreting, imparting meaning, and inevitably distorting. Learning to draw, according to Edwards, involves circumventing harmful chunks as much as building helpful ones.So it is with physics. The ideas about force, animation, and intent discussed in the laptop-and-desk example seem to illustrate just this problem. Five Easy Lessons lists many of the known misconceptions that students have somehow taught themselves in each topic of introductory physics - for example that electric current gets used up as it goes around a circuit. But I think it's likely that there are many more such obstructive thought patterns that we don't yet know exist. These might be more general notions about such things as cause and effect, what nature "wants" to accomplish, etc.I Feel DumbEducators are perpetually frustrated by what seems like an outrageous pattern. They explain something clearly. The students all claim to understand perfectly, and can even solve quantitative problems. Still, when you ask the students to answer basic conceptual questions, they get it all wrong. How is this possible?In this YouTube video, Veritasium explores what happens when you explain something clearly:Amazingly, the clearer the explanation, the less students learn. Humans have a huge array of cognitive biases. In general, these various biases work so that we'll keep believing whatever it was we believed to begin with, unless there's a really good reason not to. Someone giving a clear, authoritative physics lecture does not register in your mind as a good reason to check your beliefs, so you listen happily and rave about what a great lecture it was, all while maintaining your wrong ideas.However, with the right stimulus you can get your brain to throw out the old, wrong ideas. Entering such a state is a prerequisite to true learning, and fortunately we can detect it in ourselves. We call it confusion.Confusion is a message from your emotional mind (the part that tells your analytical mind what decisions to start justifying). It's saying, "Hey, something about our beliefs is very wrong, and this is actually important. Pay attention and figure it out."A great lecturer, instead of being clear, will confuse students by asking them to predict ahead of time what a demonstration will show, then do it, and the opposite actually occurs. Or they will ask students to solve questions that sound straightforward, but in fact the students can't figure out. Only after confusion sets in will the teacher reveal the trick.You want to defeat your biases, toss out your wrong beliefs, and learn physics to the Feynman level - the level where you create the knowledge as you go along. Even many specialists never fully get there, instead rising to increasingly-sophisticated levels of rehashing the same memorized arguments in a way that can carry them quite far and trick most people. The only way to avoid this is to spend many, many hours thoroughly confused.Have you ever lost an argument, only to think of the perfect retort two days later when stopped at a traffic light? This shows how your mind will continue working on hard problems in the background. It eventually comes up with a great answer, but only if you first prime it with what to chew on. This works for physics problems just as well as for clever comebacks, once you find good problems to grapple with. I conjecture that engaging this subconscious system requires a strong emotional connection to the problem, such as the frustration or embarrassment of being dumbstruck in an argument or the confusion of being stumped by a hard problem.Confusion is essential, but often also unpleasant. When you repeatedly feel frustrated or upset by your confusion, your mind unconsciously learns to shy away from hard thinking. You develop an ugh field.This could happen for different reasons. A common one arises in people who judge themselves by their intellect. Confusion for such people is a harsh reminder of just how limited they are; it's a challenge to their very identity. Whether for this reason or some other, it's common for students and academics to fall into patterns of procrastination and impostor syndrome when navigating the maze of confusion that come with their chosen path.I don't have the answer for this. I have heard many people tell their stories, but I have yet to figure out my own. Sometimes confusion feels awful, and my story in physics is a jerky, convoluted one because of how I've dealt with that. But once in a while a problem is so good that none of that matters. When I find one of these problems, it hijacks my mind like Cordyceps in a bullet ant, jerking me back to a fresh piece of scratch paper again and again, sometimes for days. If you reach this state over and over, you'll know Feynman meant by, "What I cannot create I do not understand"Get confused. Solve problems. Repeat. The universe is waiting for you.ReferencesIn order of appearance in this answerFeynman's Tips on Physics: Richard P. Feynman, Michael A. Gottlieb, Ralph Leighton: 9780465027972: Amazon.com: Bookssoft question - Memorizing theorems - MathOverflowThe Magical Number Seven, Plus or Minus Two (wikipedia)The Magical Number Seven (original paper)Google Translate (Chinese phrase)Knight, Randall. Five Easy Lessons pp 37Reif and Heller, 1982Viète's formulaHow To Solve It: A New Aspect of Mathematical Method (Amazon)How To Solve It (summary)How to Solve It (Wikipedia)Learn Faster with the Feynman Technique (Scott Young. His page is start to get spammy.)Study Hacks " About (Cal Newport)Anki - powerful, intelligent flashcardsSpaced repetition (review by Gwern)K. Anders Ericsson (Wikipedia)The Role of Deliberate Practice in the Acquisition of Expert PerformanceDual N-Back FAQ (gwern)Food Rules An Eater`s Manual (Amazon, how to eat)Core Performance Essentials (Amazon, exercise) Exercise is an interesting case because not everyone responds very well. For the majority of people it's worth the time.Howard Gardner (wikipedia)The Unschooled Mind: How Children Think And How Schools Should Teach: Howard E. Gardner (Amazon)The Perils and Promises of Praise (article by Dweck)Mindset, Dweck's book.Flow (psychology) (Wikipedia)Flow: The Psychology of Optimal Experience: Mihaly Csikszentmihalyi: 9780061339202: Amazon.com: BooksDavid Allen, Getting Things Done® and GTD®Online to-do list and task management (One possible GTD software)How to Setup Remember The Milk for GTDGeorge Lakoff (professional site)George Lakoff (Wikipedia)Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into Being: George Lakoff, Rafael Nuñez: 9780465037711: Amazon.com: BooksLoaded sentences (Hofstadter reviews Pinker)The Stuff of Thought: Language as a Window into Human Nature: Steven Pinker: 9780143114246: Amazon.com: BooksThe Power of Myth: Joseph Campbell, Bill Moyers: 9780385418867: Amazon.com: BooksAttention control is critical for changing/increasing/altering motivationMathematical Tools for Physics (Nearing)Being a teacher - Less WrongDrawing on the Right Side of the Brain: The Definitive, 4th Edition: Betty Edwards: 9781585429202: Amazon.com: BooksVeritasium (channel)List of cognitive biases (wikipedia)Dunning–Kruger effect (wikipedia)Ugh fields - Less WrongUseful Quora AnswersSomeone anonymous's answer to What is it like to understand advanced mathematics? Does it feel analogous to having mastery of another language like in programming or linguistics?Satvik Beri's answer to How do math geniuses understand extremely hard math concepts so quickly?Qiaochu Yuan's answer to Why is it almost impossible to learn a mathematical concept on Wikipedia? They are very difficult to follow, especially if one doesn't have a solid background in the subject.Christopher VanLang's answer to What should I do if my PhD advisor and lab colleagues think I'm stupid?What did Richard Feynman mean when he said, "What I cannot create, I do not understand"?Debo Olaosebikan's answer to What are some words, phrases, or expressions that physicists frequently use in ordinary conversation?Paul King's answer to How does the arbitrary become meaningful? How does the human mind convert things like art into emotion and experience?What are some English language rules that native speakers don't know, but still follow?User's answer to What's an efficient way to overcome procrastination?Further ReadingI feel a little sleazy writing this answer because when I mention, for example, Carol Dweck doing research on the psychology of mindsets or K. Anders Ericsson studying deliberate practice, in fact there are thousands of people working in those fields. The ones I've mentioned are simply the most public figures or those I've come across by chance. I haven't even read the original research in most of these cases, relying on summaries instead.The answer is also preliminary and incomplete. There's lots of research left to be done, and I'm not an expert in what's out there. Still, here is a guide to some further resources that have informed this answer.For an overview of the psychology of learning, I like Monisha Pasupathi's audio course How We Learn from The Teaching Company. It covers many clever experiments designed to help you build a model of what happens in your mind as you learn.Bret Victor explores software solutions to visualizing the connection between physical world, mathematical representation, and mental models. Check outThe Ladder of AbstractionExplorable ExplanationsI think it's helpful to build an innate impression of your mind as not perceiving the world directly, but as concocting its own, tailored interpretation from sense data. All your consciousness ever gets to experience is the highly-censored version. The books of Oliver Sacks are great for making this clear by illustrating what happens with people for whom some of the processing machinery breaks down.The LessWrong Sequences were, for me, a powerful introduction to the quirks of human thought, preliminary steps towards how to work best with the firmware we've got, and what it means to seek truth.Selected BibliographyThese are some physics books to which have helped me so far. I'm not choosing them for clear exposition or specialty knowledge in a certain subject, but for how I think they helped me understand the way to think about physics generally.Blandford and Thorne, Applications of Classical PhysicsEpstein, Thinking PhysicsFeynman, Lectures on Physics------------ The Character of Physical Law------------ QED: The Strange Theory of Light and Matter------------ Tips on PhysicsGeroch, General Relativity from A to BLevi, The Mathematical MechanicLewin, Walter "Classical Mechanics", "Electricity and Magnetism" (video lectures with demonstrations on MIT OpenCourseWare)Mahajan, Street-Fighting MathematicsMorin, Introduction to Classical MechanicsNearing, Mathematical Tools for PhysicsPurcell, Electricity and Magnetism----------, Back of the Envelope ProblemsSchey, Div, Grad, Curl, and All ThatThomas and Raine, Physics to a DegreeThompson, Thinking Like a PhysicistWeisskopf, "The Search for Simplicity" (articles in Am. J. Physics)ImagesFeynman's Tips on Physics, Feynman, Gottlieb, LeightonArchitectural detail- cut stone wallFile:NotreDameI.jpg

I don't think the U.S. is in decline. I'll show you the answers from a netizen on ChinaZhihu's website.Here is the original answer.If there is any problem in translation, please forgive me.美国是否在衰退？ - 知乎When everyone sings down the United States, I am not the same. If I disagree with inclusion, I just sing down a few different answers, representing only my personal views. This article may be a lot of charts or analysis data and conclusions. If I don't bother to look at it, I will come to the conclusion that I personally feel that the United States has not declined but is still widening the gap with other countries. If you read this answer carefully, you may take a breath of cool air. However, before answering the question, it needs to be explained that the widening gap in the United States mainly erodes the advantages that developed countries such as Britain, France, Germany and Japan once contended with, even monopoly industries, and also relies on the collapse of the Soviet Union. For the time being, there is no contradiction between the development of the United States and that of China.Here I would like to summarize my own thoughts in advance. I have always thought about why the United States is strong: I once thought that the strength of the United States was based on its financial/dollar hegemony, also thought that the strength of the United States was based on its military hegemony, and also thought that the strength of the United States was based on its military hegemony. Based on his superior geographical position and the view of fire across the shore of World War II, but after thinking about it, I found that the United States had become the world's first industrial country around 1900. Without the large-scale construction of higher education talents, the United States would not be able to absorb and transform the achievements of the European Industrial Revolution.In other words, my core argument is that the logical order of thinking between higher education and talent, combined with my previous thinking, has accumulated the following: Does the United States have financial hegemony - > is it that the United States has a large number of talents in finance, economics, international trade and other fields?The United States has military hegemony to escort financial hegemony - > Is it the United States with military strategy, military command, military equipment manufacturing and other fields of talent?Is the US military equipment leading the escort for US military hegemony - > an enterprise with a large number of military science and technology industries?The United States has a large number of military science and technology industry enterprises escorting military equipment - > Is it the United States military industry enterprises to provide a large number of IC, communications, radio frequency, digital images, materials, physics, chemistry, automation, machinery and other fields of advanced education personnel?American military enterprises provide a large number of higher education talents to escort military equipment R&D - > Whether need to meet two points at the same time: sub-node 1: Is the United States adequate financial allocation in the field of defense? Sub-node 2: Are there enough technological enterprises in the United States to accumulate technology in light and heavy industries?Extension of Sub-Node 1: The U.S. defense sector has adequate financial allocation to escort U.S. military enterprises - > There are enough excellent enterprises in the U.S. to provide huge tax revenue for the U.S. government?Extension of sub-node 1: There are enough excellent enterprises in the United States to provide huge tax revenue for the U.S. government to escort the U.S. financial allocation - > Is it that the United States has Pfizer, Intel, AMD, GE, Disney, Google, Microsoft and other top enterprises to achieve huge revenue in the world market?Extension of sub-node 1: There are enough top-level enterprises in the United States with huge revenue to escort U.S. tax revenue - > Is it possible for top-level enterprises in the United States to recruit top-level higher education talents in pharmacy, chemistry, IC semiconductor, materials, stereo imaging, 3D design, system research and development, drive design and other fields?Extension of sub-node 2: Are there enough technological enterprises in the United States to accumulate technology in light, medium and heavy industries - > Are they top enterprises in the United States able to recruit top-level higher education talents in pharmacy, chemistry, IC semiconductor, materials, stereo imaging, 3D design, system research and development, drive design and other fields?At this point, sub-node 1 and sub-node 2 complete the convergence. Let's continue.The United States has many fields of higher education talent for the United States top enterprises to recruit talent Escort - > Is it to meet the following two points at the same time: Branch 1: the United States has a better educational strength and system? Branch 2: The majority of all higher education graduates in the United States, including local graduates, are willing to stay in the United States for development?Branch 1: The United States has a better educational strength and system to escort higher education talents with many fields in the United States - > Is it the United States has higher education (education ontology research) talents with a sound educational system?Branch 2: Most of the graduates of higher education in the United States, including native ones, are willing to stay in the United States and develop into the escort of higher education talents with many fields in the United States - > Is it the social system in which the United States has higher education talents in social sciences, humanities, law and other fields, including equality between the United States and foreign countries, social welfare and racial differences? If the field of vision can not be perfected absolutely, how can we narrow the gap between foreign students and their home countries as far as possible?Sub-node 1 and sub-node 2 completed a convergence at this time, and I will not continue to enumerate later, starting my arguments and arguments.1. The strength of the United States is fundamental. As one of the most important educational talents in the world, the United States may not have one. It has been building higher education crazily since its founding members. Before the founding of the United States of America, there were only nine institutions of higher learning in the United States. On the 100th National Day, the total number of institutions of higher learning in the United States reached more than 700 (an average of 7 in a year). When the 200th anniversary of the founding of the United States was celebrated, the total number of institutions of higher learning exceeded 2800. Today, there are more than 4810 institutions of higher learning in the United States. In 1862, the United States Federal Government passed the Morrill Land Grant Act, which pushed American higher education into a new dimension of educational support. Soon, the United States absorbed, transformed and re-innovated science and technology from Europe by virtue of the talents of higher education, and rapidly developed to the top. It is these higher education talents who have laid the cornerstone of many American enterprises, such as machinery, electricity, medicine, aviation, aerospace, military industry, automobile, medical equipment, integrated circuits and chips. On the macro level, the economic talents of the United States have established the Bretton Woods monetary system, and the military talents of the United States have established a rapid response. Pan-layout of the global military strategic base and so on.At the end of the last century, Harvard, Yale, Stanford in the United States, Dongda in Japan, Oxford and Cambridge in the United Kingdom, Moscow in the Soviet Union, Paris in France, Munich in Germany, Zurich University in Switzerland, etc. were among the top universities in the world. But now? The United States is almost monopolistic in higher education. Take the ranking of higher education scientific research output that does not include other indicators such as international students as an example:The most frightening is also the extremely high retention rate of talents, that is, a large number of talents who go to the United States for higher education remain in the development of American technology enterprises. In 2015, the United States awarded 55,000 doctorates, 75% in science and engineering, of which 14,000 were foreign nationals, and half were Chinese, Indian and Korean nationals. Statistics on the Intention of Foreign Doctors to Stay in the United States - The number of people who want to stay in the United States is more than three times that of people who want to leave the United States. In 2015, the overall proportion of foreign Doctors in the United States exceeded 70%. The proportion of students who continue to study or work in the United States after graduation is as follows:On the other hand, a data is provided. The source of Undergraduates in seven top science and engineering universities in China (Qingbei + East China Five) is also the reference for the selection of the best group of students in China's higher education.Tsinghua University：Peking University:Zhejiang university:A total of 1 416 undergraduate graduates in 2016 went abroad to study, accounting for 25.21% of the total number of graduates.Shanghai Jiaotong University:Nanjing University :I won't list the remaining two schools. It's a bit painful to translate pictures into words.Reading the first point above,Many of China's top talents have been attracted. What about your country?, you may already have a preliminary understanding of talent cultivation and attraction in the United States. The following is part of the acceleration of industry in the United States due to better higher education talent.2. Pharmaceutical, Medical and Medical IndustriesFirst of all, the top-notch pharmaceutical industry. Among the 24 top pharmaceutical companies in the world, the United States is far ahead with 12. There are 16 top 50 pharmaceutical companies selected by the United States, which can be said to be basically at the top. American pharmaceutical companies are well-known for their high investment in R&D, with an average R&D/income of about 15-25%, compared with Chinese pharmaceutical companies, which generally do not exceed 3% and modern pharmaceuticals do not exceed 10%. In the last century, the Anglo-French Druid Troika could compete with the United States in medicine, especially GlaxoSmithKline, which was once the world's strongest pharmaceutical company. But now:Then the medical equipment industry, the United States in the world's top 10 manufacturers of medical equipment, 7, GE, Medtronic, Johnson & Johnson and other enterprises are very strong, such as Johnson & Johnson disposable ultrasound knife in many developing countries hospitals will be used 5-10 times.Medical industry, needless to say, almost all of the top students in the United States have chosen to study medicine, ranking the world's top medical institutions.At the same time, the United States, with the FDA as its core, has achieved both large-scale double-blind clinical testing and some speed-up for high-quality and cutting-edge drugs. The global proportion of innovative drugs on the market is as follows, which is only 35% in the last century in the United States, of course, the first one at that time. The fundamental reason for this change is that the speed and ability of R&D of U.S. drug companies have widened the gap with other countries. Some people in the industry once joked that the next generation of targeted drugs in the United States has not yet been resistant to drugs. Come out. Here's the world share of innovative drugs in the United StatesOnly six years after the advent of the first generation of ALK drugs, Pfizer has successfully developed the third generation of ALK.By the way, I won't mention the latter. Many countries in Europe, Japan and other countries have realized that the gap between their talents and the United States is widening. Because Europe, Japan and the United States are still in the same camp for the time being, they are also desperately trying to enjoy the dividend of the elite talents in the United States. There are too many reasons. There is a region in the United States called Cambridge, not the British one. The United States has the richest medical resources, because there are Harvard University and Massachusetts Institute of Technology, there are Massachusetts General Hospital and Harvard Medical College under the three general hospitals and other top hospitals. In other words, there are the top medical talents here, especially the newly graduated students who have the lowest cost to recruit. As a result, Switzerland's Roche Heavy Gold ($46.8 billion) acquisition of the former American cancer giant Genentech Company, with its cancer research, has tasted tremendous sweetness. It rushed to Top3, the world pharmaceutical company, and continued to set up a pharmaceutical R&D center in Marlborough, Boston, to recruit students. Novartis Switzerland, GSK UK and other companies have also established R&D centers in Waltham, Boston. Safino, France, succeeded in becoming the top 10 in the world by acquiring the former American medical giant Jianzan, and continues to expand its R&D centers here just like Roche. Japan's second tier pharmaceutical companies, such as Takeda, have also taken root here to ensure that they can use American talent to keep up with the first tier of the United States.3. Semiconductor IndustryThe United States has six top 10 companies in the world. In 2017, American semiconductor companies accounted for 46% of global sales. In 2018, U.S. wafer-free chip companies accounted for 68% of the global market share.Without comparison, there is no conclusion about the trend. Here are the changes of semiconductor enterprises in recent decades.4. IT IndustryOperating system aspectDesktop PC Operating System: The only competitor of WIN7 (65%) is WIN10 (17%), the rest are WINXP (12%) and MAC (6%). All of the above are products of American companies.Mobile Operating System: Android and iOS accounted for 98.2%, Windows Phone was the third most expensive but only 0.73%. All of the above are products of American companies. Software servicesA lot of people may not contact, feel that the software does not matter ah, not the system and APP, China also has IQY APP and Fighting Fish ah. How to say, this software is not the other software. A large number of software are used in computing, modeling, industrial design, signal processing, etc. It plays an extremely important role in scientific research and engineering. Take engineering design as an example, everyone knows what civil engineering is, but design can not be separated from ANSYS (USA, FEA) software, ABAQUS (USA, non-linear finite element analysis software), which are the most famous industrial design software. ANSYS software pays attention to the expansion of application fields, covering fluid and electromagnetic fields. There are a wide range of research fields such as multi-physical field coupling. ABAQUS focuses on structural mechanics and related fields. In addition to the non-linear solution software, there are Marc (USA, MSC) and so on.In addition to the above, you may have heard of CAD, MATLAB, Photoshop, PR and other software, all of which are products of American companies. China's chip design includes several large chip factories, which are inseparable from American Cadence and Synopsys. These two relationships are somewhat similar to Intel and AMD. Domestic chip companies buy Cadence and Synopsys. Usage rights are purchased for the longest period of time, that is, fear of being sanctioned by the United States or how.Now you probably understand that software refers to those critical software services that are used in a lot of scientific research and engineering, without which a lot of work can not be carried out.5. Aerospace IndustryAerospace has always been the integration of a country's most sophisticated technology, many years ago, American space is not lonely, Maozi and ESA play with the United States. Now the United States is so bored that it can only play with itself.NASA is undoubtedly the strongest Space Research Institute in the United States. What about engineering?ULA, a joint venture company of Boeing, USA, mainly produces Delta IV rocket, Delta IV heavy rocket and Cosmos 5 rocket. ULA has the strongest hydrogen-oxygen rocket engine RS series (invisible afterwards). The overall success rate of ULA is more than 95%, and that of Delta IV rocket is 100%. Now ULA in the United States is fully developing the next generation of Fire Rocket.Below is the Delta 4 Heavy RocketSpaceX, one of the many companies in the United States, is a technology madman named Musk (the owner of Tesla, if you don't know him). Having Falcon 9 and Falcon Heavy Rocket, Falcon Heavy Rocket is the most powerful heavy rocket in the world, but also the cheapest heavy rocket. SpaceX is the only company in the world with large rocket recovery technology.Here's the Heavy FalconULA has the world's best hydrogen and oxygen engine RS series, SpaceX has the world's best methane engine Raptor series, is the world's only full flow staged combustion cycle liquid oxygen engine, SpaceX also has the world's most reliable and inexpensive liquid oxygen kerosene engine Merlin series, SpaceX has been completed in more than two years. It has become a remarkable success in 49 successive launches.The Raptor engine is as followsU.S. Boeing, ULA is a joint venture between Loma and Boeing, and Boeing itself has an aerospace subsidiary. The company is working hard to develop a super rocket, SLS, that surpasses Saturn V. Once the rocket is flying, it will be a milestone for the United States to surpass itself. Here are the SLS under constructionBut it is interesting to note that competition within the United States has become intense. SpaceX is developing a BFR rocket, whose performance parameters surpass SLS in an all-round way. If SLS is 30 years ahead of other countries, the gap between success of BFR is amazing. The thrust of SLS is 4000 tons, but the BFR design target is 8000 tons. BFR:Apart from ULA, Boeing and SpaceX, the blue origin of the United States also has space ambitions.Blue origin in the United States, the current progress of blue origin is slower than the above three, but there are also excellent progress. The new Glen rocket engine BE-4, designed by Blue Origin, has completed full-power test run.Engines are the most difficult part of a large rocket to conquer. Maybe the first flight of the New Glenn rocket will take place in the next two years.In addition, the United States has American Orbital Science Corporation (40% of the interceptor missile market, 55% of the small communications satellite market and 60% of the small launch vehicle market), Sierra Nevada Mountain Company (small space shuttle), Bigelow Space Company (the main product space station, the largest six times the international space station), XCOR Astronautics Corporation. Division (Suborbital Spacecraft), Virgin Galaxy, Rocketlab and so on.知乎视频6. Aviation IndustryTen of the world's top civil aircraft companies, the United States occupies five. Boeing, as the world's number one airline, occupies more than 50% of the market share, followed by 30% of French Airbus, in addition to the United States there are Gulf Stream, Senas and other small and medium-sized aircraft well-known companies.The United States is the second largest aeronautical giant, and General Motors is in the absolute dominant position in the market. GE9X engine, the landmark product, is the top aeronautical engine at present. General Motors has 40% market share, followed by Ronald Ronald, the United Kingdom, with 22% market share. Pratt & Whitney has a 9% market share, and its F135 engine developed for the F35 in 2005 is probably the strongest engine in fighter aircraft.At the same time, with its terrible industrial manufacturing capability, F135 engines can produce 130 units a year. F135 engines:In the early years, V2500/RB211/D-30KP-2 and other engines in other countries were not significantly weaker than those in the United States at the same time, but now this has fallen into a situation where the gap is widening.Boeing Aircraft with GE9X:F35 vertical takeoff and landing:7. Biological IndustryThe United States continues the momentum of widening disparities in other areas.In the United States, Amgen Enjin, Gilead Sciences Geely, Biogen Idec Biogene, Celgene Sell Gene, Allergan and Regeneron rank in the world TOP10.In addition to bio-research companies, the United States has further expanded its monopoly position in bio-related agents, materials, instruments and other related enterprises, such as Invitrogen, Amresco, Gibco, MP, BD, Pierce, Sigma and so on. Biological equipment: Kodak, Thermo Fisher, Gilson, Bio-rad and so on. Thermo, in particular, has great advantages in centrifuges, quantitative analysis sensors and other fields.Thermo centrifuge:8. Economic aspectsThe United States is the only country with a population of over 100 million in the top 23 GDP per capita, 24th EditionIn finance textbooks, it has been mentioned that the stock market can be used as a barometer of a country's economic strength.9. Military aspectsLet's not go into details in this regard. Two examples are given: years ago, the small partners of F16/F15 included JAS-39, Gripen NG, Rafale, Typhoon, Mirage 2000, MiG-35, Su 30SM, Su 33, Su 34, Su 35, Fighter-10B, Fighter-11B and so on. Now F22 (1997)/F35 (2006) has been produced on a large scale (F22 184 + 8 test machines / F35 totals 380 in the world) for more than 20 years and more than 10 years, which can not be compared with F22 (1997)/F35 in terms of technology and scale.F22：The aircraft carrier Kitty Hawk, serving in 1961：The Kitty Hawk is accompanied by the Kuznetsov at the same level, but over the past 60 years, the United States has developed the first generation of enterprise-class aircraft carriers (94,000 tons full nuclear power in 1961), the second generation of Nimitz-class aircraft carriers (104,200 tons full nuclear power in 1975), and the third generation of Ford-class aircraft carriers (1120 in 2017). There is also no follower, and no other country has the industrial capability to manufacture the 1961 US corporate aircraft carrier.Ford Class Aircraft Carrier Construction in 2017：An aircraft carrier battle group consists of one aircraft carrier, two to three air defense cruisers or destroyers, two to three anti-submarine drive frigates, one to two attack nuclear submarines, and one to two logistical support ships, totaling 7 to 11 ships. There are 11 such aircraft carrier formations in the United States. The military side does not need to elaborate on this area which may be the greatest advantage of the United States. Some countries in the military field have reached the world-class level in some areas, but overall, the gap between China and the United States has narrowed in a small range, such as China's 055 missile destroyer/cruiser, Russia's S series air defense missiles, nuclear submarines, etc. The macro-wide gap is widening.10. Energy industryThe United States accounts for 90% of the world's shale oil production. Thanks to the technology of energy development, the dependence of the United States on overseas crude oil has declined dramatically. In contrast, developed countries and many developing countries are increasingly dependent on overseas crude oil.U.S. Energy External Dependence Curve：The United States has the largest number of nuclear power plants.11. Interesting aspects to noteWhen science and technology develop to a certain extent, it is possible to promote the emergence of new industries. Because manufacturing, integrated circuits, materials, solar energy and so on have been greatly improved. Many technology companies in the United States are beginning to create new industries. For example, when the once-popular VR is temporarily in silence and money in many countries, the U.S. Army intends to cooperate with technology companies to build a simulated battlefield. In the United States, the popularization of VR game equipment in Internet cafes and game halls is widespread. American companies even launch many small VRs. Movies... Of course, following the style of this reply, let's not talk about these "low-end".For a long time, developed countries have been living in a sparsely populated mode. It is very difficult for developed countries to enter their homes with optical fibers. Therefore, the network has become a problem for non-urban residents in developed countries. Later, many American companies have studied satellite interaction on the basis of substantial improvements in manufacturing, integrated circuits, materials and solar energy in recent years. Networking, if it can be achieved through technology, will not only be the domestic satellite user market of the United States, but also include 4.1 billion global air passengers and employees, 300 million seafarers and employees, about 5% - 10% (150 million - 300 million) of the 3 billion people in remote areas, the quality network demanders of the affluent classes, and 300 million times. About outdoor travel explorers and so on, how large can this market industry scale? Conservative estimates are more than $10 billion.The main companies developing this technology tree in the United States are OneWeb, SpaceX, Amazon and so on. They basically use Ka Ku band. OneWeb took the lead in launching several satellites for networking testing early this year, and SpaceX launched 60 technology verification satellites, and Amazon submitted its application to the FCC in time.OneWeb received financial and technical support from Airbus, Qualcomm, Coca-Cola, Soft Court of Japan, Ministry of Defense and other companies. In mid-year, OneWeb succeeded in Satellite Internet in Korea, with a delay of about 30-40MS and 400 Mbps per capita to watch 4K network videos of oil pipelines. This delay and speed is their goal. There are more than enough users.After the successful completion of the perfect test, OneWeb and ESA quickly reached 27 orders for mass launches in an attempt to seize the market. The cheapest large rocket launcher described here is SpaceX, but the two companies are direct competitors on the satellite Internet, so they choose to cooperate with ESA commercial launchers. OneWeb's Florida plant can produce two Internet communications satellites a day.At the same time, SpaceX is unwilling to show its weakness and wants to play a large, direct laser communication between satellites on the basis of OneWeb technology. SpaceX's first 60 verification satellites were launched into orbit in the first half of 2019.According to the news, the production capacity of SpaceX's satellite production line can reach 8 per day. SpaceX has scheduled to launch at least 120 more satellites into orbit twice in the second half of the year. This competition of Satellite Internet lets us wait and see. Of course, there are many technology companies in the United States, especially start-ups. Their daily task is to integrate the current rapid development of basic disciplines and technological innovation, and combine these scientific and technological theories and engineering capabilities to create a new product in a small way and create a new one in a big way. New industries, many familiar NBA stars invest in such enterprises. Summary of the dividing line ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Physics knows that there is a term called acceleration. The greatest premise of the decline of the United States is that the acceleration of acceleration has disappeared. If the United States has acceleration all the time, even if the acceleration of the United States is decreasing, the speed of development is still increasing from the physical point of view. The acceleration of 10 and 1 is accelerating. As long as there is acceleration, the United States will have a steady stream of nutrients from home and abroad to grow into the next Boeing, Pfizer, SpaceX and other enterprises. SpaceX successfully launched the heavy Falcon in a week, received 10W resumes at home and abroad, a large number of graduates such as Stanford, MIT, this is a good thing. A model of mutual promotion. In the US recession, let's wait until the acceleration of the US is negative before we discuss it.It's all tool translation. I just want you to have a look at different opinions.

I originally answered this about 18 months from the time I am writing this now. I am not very happy with my original edit, and I’d like a redo, with my original answer in italics at the end. It wasn’t so much wrong as it contained a lot of major and minor mistakes in the meandering I did around the question.If a space shuttle had used liquid-fuel boosters instead of solid-fuel boosters, would there have been four boosters like what Buran/Energia used?Nice simple answer I should have made: No. mission requirements and material/budgetary limitations make those decisions, neither four nor two is the “perfect” number. While there is something to be said for only having two boosters (or even only one), because the less crap flying around the upper stage at supersonic velocities the better, the Thor-Delta used any number of boosters from zero to nine, and was one of the more reliable launch systems.That neatly sidesteps all the philosophy of design/interpretation of history that thought I was well enough informed about to just run my mouth on without fact checking very hard. (I wasn’t.) But if 10k people were nice enough to read all my half sourced meandering, it seems unfair to just delete it all. So for your personal enjoyment, here’s my much streamlined new take on my original answer. But first, some confessions.(1.) I believe that permanent, sustainable, autonomous, human habitation off earth is important in intangible ways. I am aware of the tangible ways that it matters, but that’s something I know. The intangible is something I believe in.(2.) I have serious (and I think fair) concerns about capitalism’s ability to do large scale, low to zero pay off, long term planning, which is exactly what permanent human habitation requires.(3.) Within that concern, I have a particular distrust of defense contractors, who are the main producers of U.S. space hardware.(4.) Within that concern, I have no positive feelings about the U.S. government’s (rather than just a generic liberal democracy’s) method of government contracting.(5.) I just don’t like the Space Shuttle. Period. Because of how strongly I believe in sustainable, autonomous, human habitation off earth as an end unto itself, I am annoyed by any project which spends limited manned space exploration money forwarding other projects.To me, an self educated “historian” with no formal training in analyzing aerospace or politics, it looks like the Shuttle was much more about federal pork belly and a dick measuring contest with the Russians than actually developing a real human presence in space.I know that the rocket scientists and project managers who produced the Space Shuttle were much better educated people than I. Perhaps their decisions only look stupid to be because I’m ignorant, but that said the decisions look stupid. I feel like the meetings must have been very long on marketing types and PhDs and have not a single person who’s ever worked on a car, or worked the opening day of a new restaurant.“We’ll save on the cost of operating our existing built-from-scratch really expensive launch system by just shit canning the whole lot of it and starting over with a new built-from-scratch, really expensive launch system.”Huh?“Carrying a marketable payload is really hard when you dump 96% of the launch mass. Let’s carry more weight and make less of it payload!”What?“Getting a launch system to orbit safely and reliably a single time is difficult. It will make everything so much easier, if all the parts are heavier and the vehicle has to take the launch stress over and over again!”Huh?“The most expensive addition to our space craft is labor. Let’s make sure we put a lot more of that into every launch!”Are you insane?“Even though our existing heat shield system is removable, and we could always put new shields on used capsules, instead of gaining reusable experience that way, lets make a whole new vehicle with a new concept!”But why?“Oh, and that one kind of booster that you can’t turn off once it starts? Let’s use those!”Huh?“And lets give it AMAZING cross landing ability, but require a landing roll so long only like 3 air ports on the planet can let it land there.”The list goes on and on. To practical person, the Shuttle looks like Ferrari: it’s gorgeous, it’s expensive, and no one else has one, but for the business of getting a load of stuff from point A to point B it just seems like a terrible design.Here’s my more fun, but less honest and less informed original answer:Soviet engineers were convinced that the Shuttle made no possible sense.Solid fuel for a manned mission (and segmented at that)? High thrust, low isp is where heavy liquid fuel boosters really excel, and the U.S. had the fantastic first stage engine, the F-1. Why use solid fuels?A winged orbiter…when lifting bodies did everything better except hypersonic glide? Why make such a fragile airframe for such a minute increase in de-orbit to touchdown distance?Half cargo equipment and half habitat equipment? The two have totally different launch requirements, why hamstring both kinds of missions?Why put the heaviest part of the rocket (the engine) on the back of the orbiter where it does no good 99% of the time? Why not put it on the base of the 2nd stage tankage?They decided that the Shuttle must be a ruse for some sort of military mission. Note that all of those criticism are valid, and related directly to why the Shuttle was so incredibly expensive. Note also that many Shuttle missions remain classified. And finally note that when the Shuttle was grounded, the DoD built it’s own Shuttle, the X-37, because they still needed a Shuttle-like vehicle. So perhaps the famously paranoid Soviets were on to something after all.The Soviet leaders decided they needed a Shuttle to maintain military parity. So the designer, Valentin Glushko was sort of stuck with mission requirements whether they made any sense or not. He choose the liquid fuel boosters around a stout upper stage for a few reasons.(1.) There was the Proton.See the cluster of tanks around a thicker central tank? In the Proton’s case, the whole bottom section under the “cage” (stage separator) is actually one stage: the thicker tank is a shared oxidizer tank and the size smaller tanks on the side are fuel tanks. There’s a single engine under each fuel tank, and the base of the oxidizer tank is flat, with no engine.This is the UR-700, Chelomey’s much larger follow on proposal:The Proton (also called the UR-500) was designed by Vladimir Chelomey, not Glusko. But Glushko had spent many years advocating for the UR-700 rocket, and was very familiar with its benefits. You can see a lot of similarities between both the Energia and the Proton in that model.(2.) He had the gorgeous (if you are into rocket engines) RD-170. The only engine on earth that puts out more power than the F-1.The mission required four RD-170s and being his experience with the UR-700, to him this meant 4 tanks around around the larger center one, even though they were fully complete boosters, instead of fuel tanks around an oxidizer core. Like the American shuttle, he used H2/Lox engine that fired from the start of the big boosters, but mounted it on the large fuel tank instead of the orbiter. The engine, the RD-0120 was similar to the Shuttle engine…but much cheaper and disposable. It also allowed the Energia to lift more, since the weight of the engine didn’t have to be orbited.Why bolt the the booster together into a “double barrel”? My guess would be weight and conservatism. Weight because, if something is supposed to attach and de-attach, it’s generally lighter to make a small number of beefy attachment points rather than a large number of lighter ones, and conservatism because, in general, it can’t break it it isn’t there. The less parts flying off at Mach 5 the better.The Soviets also a designed a 2 tank version, the Energia-MThe point is, the mission requirements and available facilities are what make these decisions, not the number of boosters.