So You Want to Learn Physics (2016) | Hacker News Reader

So You Want to Learn Physics (2016)

susanjfowler.com

229 pointshappy-go-lucky122 comments

Well I disagree with many of the book choices, but if there's one thing that's absolutely spot-on is this:

>One big problem is that a lot of the popular books written about physics (especially those by famous physicists) are incredibly speculative and tend to present an unrealistic view of what the study of physics is all about. When you're learning physics, it's good to avoid these types of speculative books, and stick to the good ones that talk about the real physics we know exists.

Oh god yes. Why is it that whenever a lay person wants to talk about physics they talk about "11 dimensions", "string theory", or "time dilation", or any similarly crazy-sounding term that they read in a massively incorrect pop-sci article. Basically it makes it sound like physics is about all this crazy complicated and far-fetched ideas, rather than simple and beautiful principles to understand reality, which is what it is.

I don't know if I managed to convey what I mean.

> "11 dimensions", "string theory", or "time dilation"

One of these things is not like the others...

To the average pop reader's digest human experience, they are pretty close. Sure, it's interesting to know that GPS is affected by time dilation, but the hours spent on thought experiments on intergalactic travel are a distraction from all the things one can learn about their everyday life.

> all the things one can learn about their everyday life

I'm curious what topics you have in mind? My everyday life is like 90% Newtonian mechanics, 9% thermodynamics, and 1% fluid mechanics (percentages completely made up). Or are you thinking like E&M for phones and stuff?

Yeah, the frequency shift "time dialation" of Radar & Lidar for traffic tickets and even Time-of-Flight imaging for your FaceID all involve the constant speed of light or special relativity... but yes, all of magnetism can be derived as a special relativistic case of electro-statics (relativistically moving charges).

For me, the more annoying aspect to this is that the "it's all relative man" has infected even more techincal discussions to the point where engineering and settled science is treated as just more "woo woo" by people who could know better.

The derivative of time in the spacetime* tensor is just 1. There's no speed up, locally, which is what counts. The rest is just an effect of observation.

*I do not remember nor care what it's called. I'm sure you know what I mean anyway.

Why is it that whenever a lay person wants to talk about physics they talk about

Because those things sound exotic and interesting. Just like (statistically) nobody goes to the natural history museum to look at chicken-sized dinosaurs.

Hm. Perhaps you're on to something: our museums tend to present things in their true scale. However, this is not always desirable. For instance, consider the use of macro photography for inspection of the brilliant detailing of small things.

Physically scaling up small things may indeed be problematic, but with the assistance of VR or AR, one might be able to digitally scale it up. [Here I'm remembering my love of The Magic Schoolbus series.]

Another is that it dodges the reality check of math. I recall reading a bit of advice to authors of popular science articles: each equation in the text cuts your audience in half.

Although I can see the utility in setting the right expectations for people beginning their study in physics, surely it does more good than harm to get more people interested in the field itself via exposure to the most eye-catching ideas in physics, even if speculative?

It's kind of the same way that more people would be interested in computer science because of strong AI rather than binary search trees.

I have a model with two kinds of knowledge: sexy knowledge and homely knowledge. I think the internet and mass media era in general have massively endorsed and empowered the projects and acquisition of sexy knowledge. If it doesn't garner attention rapidly on a large scale, then it doesn't go on TV. The problem is that most of the real projects of science and industry are about homely knowledge. It's the little boring things like washing your hands that prevent catastrophic hospital deaths. But that's not superficially interesting, or fun, and it doesn't provide the knowledge bearer with any kind of moral or intellectual superiority by which they can affect pretensions of enlightenment. Quackery has always been a thing, but I think sexy knowledge lies somewhere before the frontier of quackery. It's true, or plausibly true, information, but it is dramatically overvalued in our time and culture.

I would argue that most scientists in general pursue their field of study in the pursuit of sexy knowledge itself. If there's no wonder to motivate, what are people working towards?

I also would like to argue that it doesn't have to "garner attention rapidly on a large scale" to be recognized by the masses, but rather just spark their imaginations in general.

Mass and speed are proportional (are they? For sake of tve argument, mass begets gravity begets accelleration). But the masses don't want massive bulks of data. They want quick information. Like, your new phone can show 4k vids whatever, and some even care that that's due to advances in nano materials and quantum optics, but to most, the physical side is uninteresting and something inherently theoretical like black holes, LIGO or LHC is only really mass compatible if broken down to show the kind of action, i.e. research, that is happens on this very planet - time travel, ripples in the fabric of space, or theosophy (god particle), respectively.

The whole quantum mechanics philosophy crossover is a huge messy confusion as a result of this (many worlds shroedingers cat) - and that even affects even many physicists.

> I would argue that most scientists in general pursue their field of study in the pursuit of sexy knowledge itself. If there's no wonder to motivate, what are people working towards?

I disagree. My opinion on whether you might get the impression is that you need to argue with "sexy knowledge" in research proposals.

For the record I'm not saying that sexy knowledge is bad. I'm saying that it has the potential to devalue homely knowledge and crowd it out of mindshare. That isn't to say that fascinating and flashy theories aren't valuable, just that they may have an adverse effect because we overvalue it.

I think this is still fair.

I mean when you study Physics you learn to use apparently confusing tools - theoretical or experimental - with confidence. Sometimes in areas that only few people find interesting/appealing, like for instance complex problems in classical mechanics or thermodynamics. Only 1% of the studies is about crazy, absolutely counter-intuitive stuff that sounds like Sci-Fi. But isn't that what differentiates the amateur from the Pro? ;)

I mean if people want to do actual Research Physics, they must either go to a University (offline or online) or be mega disciplined. In the latter case they need a few more books though/adjust them also to personal taste.

> all this crazy complicated and far-fetched ideas, rather than simple and beautiful principles to understand reality

Would you mind giving some examples of what kind of "simple and beautiful principles" you have in mind?

Depends on the level (and I am just giving some examples):

- Advanced high school: You can use conservation of energy or other "conservation laws" as a guiding principle. This lets you solve a problem with just a couple of lines of simple algebra. On the other hand, using the "naive" approach of studying the forces that act on the system would require heavy algebra and some calculus.

- College: Instead of calculating the path of a ray of light through some inhomogeneous piece of transparent matter by doing some form of raytracing, you can use Fermat's "minimization principle". They are equivalent, but a rigorous definition of the minimization principle is a single sentence, while the other approach takes a lot of work to express clearly.

- Advanced college: Conservation laws are actually consequences of symmetries. Instead of thinking in terms of a complicated expression for energies and momenta, you can say that they are consequences of the fact that the laws of the universe do not change from today to tomorrow.

Yes, the more simple and beautiful a principle is, the more abstract it is. However, the simplicity and ease of working with it makes the abstraction worth it.

Just like in C you can have your own weird struct that implements objects and higher order functions, but using a functional or object oriented language makes everything safer and easier and more readable.

> Conservation laws are actually consequences of symmetries.

For those unfamiliar, this is essentially the content of Noether's Theorem[0]. One of many beautiful contributions of Emmy Noether.

I've heard several physicists describe it as one of the most beautiful theorems in physics.

[0] https://en.wikipedia.org/wiki/Noether%27s_theorem

Conservation of energy and conservation of vector momentum directly explain the phenomenon of coastal rip currents, a mortal danger to beach-goers. Whereas if you go by the usual public sources, they're as mysterious as sun spots.

Pretty much anything in thermodynamics. Phase changes, energy, entropy, symmetry, action principles, degrees of freedom, fluctuation-dissipation theorem, equipartition theorem, etc..

Because the psychological appeal of physics for a wider audience is the same as the appeal for sci-fi: the feeling/emotion of wonder.

So you can get still get the wonder by dropping the rigor, and you end up with What the bleep or The secret

What books would you choose?

I'd go the other direction. I think if you taught every single 16 year old a basic class in surface-level understanding of time dilation/length contraction, gravity as a facet of spacetime, the two slit experiment, the twin paradox, relativistic star ships, so forth and so on - you'd see the number of astronomers/physicists skyrocket. They likely would not be able to follow the math and reasons behind, but that's not necessarily the point. Just understanding how absurd our universe really is, is something that I think is really kind of encouraging. It gives perspective as to the wonder and discoveries that await outside of the everyday bickering that people are exposed to 24/7 since the internet became ubiquitous.

Even less exciting things like seeing how the doppler effect led almost directly to the concept of the big bang is something that seems critical. That it's not (or, hopefully was not) a normal part of curricula seems odd. Even things like the mind boggling implications of the various conservation laws are just incredible. That topic is at least covered in lower education, but rarely if ever in such a way as to really elucidate how incredible these rules are, and all that can be derived from them.

I think you’d find that half or more would be completely unable to grasp the Twin Paradox, or double-slit even in principle, without the math. Probably the number would be closer to three-quarters, or even more if you factor in just how disinterested many would be. I like the idea of a world in which all 16 year olds are both capable of understanding your syllabus, and exposed to it, but I have doubts that we live in that world.

I do think that everyone should have access to such a syllabus though. More realistic if less transformative might be a program of teaching people very basic critical thinking skills. Use advertisements and Instagram posts to analyze deceptive languages and images. Show people that the world they think they live in, that’s projected all of their screens isn’t a very accurate representation of reality. Drive map-territory relations into them via the medium of political, corporate, and interpersonal deception they experience multiple times every day. Maybe half of them would get that, if it was made interesting enough to hold their attention.

The holographic universe is another popular one. We have some similar things in mathematics (e.g. anything to do with Godel).

I think, though, that if you want to understand physics, it probably makes sense to devote some of your time to understanding what physicists are excited about.

I have a feeling (and this is heavy speculation) that a lot of strong physicists were fed on pop physics and science fiction before they learned the hard science. This helps approach the subject with an inborn curiosity, which can focus your attention when learning technical subjects.

Pop physics books may not be the ideal way to do this, but it's probably better than nothing at all.

> Pop physics books may not be the ideal way to do this, but it's probably better than nothing at all.

On the other hand, they are very harmful to serious, but "boring" research proposals.

> talk about the real physics we know exists

I have some bad news for Susan.

> Well I disagree with many of the book choices

what would u recommend in its place?

Non native speaker here. Can anybody explain what "books are speculative' means ?

I went to university intending to study computing science, but switched to physics half way through under the assumption that you could teach yourself computing science more easily than physics. I wouldn't change what I learned for the world, and I'm now in physics academia, but it's funny how my job these days involves using some of the algorithms, mathematics and data structures that I was just about to start learning if I had stayed the course in computing.

My few years of study and general interest in computing has already given me a huge advantage in solving certain types of problem. I think computing science (not just software engineering) is slowly but surely becoming an essential part of many areas of modern physics research.

I agree. It seems to me that in those huge physics projects like CERN what most physicists do is programming or data analysis.

> computing science ... is slowly but surely becoming an essential part of many areas of modern physics research.

Also, this means that fundamental assumptions and the calculations are hidden from view. Recently, some physicists questioned the findings of LIGO but if I understand correctly all is decided by data analysis software and outside teams have a disadvantage to decipher it.

The LIGO result is actually excitingly available as an IPython notebook, which provides a tutorial to verify the data yourself, using entirely open source software. https://www.gw-openscience.org/s/events/GW150914/GW150914_tu... The actual signal processing isn't that complex IMO.

I don't know how open the LIGO hardware is, but it's very unlikely you would build one yourself to verify.

This is very true - I was a physics undergrad and learned to code working in a project at cern. While the underlying physics was the foundation of the project, the day to day work was all coding: processing and analyzing the huge amounts of data coming out of the experiment.

> a physics undergrad

Now imagine dozens of people with a PhD in physics doing the same. (Earning a degree in physics is hard.)

yes, that was one of the insights of the work. The people working alongside me were post-docs that were still having to put in their time as workers on other people's research projects. Particularly, in the area of experimental high-energy physics, where accelerators were needed to do the work, everyone had to jockey to get time on the accelerator (even nobel laureates like the leader of the project I worked on). It seemed like every experiment was a compromise of different people's goals in order to combine together to get enough collective clout to get access to the accelerator to even do the project. That meant the guys who had already completed PhDs at prestigious schools were still pretty low on the hierarchy (but ten years older than me). The time spent working with those guys definitely influenced my decision not to continue with a PhD...

Not just research, but applied physics too - at least, that was my experience working in the defence and energy sectors. Looking back, it’s remarkable how little of my physics studies were devoted to learning about the computational techniques I spend the majority of my time working with.

> I think computing science (not just software engineering) is slowly but surely becoming an essential part of many areas of modern physics research.

I like to say that physics, mathematics, and computer science are the three pillars of human knowledge. There's some overlap between each pillar, and we don't yet fully understand how each of them fully relate to the others, but each is essential to gathering a full picture of any phenomenon.

I think there must be more pillars than that. Biology and chemistry while related to physics are distinct (in the same way physics is not maths). More broadly, humanities and the arts are still valid areas of knowledge. Hacker news has a bias towards your three pillars, but I think it is important to acknowledge that human knowledge does go beyond CS, maths and physics.

I disagree re: biology and chemistry. Certainly they are epistemically useful simplifications of the other pillars, but they are not foundational or fundamental.

Physics is not math because it's an empirical rather than a priori exploration. We are trying to reproduce the function governing natural laws, where in mathematics we are exploring the properties of functions. Computer science in turn is concerned with the construction of mathematical structures via algorithms, and so physics will be one such construction.

I think trying to place humanities and the arts under "knowledge" is a category error. These fields don't produce knowledge as its commonly understood, as a corpus of mind-independent facts and their relationships. Certainly facts appear in these fields, such as historical facts and authorship, but I don't think building a corpus of facts is not the main purpose.

> simplifications of the other pillars

This fallacy is called "reductionism."

It's not universally accepted that it is fallacy. And for whatever it misses, reductionism is a hell of a tool that has been incredibly useful in understanding the world.

Of course, so are chemistry and biology, so blithely dismissed in the parent comment.

> Of course, so are chemistry and biology, so blithely dismissed in the parent comment.

I didn't dismiss them at all, I explicitly said they are epistemically useful, but that doesn't entail we should accept them into our core ontology.

It's a philosophy not a fallacy: https://plato.stanford.edu/entries/scientific-reduction/

Wrong. Philosophy and Mathematics are the real pillars of knowledge. Everything else can be derived from this including physics.

would you care to elaborate?

Philosophy doesn't really produce knowledge, it explores and frames questions. When we accept that the questions define a coherent domain of discourse, we create a field of study that does produce knowledge. This is how natural philosophy became science, and if ethics ever gets to this point, we'll get a moral science which will produce moral knowledge. Ethics doesn't currently produce moral knowledge.

And that's the problem with living in a philistinic society. When people think the sciences are the only noteworthy achievements of human intellect.

Wait a bit, in a few years physical and computing models will merge. #my2ctsbet

>Regardless of your learning style, you'll still need to solve the physics problems in each textbook. Solving problems is the only way to really understand how the laws of physics work. There's no way around it. Even though it can feel tedious at times, there's nothing more rewarding than figuring out a really difficult physics problem and realizing that you figured it all out yourself!

This is the only way. It's I how I moved from an EE undergrad to a theoretical physics PhD. As I come back to material it's a lesson I need to painfully relearn. (Something I re-re-re-learned in 2015 http://nbodyphysics.com/blog/2015/02/28/learn-physics-with-t...)

Calculus, too. I wonder about the author’s implication that she actually worked every problem in all of those textbooks. I suppose it’s possible, but it would take a decade, at least, if you were working full time (and forget having any kind of a social life or, god forbid, a couple of kids).

This is irritatingly common in economics also though with economics it's less often speculation and more often simplification to the point that it becomes misleading.

e.g. "black holes suck in matter around them". Many pop science physics books will make black holes sound unique in the way they are able to attract matter which misleads readers as it is just gravity being applied to a massive object.

I'll just drop a link to Susskind's "Theoretical Minimum" course:

https://theoreticalminimum.com/courses

Gerard ’t Hooft goes here too I think: http://www.goodtheorist.science/

Though I think Susskind's lectures and books are truly the best starting point for say, an engineer who wants to go back and do physics from the ground up.

The author recommends some interesting popular books:

1. The Feynman Lectures on Physics

2. The Character of Physical Law by Richard Feynman

3. Deep Down Things: The Breathtaking Beauty of Particle Physics by Bruce Schumm

4. The Particle Odyssey by Frank Close

5. Weinberg's The First Three Minutes

IMO someone who seriously wants to learn physics should read these books after they have gone through the typical undergraduate university books (classical, E&M, quantum, stat-mech, etc.) I would not recommend reading popular books until after you already understand the basic ideas of physics. Popular science books are like dessert.

The Feynman Lectures are not pop science, but a textbook series based on his undergraduate courses.

I agree, they belong in the “Undergraduate Physics“ section.

I didn't mean to imply that The Feynman Lectures in particular were "pop science". They are more akin to a very condensed overview of an undergraduate curriculum with interesting motivating examples hand picked by Feynman. They are not a substitute for undergraduate courses, and I'd advise most students to read them after they finish their core undergraduate courses.

The Feynman lectures were specially designed for creme de la creme undergrads who already did a course in physics in high school. They are a terrible way for a noob to try to learn.

Also strange that the author warns against exotic topics and then 3/5 of these recommendations are exotic things 99.9% of readers will never encounter.

My major subject in highschool (2001-2004) was science. Now I work as a software developer.

Yes I admit my physics knowledge is already rusty, and would like to refresh it. On a glance, The Feynman Lectures looks pretty doable...

I also recall hearing that as an undegrad curriculum, the lectures never worked well (even when feynman himself was teaching them). His way of understanding physics is beautiful but not intuitive for most people. I read them after getting a degree in physics and it was fascinating to see his approach precisely because it was so different (and elegant) than the way it is typically taught, but I could not have understood them nearly as well if I had not already learned the concepts in a more traditional way.

All that is to say- The Feynman lectures are wonderful, but I would not recommend them as a first text.

I disagree. As someone who doesn't know much about Physics, certain things I read in the Feynman lectures today still stick with me. Like if you drop a heavy object onto the floor, its temperature rises by a minuscule amount lol.

> Like if you drop a heavy object onto the floor, its temperature rises by a minuscule amount lol.

Tidbits like this are not a substitute for a working knowledge of physics. The Feynman Lectures are not a substitute for undergraduate courses. You'll get more out of the Feynman Lectures after completing the main undergraduate courses.

I'm not sure what you define as a 'working' knowledge of Physics, but to get to a research level of physics requires more than a few introductory physics course also. I'm not saying the Feynman lectures is a substitute for learning any specific part of Physics, but it is useful for understanding basic concepts and also understanding how those concepts can fit in to our everyday lives.

What I disagreed about in the post I replied to was the position that it wasn't "intuitive" or a good first text for beginners.

Counterpoint: "Memories of Feynman's lectures" at http://www.feynmanlectures.caltech.edu/I_90.html

Every time this topic comes up, someone says they heard nth-hand that the lectures didn't work. I suspect it's folklore that grew out of Feynman's disappointment expressed in his preface. I studied them together with the official text in my undergrad courses, and found them helpful, FWIW.

They're definitely aimed at the type of student who gets into Caltech. My general advice would be to give them a go if you're interested, because they're wonderful, but be open to switching to other texts if it's not working so well.

I kind of think the whole OP should be subject to the same caveat: Susan Fowler is probably not just hardworking but very very smart, and you shouldn't necessarily expect comparable results. It may go like the guy who tried to become a golf pro on the 10,000-hours theory: https://en.wikipedia.org/wiki/Dan_McLaughlin_(golfer)

>Also strange that the author warns against exotic topics and then 3/5 of these recommendations are exotic things 99.9% of readers will never encounter.

I don't think you understand what "exotic" means in this context. Literally everything on this list except QFT is something pretty much every physicist will study. (And every theorist will study QFT.) No coincidence that it's almost topic for topic what I studied in grad school. This is "how to actually learn physics", not "how to learn a subset of physics."

Exotic topics would be quantum loop gravity or supersymmetry; things which sound cool but aren't foundational in the same way.

Susan Fowler's life story totally impresses me.

She is world-renowned for MeToo/Time Person of the Year, but her achievements in physics through sheer will and hard work, even though her upbringings did not give her much in that direction, makes me think there is a movie in it.

what are her achievements in physics?

Bottom line is: work your ass off for at least 5 years, and maybe you'll have a chance to get it.

At least, that's honest advice!

If you work hard for 5 years you will get it, it’s not a chance

Mmh maybe you can learn enough to understand what people are talking about generally, but there is no guarantee that you will be any good at it

Well, this depends on the level on which you want to be. A good way to start is with an elementary (i.e. non-calculus based) physics course. Despite being called "elementary," it might get you a long way towards learning a lot of non-trivial, often quite complex - and useful - physics. This could take a few months to a year. It will introduce you to vector algebra and the practical use of trigonometry. The next round would be a "general" course. It is the best chance to learn much of the "high-end" physics a "normal" person or an engineer will ever have. This course uses some simple ways of doing calculus and vector analysis, much of which will be explained as you go. Be prepared to spend a couple of years on this course. After that, you could cut your teeth into a traditional course on theoretical physics (e.g. Landau and Lifschitz). Not many people will end up there, and there may be little practical benefit for most of us. This course will require much of the traditional higher math. There is no telling how many years and how big an effort you will have to devote to this. And, finally, there's the "modern" theoretical physics, which is heavily based on modern (abstract) mathematics - very cool stuff indeed!

For more advanced topics, this is an amazing book that covers many graduate topics in a unified and consistent notation: https://www.amazon.ca/dp/0691159025

Draft of the book is available here for free: http://www.pmaweb.caltech.edu/Courses/ph136/yr2012/

Warning: this is very advanced material... I'm still on Chapter 1.

Also Landau and Lifshitz, Course of Theoretical Physics.[1]

Released to public domain on archive.org: https://www.reddit.com/r/Physics/comments/1dmxq7/our_beloved...

[1] https://en.wikipedia.org/wiki/Course_of_Theoretical_Physics

I'd like to say that Mach's Science of Mechanics is a timeless book and I would recommend to anyone who hopes to like physics. It's so different than modern textbooks. You get the feeling of learning new things as he explains each phenomenon with simple mathamatics and often ingenious ways.

https://www.cambridge.org/core/books/science-of-mechanics/D8...

Recommending Griffith to study quantum mechanics is just plain wrong. It's inconsistent, have many gaps in the material. There's a book superior in many regards to Griffith - the "Quantum Mechanics: Concepts and Applications" by Zettili.

While I didn't like her saying that Griffith's is the book, in my experience, there is no the book for QM. Griffiths is good, but should be supplemented with another.

On the other hand, all of Griffith's works are very approachable - he's a gifted writer, and he seems to have an incredible knack for helping you find the core idea in something. I think all of his books should be the first word on their respective subjects - but not the last word.

There's an astonishingly large number of books on basic QM (only, perhaps, comparable to the number of books about differential forms :). It is probably because each author feels that something is missing or unclear or outdated in all other books. And this is despite the fact that QM in its fundamental shape has been complete since mid-1920s.

A few more good pop physics books:

Maxwell - Matter and motion. Written by THE Maxwell, what more do you need to know? long out of copy-write and available on the web for free

Born - The restless universe. discusses atomic theory and describes some of the more down to earth parts of quantum theory, especially how the theory explains quantitative properties of atoms and the periodic table.

Einstein & Infeld - The evolution of physics. pseudo-Historical exposition taking us from the mechanical universe to fields to quanta, and from Galilean relativity to Einstein relativity.

Reichenbach - the philosophy of space and time. technically philosophy of science, not pop science, from the logical positivist school of the Vienna circle. very readable discussion of abstract mathematical geometry and various relativity principles, if you don't mind skipping some of the more bloviating bits.

Pask - Magnificent Principia. Fantastic overview of Newton's Magnum Opus, although it doesn't give enough historical context to what newton was building on. Assumes some knowledge of calculus.

Hmm...I think I have (somewhere) a copy of that Born book, signed by Born, courtesy of my Dad who I suppose must have run into him in Edinburgh in the 50's.

A bit more on the Maxwell book: it's a real textbook rather than "pop physics" in the usual sense, but written for people with only a high-school level of math (algebra and geometry). Wonderful explanations -- for one, iirc, the derivation of Kepler's conic-section law which Feynman later rediscovered and presented in "The Motion of Planets Around the Sun" -- although the prose style is rather stuffy and Victorian, and Feynman has him beat there.

Are you sure we're thinking of the same book? The one i'm referring to [1] uses basic algebra (fractions, exponents, variables), only a couple of times in the entire exposition if i remember correctly. Its precisely what I would think of as good, non-fake popular physics. Edit: On second thought, I suppose this really isn't "popular physics in the usual sense" as you described it, so we probably are referring to the same text!

https://archive.org/details/in.ernet.dli.2015.151311/page/n7

Yes, that's the one.

To put things in perspective, Susan is incredibly talented. She went from barely knowing high school math to enjoying advanced mathematical physics in fewer than three years, which means in this three years, she learned Analysis (not Steward Calculus, but at least Baby Rudin, mind you), Differential Equations, Linear Algebra, Abstract Algebra that covers at least groups, rings, and fields, Functional Analysis, Advanced Probability and Mathematic Statistics, Differential Geometry, to say the least. Besides that, she also needed to learn mechanics, E&M, Quantum Mechanics, and what not. She achieved all these in her part time as she was majored in Psychology. What's even more amazing is that she didn't find her latent talent until she went to college, and she could immediately enjoy Feynman's textbook with almost zero background in Physics!

Bravo! Bravo!

As a new-comer to the topic of manifolds, learning it from math textbooks is painful. That seems to be the case even if you're reasonably strong at analysis, topology and linear algebra. I find textbooks written for theoretical physicists much gentler read. Physics textbooks can be a good place to start learning, say, differential geometry even if you don't care about physics (I don't).

Caught this video the other day on Youtube. It's a archival 1959 lecture from MIT demonstrating light's wave particle duality. Using only a visible light source, photo-multiplier, and oscilloscope. Just remarkably clear and simple. It's amazing how much more the memory retains with a demo. And I can't help but think quantum computing could be made accessible to a wide audience in this way.

The Physics of Light (1959) John King-MIT-Electromagnetic Radiation

https://www.youtube.com/watch?v=bnSH6YDFXfk

This couldn't have come at a better time for me. I was listening to Kara Swishers interview with Elon Musk[1] and he touched on lots of physics related concepts related to all of his companies. The interview made me want to learn more about physics.

[1] - https://www.recode.net/2018/11/2/18053424/elon-musk-tesla-sp...

Elon Musk talks about arguing from first principles and claims this is the physics way without going into details. What else did he say about physics that you liked?

When he was going into the Boring companies tunneling evaluation trying to figure out weather current tunneling tech was power constrained or heat constrained. Also he mentioned the supersonic jet design that he has. There were also some undertones with the Tesla Roadster, Tesla Pickup truck and SpaceX BFR.

Ok, thanks for giving details. But these can be classified more like engineering issues. I don't know if you agree.

The Mechanical Universe (1986) [video] https://news.ycombinator.com/item?id=17793483

Previous discussions:

https://news.ycombinator.com/item?id=12691963

https://news.ycombinator.com/item?id=13684303

Books are too low bandwidth. You will get stuck, mostly on trivial stuff. Then what do you do?

My advice is to find a teacher. If they are any good they will speed up the process by one or two (or more) orders of magnitude. Even the professionals do this.

>You will get stuck, mostly on trivial stuff. Then what do you do?

Find other books. There's a reason why university libraries have old editions of the same books and very similar books on the same topic.

This is great and, in my experience, non-trivial advice. I often used to get stuck on a mathematics textbook, and wouldn't know how to go forward. Turns out, sometimes different textbooks covering the same topic will be much better, or even just will be better for teaching one specific concept.

What works for me is to combine the two. I can absorb most things from books. Then, when I get stuck, I ask the advice of someone who knows. I was actually surprised how inexpensive this can be these days and how much a passionate teacher can give you these days in terms of inspiration and opening your mind to new perspectives regarding something you (thought you) already knew.

Yeah - I dug out my old caculus textbook a while ago and started trying to work all of the problems in it. But there are a handful I just can’t get, no matter how long I work on them. It would be nice to give in and ask somebody who knows the material better than I do where I’m going wrong (although I’m sure it will probably be something stupid...)

In my experience these problems get solved extremely quickly once you realize where the problem is, so I tend to collect a small list of these and then call one of these tutors offering lessons to university students.

Not everyone can afford thousands of dollars for tutoring. But forums and MOOCs are good.

Do you have any physics forums to recommend off the top of your head?

There are often interesting discussions under each video on Khan Academy, I know this one too https://www.physicsforums.com/, and this one in French https://zestedesavoir.com/forums/savoirs/sciences/

Having completed a graduate level Physics education, I can attest that the selection of topics is solid.

(Can't comment on the books, I learned in a different language where other books tend to be used).

Assuming it's German, would you like to list some of your favorites?

I've noticed that I mostly read English textbooks on all kinds of subjects, because it's easier to get recommendations on HN or sites like chicmath.

Oh, it's been a long time :-), but I'll try to dig through my memory.

I think I liked the Gerthsen, our Profs also recommended Demtröder, which was OK, but somehow I never liked it as much.

In theoretical physics, Nolting and Fließbach were good -- though I cannot remember which topic I learned from where.

I did my Diplomarbeit on spin transport in mesoscopic systems, and really liked "Electronic Transport in Mesoscopic Systems" by Datta, which at the time seemed to be the only accessible and clear writing on the subject.

Disclaimer: I tended to go to the lectures very regularly, and mostly learned from there, so the books very mostly supplemental material for me.

Is there a similar list for Mathmatics somewhere?

Not for self-study, but still interesting: https://www.ocf.berkeley.edu/~abhishek/chicmath.htm

"How to Become a Pure Mathematician (or Statistician)"

http://hbpms.blogspot.com/

Wow what an amazing list. It will still take many years to learn all this material, but I think that a dedicated student could follow it and physics up big time! My time estimate for someone with normal intelligence level (i.e. not genius), starting fro scratch and learning part-time, would be 2-3 years. It's totally worth it though for the analytical power that learning physics gives the learner.

Some notes/links below:

> Before you begin studying physics and working through the topics in the sections below, you have to be familiar with some basic mathematics.

That is very true and often a big obstacle for people who have been out of school for some time. Note it's not enough to just be familiar with the concepts—you must achieve fluency with the procedures so you can use them as building blocks for later studies. For example, it's not enough to just read about the quadratic formula (-b ± sqrt(b^2-4ac))/(2a) and use it a few times, spending 5 minutes each time to think about the steps, plugging in the vars, etc.

Because solving quadratic equations is used so much in math and physics, you have to package that procedure as a reusable routine that you don't think about anymore and you can apply almost without thinking, in under 30 seconds. This "fluency with the basics" will ensure you're not slowed down when you reach the more advanced topics where solving quadratic equations is used.... and there is only one way to build fluency...

This. A thousand times this. I wish someone told me that when I was studying. It may not be fun to get stuck, go down the wrong path, doubt your abilities and feel stupid along the way, but that's what growth looks like. If every time you read a solution to a problem provided by someone else you gain one "knowledge unit," then finding the solution on your own is > 10 knowledge units. Forget 10x engineer, be a 10x learner—solve some problems!

> 1. Introduction to Mechanics [...] the basics of motion in a straight line, motion in two dimensions, motion in three dimensions, Newton's Laws, work, kinetic energy, potential energy, the conservation of energy, momentum, collisions, rotation and rotational motion, gravitation, and periodic motion. > You'll need to learn calculus while working through University Physics. >

Shameless plug, I wrote a book called No Bullshit Guide to Math and Physics that covers these exact topics. It would be a great starting point for someone who wants to review high school math and learn mechanics and calculus in an integrated manner. Here are some links if anyone wants to check it out:

- preview: https://minireference.com/static/excerpts/noBSguide_v5_previ...

- https://minireference.com/static/tutorials/conceptmap.pdf

- condensed printable tutorial: https://minireference.com/static/tutorials/mech_in_7_pages.p...

- reviews: https://www.amazon.com/dp/0992001005/noBSmathphys

> ...the pure joy of understanding the universe around us is one of the most beautiful experiences you can ever have in life.

But you do not need to study physics for 25 years in order to understand how the world works. Academic physics that she wants us to learn to undersdand the world is just a new academic subject invented or formalized in the 19. century. Archimedes knew 0 (zero) physics and made huge discoveries. Galileo was not a physicist in the modern sense of the word. Even Newton was not a physicist but a natural philosopher. Physics today is a professional field. By studying physics textbooks you will only gain enough knowledge to pass physics exams. It's much better to go out and look at nature directly. If you need specific mathematics just learn that part, solve your problem and move on. But academic physics, as she clearly mentions,claims to build on previous knowledge. This is the way of scholasticism. Scholastics claim that without spending two years studying calculus you cannot invert a matrix. (Because they make a living teaching you calculus.) This is not true. Knowledge is not linear. I can study and learn matrix operations with zero calculus knowledge. The opposite of scholasticism is just-in-time knowledge. Whatever I need I can look it up.

But thanks for posting this. There are good resources in it.

A lot of times you don't know what you need. The point of a good curriculum is to help you avoid those situations as much as possible.

If the goal is to try to understand nature, make your own curriculum. Most people, myself included, initially believe the physics hype and believe that by studying academic physics they will gain new understanding of nature. I believe this is not the right way. It is better to start by asking a specific question. For instance, I am curious about what matter is. So I ask myself What is matter? and try to answer this question. I divide my question into smaller questions. Until I find a question easy enough to answer. I take it from there. But if I enter a physics curriculum in a university, I won't be able to ask this question for 20 years. The answer will always be in the future.

When you want to learn and use the simple abstractions that are just the other side of complexity that generalize the problem you are working on and its solution, what do you do? Do you hope for one?

Not sure why you were downvoted. I agree that the average popular person will get more out of physics doing things they can (re)discover themselves, like Archimedes work on bouyancy and Newton's work on optics. Too many folks are stuck in the read/cram/exam mentality from competitive schooling.

> The opposite of scholasticism is just-in-time knowledge. Whatever I need I can look it up.

I understand the temptation to think this way but I really disagree. Scholasticism has serious problems but the solution is not 'just-in-time knowledge'.

Scholastacism has been such a successfull approach for physicists exactly because the human mind is simply not equipped to approach much of modern physics. The scholastic traditions are in place to augment and fix our inherent mental deficiencies and prepare us to be able to understand physics.

Approaching physics is not a knowledge problem. Its an understanding problem and true understanding takes work, not informaation delivery.

I think I appreciate the point you are making, but you have gone a little too far in making that point. I've gone through a physics education, and I can attest that one can learn the material, be good at taking exams, and still do a poor job of applying it to the real world.

The other extreme is as problematic, though. Knowing certain formalism in mathematics can really help in expressing a physics principle - and at times it takes a fair amount of seemingly pointless formalism to get to that point.

>Scholastics claim that without spending two years studying calculus you cannot invert a matrix. (Because they make a living teaching you calculus.)

I have no idea where this is coming from. In my education, we were taught matrix inversion a full year before calculus. I've studied matrix inversion multiple times in my academic career, and I don't remember calculus being invoked once.

And to be frank, I'd be extremely wary of anyone claiming strong physics knowledge without learning calculus. Physics gained by leaps and bounds after calculus was introduced. It is the subject one can apply calculus most easily to, and is perhaps the reason we know more physics than any other discipline out there.

> wary of anyone claiming strong physics knowledge

Well, that depends. Faraday was a great physicist (his claims, whatever they may have been, notwithstanding).

Are you suggesting that Faraday did not know calculus?

According to Wikipedia, "his mathematical abilities, however, did not extend as far as trigonometry and were limited to the simplest algebra."

> In my education, we were taught matrix inversion a full year before calculus.

Thanks for correcting that. I need to find a better example. What I’m trying to say that is that, the academia or scholasticism teaches you a set curriculum. I think this is not the most productive way of learning. As an analogy, I don’t need to understand and memorize all the symbols of a programming language to write a program. I can have a basic understanding and then I can look up the rest as needed. Scholasticism doesn’t allow this.

> But you do not need to study physics for 25 years in order to understand how the world works.

True, that. But to each their own, and so everyone has a different requirement as to the depth of such knowledge to be considered an understanding. A squirrel knows enough about "how the world works" in order to survive - more, perhaps, than we humans do (because we couldn't survive in those conditions). Likewise, a blacksmith may have more firsthand knowledge about the properties of iron and its alloys than a highly-trained theoretical physicist...

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