If Susan Can Learn Physics, So Can You (2013)
fledglingphysicist.com
fledglingphysicist.com
I've tried different teachers, my friends have tried tutoring me, I've tried Khan Academy. No matter what I do, the information just won't stick. The connections in my brain aren't made. What I don't understand is I learn other subjects relatively well. It's just math I can't grasp which really sucks because I love science and cryptography; two fields I imagine I could appreciate more with a solid mathematical background.
It's worth noting I have some of the symptoms of dyscalculia, so perhaps my brain isn't really built to do math and is why I struggle so much?
It's frustrating when I see "anyone can learn math!" because I've gotten shit from people in the past like "you can't be a good programmer if you're bad at math". I feel like we need to be more accepting that people have strengths and weaknesses in different areas.
I'm tired of feeling ashamed to be bad at math, especially as I'm not sure it's even my fault anymore.
Learning QED and general relativity is often unobtainable even for people who are 'good at math'.
Yes but note that verbal and math scores are highly correlated. Likewise, basketball and football are different skills, and some people are much better at one than the other, but if we look over a population, being very good at one is a strong predictor that you are much better than average at the other.
Lately I feel like I'm hitting a brick wall with cryptography. For example, I know what algorithms are secure but I can't tell you why as I don't understand the math behind it. I took the Cryptography 101 course on Stanford which used discrete probability. I didn't get very far into the course.
It's possible some of this just comes from me trying to fix the feeling ashamed problem but it's just making me miserable. What I ought to do is stop beating myself up.
My suggestion, it worked for me: buy a lot of paper, like, thousands of sheets. Take some books with the problems (and also with the solutions) then work through, maybe more than once. Don't say you haven't tried until you actually used all these sheets to write your own derivations of the solutions. If you once see the solution, you have to try the second time without looking. I could not learn by not really doing it, a lot, and I don't think anybody can. You can't just "read" it as you read history books, you have to "work" it.
A lot of people simply can't imagine themselves sitting and filling the papers with formulas (also in the comments here), but don't have problems spending months doing video games, for example. It's this "belief" that's limiting.
On another side, you need to have some kind of context too, but you have to find the interactions of the context and the actual work you do yourself. I like the "historical" context, because the big steps in math were traditionally not accidental. Archimedes invented the kind of "infinite" methods to calculate volume of some solids, and the methods remained forgotten, people remembering just results, Newton also invented a new math just to solve the problems he considered etc. For you, you have to adjust your steps to the knowledge you already have: if you know little, you can't avoid spending time learning the basic stuff. You have to work through, step by step.
Maybe also watch the documentary about Fermat's Last Theorem as an example of how it looks like doing math.
I could only do very basic math because I got bored, or my retention rate was very low. I'd go through the excercises but it wouldn't stick in my brain.
Eventually I figured out I just couldn't handle theoretical, like on the paper, stuff. So I started making up scenarios where what I were trying to learn would actually be applicable and create small programs that illustrated it, and suddenly I started to actually remember the stuff.
What I'm looking for is theoretical knowledge, and that's something else I struggle with. Can I still get that with more hands on experience?
For instance, something I find fascinating are One Time Pads. They're perfectly secure, given len(k) >= len(m); so the key must be the same length as the message.
As far as I understand, it's because each possible key may produce any possible message which I think is expressed:
Pr(x) = 1/|U|
I probably wrote some mistakes there. I was able to pick this concept up, I think as it just made sense to me; maybe I was able to visualize it or I could just think it through and realize the conclusion made sense.
Does discalculia have to do with numbers and calculations exclusively? It's not very hard to cook up math problems where the numbers are well-hidden so that you don't touch them directly. A lot of induction arguments are like that. Have you ever seen a math proof? The reason I am asking this is because your writing seems lucid enough and math proofs are nothing but tight explanations why a statement is true.
Take a look at this free book by Richard Hammack and see if you like the flavor of it because that's how much of math is: http://www.people.vcu.edu/~rhammack/BookOfProof/
I usually come to understand the concept through experimentation that way, and from that point the actual notation doesn't matter as much (although it's still like reading a foreign language, to a certain degree).
Do you have some contact information? I couldn't see anything in your profile. Mine isn't great but does have my Keybase which should lead you to my Twitter and website.
First session would be talking generally about how much you want to learn and figuring out what your definition of "success" would be, possibly with a timeline, and quizzing you with a ton of simple problems to see how much you know now and what confuses you. Ideally we'd find out in the first session if there's one concept or procedure you have the most trouble with and we can start hacking away at it.
Another mistake is the idea which the article rightly denies, namely that you have to be smart enough to learn X.
The author makes a mistake too: she thinks she can predict the rest of her life. ("I realized I actually wanted to study physics for the rest of my life.") This last idea is related to the question adults frequently ask children, "What do you want to do when you grow up?"
The limiting factor in all these cases is how genuinely interesting you find the field and how much you want to learn it now. Which is a property of the ideas and the problems as much as of your personality.
I'll go with psychometrics on this one.
About the cry-for-help part: I recently started reading Visual Group Theory http://web.bentley.edu/empl/c/ncarter/vgt/ which looks to be gentle and illuminating. The style so far is quite different from a typical math textbook. Another book I've read more of was Turtle Geometry by Abelson and diSessa (the same Abelson who cowrote SICP). It can get difficult, but it's also very unusual: it's about exploring mathematical ideas for yourself by programming, and includes both hints and solutions to its suggested problems.
Did you try the exercise dashboard on Khan Academy? https://www.khanacademy.org/exercisedashboard
I've tutored math for the SAT. My anecdotal impression is that many people missed a few bits of math in the early grades, then spent the entire rest of their math careers hopelessly behind.
So, for example, algebra might be difficult because of a gap from grade two about not knowing part of a times table.
If my hypothesis is correct, that would call for approaching math from a total beginner mindset, and taking nothing for granted. For example, there is much to contemplate in a triangle, or in mental tricks for adding small numbers.
Practice is important. That's why I like Khan: for every concept, they give you exercises you can do to the point of mastery. I believe it also does review exercises so you keep working on the knowledge.
A sense of play and fun is important, and helps with practice. My dad is excellent at mental arithmetic: when he sees a license plate, he'll add the numbers together for fun, or multiply them, etc.
Another app I like is Dragonbox. I'm not sure how far it will take you, but the goal is building intuition. Again, beginner mindset is important. It's intended for kids, but for all intents and purposes you are on the same level as a kid – and that's fine!
https://itunes.apple.com/app-bundle/db-complete-math-pack/id...
Another important element is that people who are good at math have usually just figured out small tricks that make certain calculations easier, and help them visualize concepts.
I'm not entirely sure how to teach them, but while reading Isaac Asimov's autobiography I came across this reference to a short book he wrote on exactly that topic. Asimov is a wonderful writer and this may be an excellent primer:
https://www.amazon.com/Quick-easy-math-Isaac-Asimov/dp/B0006...
Finally, I recommend studying for the SAT math section. The questions test math in somewhat novel ways. They're fun and reward creative thinking. And as a bonus, there are books written to help you figure out this kind of math, quickly. I really, really like Pwn the SAT. My students got a lot better just by using it: it teaches you how the author thinks, and really breaks things down simply.
SAT practice tests: https://www.amazon.com/Official-SAT-Study-Guide-2016/dp/1457...
Pwn the SAT: https://www.amazon.com/PWN-SAT-Guide-Mike-McClenathan/dp/152...
(Note: The SAT changed in 2016. You could also use the earlier SAT test booklet (the blue book) and the earlier Pwn the SAT for this exercise)
I don't think any single concept in math is particularly hard. What's hard is that even high school math requires mastery of a few hundred concepts. So you can learn one, but it goes away.
The tools I outlined above are the best I know to solidify math knowledge and make it habitual. I believe any reasonably intelligent adult could use these to learn math.
It is, however, a large subject, and I expect it would require months of focussed work practicing these for every day. But I believe it's doable. I'm basing this on my experience with students who were "bad at math". They made great strides.
I hope this may be of some use! Feel free to reach out if you want to talk about it further. My email is on my profile.
You must rethink how you think about math fundamentally. This video and paper are like poetry - short but demanding. Watch this video and read the paper. Really think about it in your own way, don't try to force your mind into an unnatural construction.
As punishment for my laziness, my legal guardians beat the hell out of me. Maybe I would learn to apply myself, they said, between blows.
10 years later, I was diagnosed with a non-verbal learning disorder/disability. I ///couldn't/// learn math the way it was being taught, nor science, economics, english, history, or any other topic I'd tried my hand at. In reality, I had burned out in the first few months of being elevated from one class to another and never had the chance to recover (just ignore the physically and psychologically abusive home life I had).
In spite of this, I struggled my way through a CS degree, which is effectively worthless to me because of the disability. The whole time, I had friends, colleagues, family, tell me that I'm lazy and just need to suck it up and do the work. Not one of them had the slightest idea of what I was going through and what was necessary to complete the courses of study - approximately 3x the work required for the same grades. The disabilities support office provided me with only written notes, absolutely inappropriate assistance given my difficulties with written materials.
My degree was a waste of time, money, and effort, because nobody will ever look twice at me. I'm overqualified and no support services are able or willing to help me, many employers won't hire me because in their minds, they'll train me up (and pay minimum wage) then ungrateful-old-me will jump at the first decent job to come my way. I've previously noted interviewers would shout and swear at me for wasting their time, threatening to bill me at their consultant rates. One employer who knew of my disability later told me that I couldn't have told him about it, because if I had he would never have hired me. My present employer hired me for a non-IT role, and then later on told me it was expected that I would provide IT support for all the office staff for no extra money - I was already working 30 extra hours a week without pay.
You may be able to bring your abilities up to a useful level, I don't know, but the question you should consider is whether it's worth the time and effort. It may well be that any perceived benefit is far outweighed by the costs and struggle. I would strongly recommend professional assessment, as being diagnosed with my disability has probably saved my life, and very much my sanity. I do get tired of people telling me that it's just an excuse and that I'm really just lazy - non-verbal learning disorders are far more than simply "I don't understand what I don't read." One genius once told me that everybody had to learn body language, I just had to force myself to do it, work harder and I'll get it. Apparently he didn't.
Don't be ashamed about your lack of ability, be ashamed for the people who think you can because they could, that you just need to apply yourself, because they never will be ashamed of their prejudice.
Are you self-diagnosed with dyscalculia, or was that a diagnosis from a professional after testing?
I'd strongly recommend working through Coursera's Learning How to Learn.
What seems to have helped me was to drill on an abacus, specifically an IOS app called Know Abacus. I also had a physical abacus to play with and that was really fun. I'm brushing up my skills with Khan at the moment, and I've noticed that after the abacus drills, my gut instincts were better about spotting issues or knowing what to do.
I think the abacus helped by making math operations a physical action (move 2 beads then move 2 beads to add, then see & count 4 beads) compared to a mental projection action (think of 2 things then think of 2 more things and remember I have 4 things because 2 + 2 = 4).
Edit: for reference, I am American who went through US public schools in a variety of states. The abacus training was completely absent from my primary education unlike perhaps some of our fellow HNers from Asia.
Where I live, physics and math are a part of obligatory general education, so you'll definitely have to study them until you're 15. After that, if you stay in the general education system (which is true for 95% of people who plan to go to college), you'll have to learn them for 4 more years. Sure, some people will develop a likeness/talent for it and others will hate it, but everyone needs to pass. Only when you go to college at 19 will people start telling you that perhaps you need to be a physics person to study physics and that it's not for everyone.
Art, on the other hand, is considered something magical and depending entirely on your talents right from the start. Art subjects barely touch on any practice, you have to learn a bit about the history and you pass. But I feel it's absolutely the same. Everyone can (and IMHO should be forced to) learn to read sheet music, play a simple tune on the recorder, draw still life with correct shading and proportions, write a short poem etc.
Personal involvment would give people a much deeper understanding of the topic. I mean, imagine if physics only consisted of everyone learning about Newton, Galileo and Einstein with just the smart kids doing calculations.
Perhaps it's to combat entrenched prejudice. Back then we would make jokes about "Physics for Women", i.e. the non-calculus kind for non-majors. Everyone who would joke like that would know that physics is for anyone, just look around the lecture hall where 25 % of the audience are female, but talking like this he would pretend to be a Neanderthaler from an era thankfully past.
Forward to the present, where in Britain they make physics more "accessible" by watering the subject down. That doesn't help groups that are traditionally excluded, they need to be included, forceful if necessary.
Same thing holds true for the Arts.
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I think it's a false premise that the subject is hard in the first place. Why is it hard ? Because you have to get the "right answer" on your test/homework. Ok, but why do you have to get the "right answer" ? Why do I get zero points for a problem when I put 0.33 and the answer was 0.145 ? That is utterly ridiculous. Why are we using logical AND on all a problems steps ? Oh, you made one mistake, no points for you!
And before someone brings up "partial credit", That's myth that meant "pity points", not "9/10 points, minus one because you f-ed up your algebra or minus sign". You should be tested on the process of solving a problem, not whether you got 0.33 as your final answer. In the real world, even if you do exactly what the book says(!) you won't get 0.33. Your measuring apparatus wont be calibrated, there will be noise, other sampling errors, defects in materials, etc. If you start the test out with this bullshit premise that IF( ANSWER == 0.33 ) THEN grade='a'; then you're not testing them on physics, you're testing them on how detail oriented they are and how well they can concentrate without making a mistake (like the Japanese show "Unbeatable Banzuki"). If that's your class, then call the class "Following Detailed Processes I" or "Doing N steps without ever making a mistake II", dont call it "physics". You should be able to get an A without ever getting the "right answer", so long as you demonstrate that you know the concepts and what the equations represent and how to apply them. Not contorting yourself to do the work of a machine, like a sadistic hazing ritual.
Edit:
And I almost forgot about the fun little thing they do in college where the course covers topics {A,B,C}, yet they test you {A, B^-1, and C-d}, you know, just a little bit different* material or problem formats than what they lectured about. Just different enough that they dont resemble any of the quiz or homework problems. If you want to test me on Ax^2+bx+c, then test me on Ax^2+bx+c, not on problems I've never seen before.
</RANT>
The point, poorly summarized, is that it resembles math education where a soltary focus on calculation distracts from learning how to do the type of math that only professional mathematicians seem allowed to do now.
It's worth reading if only to see how it often seems like the grass is greener for the educational environment of other fields.
[1] https://www.maa.org/external_archive/devlin/LockhartsLament....
“Right. I don’t believe in the idea that there are a few peculiar people capable of understanding math, and the rest of the world is normal. Math is a human discovery, and it’s no more complicated than humans can understand. I had a calculus book once that said, ‘What one fool can do, another can.’ What we’ve been able to work out about nature may look abstract and threatening to someone who hasn’t studied it, but it was fools who did it, and in the next generation, all the fools will understand it. There’s a tendency to pomposity in all this, to make it deep and profound.” – Richard Feynman, Omni 1979
She also authored this previously discussed post about physics: https://news.ycombinator.com/item?id=12691963
Kids should be allowed to take more risks to learn different things.
She's criticizing how people get pigeonholed -- not just early in their careers but early in childhood -- as being "math people" or "physics people" or "humanities people". And that those categories and labels limit people who in fact are capable of learning and enjoying STEM subjects.
It's like how there's an unspoken rule in some corners of the tech industry that someone who first picked up programming later than high school can never be a "real programmer". Which is bullshit and does both individuals and the industry a major disservice.
I worry that after I adopt, my daughter is going to fall into the same trap.
Otherwise maybe point out other complex things that are doing.
Depends on why they think they are incapable of doing it. Whatever the reason, it is possible that they do not see value in learning it and putting in effort. It might be that they failed in the past - or never tried because they always assumed they can not do it.
However, if your worry is the kid, then talk about that worry with them directly. Don't go around trying to manipulate them into learning something they do not care about. Just say that you worry about the baby picking up the attitude and thus having less options in life (and growing up less capable as a result). Healthy kids are super good in picking up attitudes like that, so the worry is well grounded.
Your wife might be more open to not make herself less capable then she is in front of kid for the sake of kid then to spend a lot of effort on something she does not care about.
Don't underestimate the drive for people to lie or greatly exaggerate their achievements over the internet.
I personally find the post not entirely believable. E.g.,
- First she says "I had learned nothing beyond sixth grade math: no algebra, ...". Then she says "I had been lucky enough to be introduced to ... some algebra ..."
- "You see, I had no formal education". Oh wait, that still leaves out the possibility of thousands of hours of khan-academy, and youtube and what not, for math, physics, programming, during high-school, summers, evenings, freshman college, sophomore college, etc, etc. (Yeah no.).
- She was ignorant in math and physics in June 2012, took a QFT class around Dec 2012, and had an eye opening experience. It's good poetry but not clear what she meant by that. (could be as simple as sitting in a QFT class without credits, and being able to follow some of the discussion)
- She was taking QFT in Dec 2012, and yet she graduates with BA in physics as last as May of 2014 (from her profile page). So very likely QFT was a giant namedrop, and if you ignore that, spending 2 years on undergrad math and physics coursework, when you've already taken logic and set theory, leading up to a bachelor's degree is pretty routine for most students.
- She worked on the ATLAS project. But. Doing data analysis and "helping design electronics". That sounds like a computer nerd who liked to dabble into physics just for the sake of picking a major for the degree (not that hard).
She may not have been "a physics person" for a long time, but she certainly became one!
I don't know what her IQ really is, I don't think astronomical, but it is certainly very anomalous. I only have a truly deep perspective on my own abilities, and just based on this I think I can say somewhat confidently she is at least a generation above mine in general ability-, for myself, having jumped from standard engineering undergrad, to software engineering and algorithm design, to applied physics, and now finally to nanoelectronics , each of which I can say I somewhat mastered within the space of a year-1.5yrs, and statisically I konw I am 3.5-4 standard deviations above mean (at age 10 and 14 I tested 164 and 158 respectively), but all of that did not give me the power to so quickly grasp QFT- remained incomprehensible to me in my first year grad school classes, and probably always will, unless I invested massive time into mastering it.
But I want to comment on another thing I find highly strange, which is that someone of such rare intelligence would leave academia (ostensibly she was at one time considering staying in Physics as a grad student) back to software architecture, rather than gravitating to the edge of mathematical physics- or continuing to follow that road to reality, to riff on Penrose. Indeed, I found myself following the inverse path. And ultimately, Moffat & his correspondents in our generation,- possibly another lady, like Pasterski looks like one possible member of this cohort- will be the ones to pave the next part of it.
(Disclosure: I am already enrolled in a online-university program here in Germany, which is almost free, but so far I only took two exams on rather practical subjects I had no problems with).
(This was in the 80's, well before the current attempts at cross-state standardization.)
In my case, it did not cause me any particular trouble, as I was able to teach myself what I missed. My parents had predicted that this could be an issue, so they made sure I had the resources I needed. But if they had not been proactive, I could have easily graduated HS without ever having taken certain core classes.
scored very high on verbal part of ACT and got scholarships
She apparently went from 6th grade math to graduate quantum mechanics in a year and a half. This is highly atypical and is surely not an example of a "not smart" person overcoming and managing to learn some physics.
Furthermore, if your goal isn't to do research work but rather to be able to follow along an average research article using the basic framework of QFT, you can also cut out much of the lab work. Susan is clearly considerably above average in intelligence and a quick study, and I'm impressed by her perseverence, but I don't think this is at all beyond what any good theoretical physicist could have done. It's just that they went a different path, going through the university system, a path with its own advantages, but brevity is not among them.
EDIT: she was homeschooled, which explains it...more info https://www.susanjfowler.com/blog/2016/8/15/20-unconventiona...
Obv. profoundly smart
The question is, is her almost overnight success reproducible by other smart people. Let's say you know calculus and linear algebra, QM is doable, I suppose. But still...mind blown. Even Ed Witten with a physicist for a dad still took 4-5 years to learn the stuff.
What may be MORE interesting to see, not just for HN folks but in general, would be a parameterized set of possible/reachable (as well as 'stretch') goals, for folks interested in learning more about math/physics/cs at various bands of natural/innate ability. While these bands may not be set in stone and raw effort may help level up someone up one tier above their 'home' range, it is for instance frankly impossible for at least 99% of folks to ever become competent at QFT - and likely, 95-99% cannot even grok it in part.
The average person hears things like this and only gets demoralized. Its just like the lean in campaign. What worked for the 1% isnt going to work for the average person.
I have tried learning physics, linear algebra, calculus, abstract algebra, discrete maths, proofs, drawing, game development, compiler construction, operating systems, to write, sound synthesis, music in general and many more. In the past year. I'm not thick so I have varying degrees of success but I never make much progress. The interest lasts from a few days to a few weeks.
Computer science and programming are ones I just so happen to keep coming back to at closer intervals. I just wish I wrote more code, built more projects. There's a lot to learn and that is what lies in larger, more important projects. I know if I could get past this, I could make a positive, if only somewhat, contribution to our field.
I have ADHD, I take my medication everyday. It helps but it isn't a silver bullet. I have learned more in the past year with medication that I have the years before. It is a problem that does not seem to be going away.
Sorry Susan, I really admire your path. You've done well and it's inspirational. I just don't think I can learn psychics like you.
I strongly suspect that even just mixing questions from previous parts of the course into the homework would be enough to make a substantial difference; grinding through a sequence of problems that all make use of essentially the same techniques before moving on to another set is a completely brain-dead way of trying to learn.
1. Read into something for a while 2. Realise I'm deficient in X 3. Repeat 1 with X until I get into a state where I feel "blah I can't focus on anything long enough to get ahead" by which point I either:
A. Indulge in a stimulating video game (complex ones from paradox are best but I enjoy Civ too).
B. Explore my spiritual side and try to get a grip on whovi really am and why I am this way until...
I span out of my rut and get back on the mouse wheel.
I'm interested in all those things even though I wouldn't want to pursue a career in most of them. But I realize I spend X hours a day doing nothing, and I could spend those hours learning all kind of stuff, including for a career, even if I didn't to do it.
Instead of meaningless TV shows and movies I'll forget, and infinite amounts of Internet distractions, I could be an expert in Python or welding, for that matter. I could be making 5 times my income and change my life dramatically within 2-years, guaranteed. No more hoping, wishing, wanting, dreaming.
But I won't. I can't. I'm not.
Do I have ADHD? Do I need an amphetamine to focus me? If it doesn't work for you that well, what's the cure?
I don't believe in ADHD but I don't know anything for sure anymore. I am a pragmatist and open-minded. I'd gladly do anything to just focus on one thing.
I've known ADHD people with extreme self-control (amazing time planning), persistence and will to learn but when they tried concentrating it wouldn't happen. Either something in their brain can't click to grok the subject or they get constantly distracted by their thoughts. The time they put into the subject is huge but they get so little from it.
I've tutored several and am amazed at how well they try to avoid the problem by being better organized but their brain sometimes just can't focus on the important stuff which limits their ability to learn stuff that requires serious attention as quickly as others.
But I do spend time on them. People think I'm a weirdo for even reading a math textbook outside of uni. I don't care: I am who I am.
For example, artists and gamedevs go through tons of anxiety and (usually) ultimately fail and need to find an alternative career. Or, even if they succeed in some manner (i.e. an artist getting a AAA concept artist position), they may become so overworked that they reach burn out pretty fast. Another alternative career I have in mind: being a developer/researcher in an area that's a blend between programming and maths (signal processing, CAD, computer vision etc.) looks interesting on the surface (i.e. I love to study the concepts, implement them in matlab etc.) but I'm afraid that I would end up in some company as an overworked and unhappy faceless cog. That's partly because I feel there's only so much truly interesting work available in this field, and it will most likely go to extremely talented people who have PhDs from MIT in this field - leaving "normies" like me to just do the mundane implementation, bug fixing etc.
I feel like I'm chained by the proverbial golden handcuffs. I can make six figures working on boring and tedious code remotely from my home in a very cheap country (I'm easily in the top 1% of income here). Doing the researcher/developer route would probably require moving to some other country, and thus trading some possible increase in job satisfaction for loneliness and alienation.
Life is hard.
If I had a guy that comes and whacks me in the head every time I think about quitting a job, I'd probably already be retired.
That happens to me a lot with other topics as well. I get intrigued by something, play with it enough to memorize a few details without really understanding them, then forget about the whole thing for awhile, and then come back to find a deeper understanding without apparent effort. Does anyone else feel that way?
Absolutely. I notice it most with math. I try to reconstruct my intuition by sheer force of will, then give up in frustration because my mind will not move. When I wake up, the intuition is just there, as if something was updated or placed. It's not always overnight. Sometimes it's days or weeks, and some things I'm still working on after many years.
My other problem is I spent tonnes of time learning and then never do anything with it. A lot of the stuff I learn often becomes useful mental models - calculus and the idea of continuity and change did this. It felt like a new way to look at the world.
The problem is you can have infinitely many ways of looking at the world but it means nothing if you don't do anything with it!
Have you ever you've ever had a problem you just couldn't solve, that was really hairy and beat you up all night that was suddenly trivial and obvious when you woke up the next morning? Same process, apparently. Basically your background subconscious or a lower level part of your brain goes and picks through all your knowledge that isn't readily available to your consciousness.
I once read that reading code is a lot more important to learn coding.
If you have the drive to put in this "most difficult" effort, utilizing "every minute" of your days closing the gap then you can learn like Susan.
I think the people who aren't "math people" or aren't "physics people" just aren't willing to put in much effort to learn it. They probably aren't all-consumed by it like Susan is.
It's not that these subjects are inaccessible to some people, it's that some people don't want to learn these subjects.