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As (failed) physics major, it sounds so strange to hear someone claim to be good at math but not physics. To me physics is 98% math. It's a few empirical fact

by ta75757 12y ago

As (failed) physics major, it sounds so strange to hear someone claim to be good at math but not physics. To me physics is 98% math. It's a few empirical facts from experiments and then bucketloads of math.

MarkPNeyer 12y ago
i was a physics major, too. the student in our year who was best at math had trouble with the "hand wavy" stuff we'd do. "well, this term is basically zero, so we'll just remove it" and then she'd pull her hair in frustration, like "how can you just do that? how is it still valid?" it wasn't enough to tell her "well it still gives us the valid results" - she had to be able to interpret every portion of an expression and then make intuitive sense of it. at first i was annoyed with this habit of hers, but eventually i started doing it to. for a lot of really math-minded people, hand waviness is anathema, and physics was full of "2 + 2 = 5 for sufficiently large values of 2, so we'll just assume that to make things easier"
- _pius 12y ago
  "well, this term is basically zero, so we'll just remove it" and then she'd pull her hair in frustration, like "how can you just do that? how is it still valid?" I've tried to teach friends with that hangup and found it difficult. Those people weren't good at math, though. I feel like with mathematicians, you should just be able to explain with limits.
  - sedachv 12y ago
    > I feel like with mathematicians, you should just be able to explain with limits. Assuming the limit exists without actually proving the sequence converges is going to produce total junk. Jaynes spent a good portion of Probability Theory illustrating this.
    - _pius 12y ago
      I'm just talking about using the concept of limits as a teaching tool, not assuming a particular limit exists.
      - sedachv 12y ago
        Yes, this is why the mathematicians are pulling their hair out! You can't just drop terms when you feel like it.
- TeMPOraL 12y ago
  I feel that the right approach (at least it worked for me) is to tell the matematician - "see, this term is very close to zero for all practical inputs we can see in real life (proof of which will be left as an exercise for you), so - as you can see from the structure of the equation - we can safely drop it without introducing any significant error to the end result. Yes, the result will be a little bit less accurate; no, no one will notice. And if you happen to encounter a high-energy (or whatever) problem, you can always go back and use the full equation". Explicitly accepting that each handwave introduces errors and imprecision but that sometimes those errors are below what we can measure (or care about) should be acceptable enough for a math-minded person.
enjo 12y ago
Physics is applied math and I think that is an important distinction.
- sedachv 12y ago
  ^ This. I ended up majoring in pure mathematics as an undergraduate after finding out that applied mathematics courses had too much material to memorize after finding out that physics courses had too much material to memorize. Pure math was so much easier.
  - phkahler 12y ago
    You and the person who started this thread seem to think that way. I find there is just as much to memorize in math. fields, rings, groups, and all sorts of things. Oh and those greek letters. I like math and physics and stuff but I never thought there was significantly less memorization in math. Calc 2 techniques of integration and then DiffEq seemed like a lot of special cases that had unique solutions we had to remember.
    - sedachv 12y ago
      > fields, rings, groups, and all sorts of things. Each of those is just a definition and a handful (literally like 5 or 6) of axioms. If I memorized the axioms and a few key theorems I could usually derive everything else in the homework and on the exams. Most mathematical objects have very similar structure and the rest is just maps (morphisms) between them. > Oh and those greek letters. That's actually a very valid point. It took me a few years after graduating to realize how much myself (and I suspect many other students) are hampered by not knowing the notation well enough. Most people just assume you (and they) know what it means and never think about the actual definition and ambiguities. Even not being able to pronounce Greek letters definitely makes you less able (or at least less confident) to reason with them. > Calc 2 techniques of integration and then DiffEq seemed like a lot of special cases that had unique solutions we had to remember. That's the applied math part of calculus. The pure side is just "here's a compact/open/whatever set, prove for any point in it this property holds." Then you find out no one cares about either and it's all just numerical algorithms.
Iftheshoefits 12y ago
Math is certainly required to understand the theory and to synthesize experimental observations into a working model, but I wouldn't put it at more than 50-60%. Most of the math is fairly basic relatively speaking, even at the highest levels of physics.
- soup10 12y ago
  Relative to what lol. What other applied field has more advanced math?
  - Iftheshoefits 12y ago
    I don't know about other applied fields but I was referring to the field of math itself with that remark.
  - sedachv 12y ago
    Economics and quantitative finance.
  - ArkyBeagle 12y ago
    I didn't get that far in math, but in physics classes after Junior Physics Lab , I once or twice questioned the assumptions. There's always a theorem you don't know about. There is a lot to math.
deeviant 12y ago
I would say math is necessary but not sufficient to be successful in physics. Also, if somebody has the aptitude but not the drive, failure can certainly be an option.
Micaiah_Chang 12y ago
There are some skills in physics which are sort of foreign to the math method of problem solving. (Speaking as a physics major) For example, picking a nice reference frame in simple mechanics problems is something that a physical intuition is good for. Same with spotting symmetries in an EM problem. Also, in physics you need to have a good grasp of what to ignore because they have only a small effect on the solution or because it operates on a different scale (fringing effects, transient solutions in ODEs), which often relies on a very hand-wavey type of reasoning. Essentially, physical intuition often does not map to mathematical intuition I have not taken enough math to actually speak for them; this is mostly gleaned from talking with math major friends and my own speculations.
- jules 12y ago
  I majored in math and physics. The same kind of intuition that you use for physics you also use for math. In physics you may call it choosing a reference frame, in math you call it choosing a coordinate system. At least for me it's exactly the same kind of thinking. You hit the nail on the head here though: > Also, in physics you need to have a good grasp of what to ignore because they have only a small effect on the solution or because it operates on a different scale (fringing effects, transient solutions in ODEs), which often relies on a very hand-wavey type of reasoning. Physics is often taught in an exceedingly vague and hand-wavey way. Physics students have to learn to ignore that nagging feeling that something is not quite right. This is impossible for a mathematician. A mathematician wants to cleanly separate the math from the problem that is being solved using math. The problem specification consists of a list of assumptions, and the solution of the problem consists of 100% rock solid math. Physicists weave the two together, so that in the end it's often not clear what is actually being assumed. Furthermore, it's usually not explained based on which experiments those assumptions are justified. A counterexample is special relativity. There it's clearly assumed that the speed of light is constant, and the experiments on which that assumption is based are explained, and from there it's mostly logical deduction. In other topics that is sadly not the case. I would love a physics education where you start with the experiments and work from there, instead of saying "Bam! Here are Maxwell's differential equations. Now deduce things from that based on hand-wavey arguments". I don't mean having the students perform the experiments themselves, just describe what somebody else did and what the results were, and why that led people to believe that the laws of physics are as they are. To make time for that, we should remove the endless by hand solving of special cases of special cases. We live in the 21st century. Instead use numerical methods everywhere, which easily tackle the general case. Got n electrons with initial positions and initial velocities, and you want to see what happens? No problem. /rant
dilap 12y ago
a lot of it is just cultural approach. math people tend to like to rigorously define everything they're doing, and work from there. physics is more like "what can we make up and fudge and twist and bend and then get the right answer." there's a lot of people who aren't as comfortable working in that less-defined context. some of this is maybe inherent to the aim of physics, some of it is just physics machismo culture, and could be better, imo. (i was a physics and math major at oregon.)
- digikata 12y ago
  I don't think it's just cultural. Ultimately in physics you are often faced with a pile of observations from nature that you have to make sense of. Vs math, where you usually have a mass perfectly defined err.. well math that you're trying to build forward upon. I think the best advances in both math and physics are made with people with an excellent grasp of when to move forward with existing constructs, and when to start shaping new ones...
  - dilap 12y ago
    totally agree -- some of it is inherent to the endeavor of physics. but some of it is just hazing...
dxbydt 12y ago
True, but a lot of chemistry is mostly math too, and I flunked organic chemistry the first time. I think its because there is some domain knowledge involved in these subjects, which you have to actually care about. I don't particularly care which element has how many isotopes and what the valency is and how many other elements it can bond with, though I did memorize the atomic weights of all the elements in the periodic table and Avogardo number and few such stats. Those things helped a little, because I was ultimately able to pass my chemistry exams just by solving the numerical stuff and ignoring the chemical stuff. I handled physics in same fashion . There's something called the distance equation, where you can express the distance travelled by particle in terms of velocity and acceleration. We had to simply memorize that and use it in problems. I forgot what it was in the exam. So I just derived it from definitions. The teacher was quite surprised, because at that stage we hadn't been taught calculus, so how did I derive it ? Well, I had solved calculus problems by myself, so I just did this - http://pastebin.com/T6PrePh8 http://pastebin.com/T6PrePh8 These things helped me get by.
- delian66 12y ago
  >> I forgot what it was in the exam. So I just derived it from definitions. Hah, I did the same :-) ... unfortunately I also forgot the conventional names, and just used 's' (for speed) instead of 'v', and 'd' (for distance) instead of 's'. My teacher did not object the derivation at all, but told me that the results are wrong, because of the letters used ... Well, point taken - now, I try to pay extra attention and memorize idiosyncrasies like naming conventions ... it saves time when communicating with others.
  - mirchiseth 12y ago
    That reminds me of a sessional (mid semester exam in India) when I got confused on speed of light being 3x10^8 m/s or 3x10^9 m/s. Strange are the ways of mind. I knew the relation between c and electric constant and magnetic constant. So derived it from that.
- cli 12y ago
  Organic chemistry is the least or one of the least math-intensive chemistry subjects at the undergraduate level.
s-phi-nl 12y ago
Note that he says "I wasn't particularly good at history or physics" (emphasis added), not "I was not any good at physics." As other comments point out, there is enough to physics besides math that someone (who was good at math) could easily do well in physics without being considered exceptional.
analog31 12y ago
I was a math + physics double major in college, plus I was also deeply into programming, electronics, and music. In my view, the starting point for physics is a deep curiosity about how things work. But I'm not sure that aspect of it is ever taught. Rather, it's assumed that good physics students arrive at college, having developed that instinct on their own as kids -- taking things apart, breaking things, asking questions, maybe having curious parents. Instead, the emphasis in teaching physics is almost purely on the math. Certainly, what defines physics as a unique discipline is the interest in studying problems that lend themselves to mathematical analysis. Solving the textbook problems involves identifying the equations corresponding to the wording of the problem, then solving the equations. That's a skill, but it's not really physics. I got through my physics courses on the strength of my math skills, but was extremely fortunate to have picked up the empirical half of physics on my own, through my hobbies, and from the curiosity about nature that my parents encouraged. But if someone lacks that background, I could see them being good at math, and maybe getting a good way through school physics, but never really getting physics as an end unto itself.
UrMomReadsHN 12y ago
I enjoy math and I hate physics. :)
tim333 12y ago
There's a lot of physics that isn't maths - more visualising how stuff works. Feynman's quite interesting talking about it here https://www.youtube.com/watch?v=obCjODeoLVw https://www.youtube.com/watch?v=obCjODeoLVw
- DavidWanjiru 12y ago
  I remember in high school when I was in Form 3 (the penultimate high school class in Kenya, typically at age 16, give or take, more give than take), we were taught about wave interference and the double slit experiment. As a thought exercise, our physics teacher verbally explained various scenarios and asked us what would be observed. In one such scenario, alternating dark and bright lines would be observed, and I was the only one in my class who could visualize it. He took to calling me The Thinker henceforth. Tl;dr? That whole visualizing thing in physics? IKR?
nichochar 12y ago
I disagree so much! Math in physics (at least most of the physics I have done, which covers classical 19th century stuff mostly) is just a tool, if you can take a shortcut, take it! If you can approximate and cheat, do it! What matters in physics is the path from observation to modeling. Math is but a tool. Now I agree that the math gets rather solid, but it's nothing compared to real math at an equivalent level. I think my experience is particular because in France where I studied, you study both in parallel very intensively. So the math in physics always kind of seems trivial to you... But still my best physics teacher taught me that it was way more about the "feel and model" than the "exactly prove" that mathematics consists in. Gosh I miss those days :)
S4M 12y ago
Funny you should say that. During my undergraduate, I got almost fired from my University for being one of the top students at maths and one of the worse in physics - it was in France, a bit different than in the US. I recall that a physics chapter would start by "we take the Maxwell equations as [complex formulae]..." and for the life of me I wasn't able to understand them, or see where the teacher took that from. On the other hand, maths seemed more logical, and even now - almost 15 years later - I can correctly recall my undergraduate maths classes, because I have them so well ingrained in me, because I could understand how various ideas connected to each other.

by ta75757 12y ago

MarkPNeyer 12y ago

i was a physics major, too. the student in our year who was best at math had trouble with the "hand wavy" stuff we'd do. "well, this term is basically zero, so we'll just remove it" and then she'd pull her hair in frustration, like "how can you just do that? how is it still valid?" it wasn't enough to tell her "well it still gives us the valid results" - she had to be able to interpret every portion of an expression and then make intuitive sense of it. at first i was annoyed with this habit of hers, but eventually i started doing it to. for a lot of really math-minded people, hand waviness is anathema, and physics was full of "2 + 2 = 5 for sufficiently large values of 2, so we'll just assume that to make things easier"

_pius 12y ago
"well, this term is basically zero, so we'll just remove it" and then she'd pull her hair in frustration, like "how can you just do that? how is it still valid?" I've tried to teach friends with that hangup and found it difficult. Those people weren't good at math, though. I feel like with mathematicians, you should just be able to explain with limits.
- sedachv 12y ago
  > I feel like with mathematicians, you should just be able to explain with limits. Assuming the limit exists without actually proving the sequence converges is going to produce total junk. Jaynes spent a good portion of Probability Theory illustrating this.
  - _pius 12y ago
    I'm just talking about using the concept of limits as a teaching tool, not assuming a particular limit exists.
    - sedachv 12y ago
      Yes, this is why the mathematicians are pulling their hair out! You can't just drop terms when you feel like it.
TeMPOraL 12y ago
I feel that the right approach (at least it worked for me) is to tell the matematician - "see, this term is very close to zero for all practical inputs we can see in real life (proof of which will be left as an exercise for you), so - as you can see from the structure of the equation - we can safely drop it without introducing any significant error to the end result. Yes, the result will be a little bit less accurate; no, no one will notice. And if you happen to encounter a high-energy (or whatever) problem, you can always go back and use the full equation". Explicitly accepting that each handwave introduces errors and imprecision but that sometimes those errors are below what we can measure (or care about) should be acceptable enough for a math-minded person.

enjo 12y ago

Physics is applied math and I think that is an important distinction.

sedachv 12y ago
^ This. I ended up majoring in pure mathematics as an undergraduate after finding out that applied mathematics courses had too much material to memorize after finding out that physics courses had too much material to memorize. Pure math was so much easier.
- phkahler 12y ago
  You and the person who started this thread seem to think that way. I find there is just as much to memorize in math. fields, rings, groups, and all sorts of things. Oh and those greek letters. I like math and physics and stuff but I never thought there was significantly less memorization in math. Calc 2 techniques of integration and then DiffEq seemed like a lot of special cases that had unique solutions we had to remember.
  - sedachv 12y ago
    > fields, rings, groups, and all sorts of things. Each of those is just a definition and a handful (literally like 5 or 6) of axioms. If I memorized the axioms and a few key theorems I could usually derive everything else in the homework and on the exams. Most mathematical objects have very similar structure and the rest is just maps (morphisms) between them. > Oh and those greek letters. That's actually a very valid point. It took me a few years after graduating to realize how much myself (and I suspect many other students) are hampered by not knowing the notation well enough. Most people just assume you (and they) know what it means and never think about the actual definition and ambiguities. Even not being able to pronounce Greek letters definitely makes you less able (or at least less confident) to reason with them. > Calc 2 techniques of integration and then DiffEq seemed like a lot of special cases that had unique solutions we had to remember. That's the applied math part of calculus. The pure side is just "here's a compact/open/whatever set, prove for any point in it this property holds." Then you find out no one cares about either and it's all just numerical algorithms.

Iftheshoefits 12y ago

Math is certainly required to understand the theory and to synthesize experimental observations into a working model, but I wouldn't put it at more than 50-60%. Most of the math is fairly basic relatively speaking, even at the highest levels of physics.

soup10 12y ago
Relative to what lol. What other applied field has more advanced math?
- Iftheshoefits 12y ago
  I don't know about other applied fields but I was referring to the field of math itself with that remark.
- sedachv 12y ago
  Economics and quantitative finance.
- ArkyBeagle 12y ago
  I didn't get that far in math, but in physics classes after Junior Physics Lab , I once or twice questioned the assumptions. There's always a theorem you don't know about. There is a lot to math.

deeviant 12y ago

I would say math is necessary but not sufficient to be successful in physics. Also, if somebody has the aptitude but not the drive, failure can certainly be an option.

Micaiah_Chang 12y ago

There are some skills in physics which are sort of foreign to the math method of problem solving. (Speaking as a physics major) For example, picking a nice reference frame in simple mechanics problems is something that a physical intuition is good for. Same with spotting symmetries in an EM problem. Also, in physics you need to have a good grasp of what to ignore because they have only a small effect on the solution or because it operates on a different scale (fringing effects, transient solutions in ODEs), which often relies on a very hand-wavey type of reasoning. Essentially, physical intuition often does not map to mathematical intuition I have not taken enough math to actually speak for them; this is mostly gleaned from talking with math major friends and my own speculations.

jules 12y ago
I majored in math and physics. The same kind of intuition that you use for physics you also use for math. In physics you may call it choosing a reference frame, in math you call it choosing a coordinate system. At least for me it's exactly the same kind of thinking. You hit the nail on the head here though: > Also, in physics you need to have a good grasp of what to ignore because they have only a small effect on the solution or because it operates on a different scale (fringing effects, transient solutions in ODEs), which often relies on a very hand-wavey type of reasoning. Physics is often taught in an exceedingly vague and hand-wavey way. Physics students have to learn to ignore that nagging feeling that something is not quite right. This is impossible for a mathematician. A mathematician wants to cleanly separate the math from the problem that is being solved using math. The problem specification consists of a list of assumptions, and the solution of the problem consists of 100% rock solid math. Physicists weave the two together, so that in the end it's often not clear what is actually being assumed. Furthermore, it's usually not explained based on which experiments those assumptions are justified. A counterexample is special relativity. There it's clearly assumed that the speed of light is constant, and the experiments on which that assumption is based are explained, and from there it's mostly logical deduction. In other topics that is sadly not the case. I would love a physics education where you start with the experiments and work from there, instead of saying "Bam! Here are Maxwell's differential equations. Now deduce things from that based on hand-wavey arguments". I don't mean having the students perform the experiments themselves, just describe what somebody else did and what the results were, and why that led people to believe that the laws of physics are as they are. To make time for that, we should remove the endless by hand solving of special cases of special cases. We live in the 21st century. Instead use numerical methods everywhere, which easily tackle the general case. Got n electrons with initial positions and initial velocities, and you want to see what happens? No problem. /rant

dilap 12y ago

a lot of it is just cultural approach. math people tend to like to rigorously define everything they're doing, and work from there. physics is more like "what can we make up and fudge and twist and bend and then get the right answer." there's a lot of people who aren't as comfortable working in that less-defined context. some of this is maybe inherent to the aim of physics, some of it is just physics machismo culture, and could be better, imo. (i was a physics and math major at oregon.)

digikata 12y ago
I don't think it's just cultural. Ultimately in physics you are often faced with a pile of observations from nature that you have to make sense of. Vs math, where you usually have a mass perfectly defined err.. well math that you're trying to build forward upon. I think the best advances in both math and physics are made with people with an excellent grasp of when to move forward with existing constructs, and when to start shaping new ones...
- dilap 12y ago
  totally agree -- some of it is inherent to the endeavor of physics. but some of it is just hazing...

dxbydt 12y ago

True, but a lot of chemistry is mostly math too, and I flunked organic chemistry the first time. I think its because there is some domain knowledge involved in these subjects, which you have to actually care about. I don't particularly care which element has how many isotopes and what the valency is and how many other elements it can bond with, though I did memorize the atomic weights of all the elements in the periodic table and Avogardo number and few such stats. Those things helped a little, because I was ultimately able to pass my chemistry exams just by solving the numerical stuff and ignoring the chemical stuff. I handled physics in same fashion . There's something called the distance equation, where you can express the distance travelled by particle in terms of velocity and acceleration. We had to simply memorize that and use it in problems. I forgot what it was in the exam. So I just derived it from definitions. The teacher was quite surprised, because at that stage we hadn't been taught calculus, so how did I derive it ? Well, I had solved calculus problems by myself, so I just did this - http://pastebin.com/T6PrePh8 http://pastebin.com/T6PrePh8 These things helped me get by.

delian66 12y ago
>> I forgot what it was in the exam. So I just derived it from definitions. Hah, I did the same :-) ... unfortunately I also forgot the conventional names, and just used 's' (for speed) instead of 'v', and 'd' (for distance) instead of 's'. My teacher did not object the derivation at all, but told me that the results are wrong, because of the letters used ... Well, point taken - now, I try to pay extra attention and memorize idiosyncrasies like naming conventions ... it saves time when communicating with others.
- mirchiseth 12y ago
  That reminds me of a sessional (mid semester exam in India) when I got confused on speed of light being 3x10^8 m/s or 3x10^9 m/s. Strange are the ways of mind. I knew the relation between c and electric constant and magnetic constant. So derived it from that.
cli 12y ago
Organic chemistry is the least or one of the least math-intensive chemistry subjects at the undergraduate level.

s-phi-nl 12y ago

Note that he says "I wasn't particularly good at history or physics" (emphasis added), not "I was not any good at physics." As other comments point out, there is enough to physics besides math that someone (who was good at math) could easily do well in physics without being considered exceptional.

analog31 12y ago

I was a math + physics double major in college, plus I was also deeply into programming, electronics, and music. In my view, the starting point for physics is a deep curiosity about how things work. But I'm not sure that aspect of it is ever taught. Rather, it's assumed that good physics students arrive at college, having developed that instinct on their own as kids -- taking things apart, breaking things, asking questions, maybe having curious parents. Instead, the emphasis in teaching physics is almost purely on the math. Certainly, what defines physics as a unique discipline is the interest in studying problems that lend themselves to mathematical analysis. Solving the textbook problems involves identifying the equations corresponding to the wording of the problem, then solving the equations. That's a skill, but it's not really physics. I got through my physics courses on the strength of my math skills, but was extremely fortunate to have picked up the empirical half of physics on my own, through my hobbies, and from the curiosity about nature that my parents encouraged. But if someone lacks that background, I could see them being good at math, and maybe getting a good way through school physics, but never really getting physics as an end unto itself.

UrMomReadsHN 12y ago

I enjoy math and I hate physics. :)

tim333 12y ago

There's a lot of physics that isn't maths - more visualising how stuff works. Feynman's quite interesting talking about it here https://www.youtube.com/watch?v=obCjODeoLVw https://www.youtube.com/watch?v=obCjODeoLVw

DavidWanjiru 12y ago
I remember in high school when I was in Form 3 (the penultimate high school class in Kenya, typically at age 16, give or take, more give than take), we were taught about wave interference and the double slit experiment. As a thought exercise, our physics teacher verbally explained various scenarios and asked us what would be observed. In one such scenario, alternating dark and bright lines would be observed, and I was the only one in my class who could visualize it. He took to calling me The Thinker henceforth. Tl;dr? That whole visualizing thing in physics? IKR?

nichochar 12y ago

I disagree so much! Math in physics (at least most of the physics I have done, which covers classical 19th century stuff mostly) is just a tool, if you can take a shortcut, take it! If you can approximate and cheat, do it! What matters in physics is the path from observation to modeling. Math is but a tool. Now I agree that the math gets rather solid, but it's nothing compared to real math at an equivalent level. I think my experience is particular because in France where I studied, you study both in parallel very intensively. So the math in physics always kind of seems trivial to you... But still my best physics teacher taught me that it was way more about the "feel and model" than the "exactly prove" that mathematics consists in. Gosh I miss those days :)

S4M 12y ago

Funny you should say that. During my undergraduate, I got almost fired from my University for being one of the top students at maths and one of the worse in physics - it was in France, a bit different than in the US. I recall that a physics chapter would start by "we take the Maxwell equations as [complex formulae]..." and for the life of me I wasn't able to understand them, or see where the teacher took that from. On the other hand, maths seemed more logical, and even now - almost 15 years later - I can correctly recall my undergraduate maths classes, because I have them so well ingrained in me, because I could understand how various ideas connected to each other.