big barrier to my ambitions in physics

Discussion in 'Physics & Math' started by ameda, Aug 1, 2004.

  1. ameda Registered Member

    Messages:
    5
    I used to study the nonmathematical portions of physics alot but eventually stopped, ive started to get into it again and maybe want to get my degree in it but one thing has always prevented me from doin it. I never thought that i could come up with the mathematical equations to do theoretical physics. It seems to me the only way to come up with them is through trial and error. Can someone tell me if this is the case and if not show me an easy example of how to take raw data and turn it into an equation that will describe all values of said data. I got A's in math but i could never actually apply it.
     
  2. Google AdSense Guest Advertisement



    to hide all adverts.
  3. MacM Registered Senior Member

    Messages:
    10,104
    I'm sure there is a better way for those knowledgable in mathematics but I always do it trial and error. I look at the data and see the freqeuncy of change in doubling, tripling or quadrupling and then try to decide what range of multipliers or exponents to use.
     
  4. Google AdSense Guest Advertisement



    to hide all adverts.
  5. AD1 Registered Senior Member

    Messages:
    249
    What is the extent of your mathematics and physics education? If you keep improving your numeracy and your understanding of physics (not non-mathematical physics) it will gradually make more sense, and you will eventually learn how to construct your own equations for describing physical phenomena.
     
  6. Google AdSense Guest Advertisement



    to hide all adverts.
  7. Firefly Registered Senior Member

    Messages:
    1,330
    What ARE the non-mathematical portions of physics??!
     
  8. orange Registered Senior Member

    Messages:
    207
    The more you study math and physics the more you will understand how to build equations. You have all you need - ambition!

    Personally, I don't trust trial and error. If you know your math, you should be able to do the whole thing right the first time.
     
  9. ameda Registered Member

    Messages:
    5
    By non math physics i mean just reading all the normal books youd find in a book store and not doin the problems in textbooks just reading them.

    I guess i just dont see it. Im sure your right in the fact that the more you study math then you can make equations and formulas, but i can solve any nonword prob in a math book but i still cant even begin to understand how to figure out equations and formulas that have not been developed before.

    I appreciate the feedback i hope there still is some hope for me.
     
  10. orange Registered Senior Member

    Messages:
    207
    Don't be so hard on yourself..

    Please Register or Log in to view the hidden image!

     
  11. ameda Registered Member

    Messages:
    5
    I have to be hard on myself i feel that i have to prove to myself that i can do this before i go to college because since i want to do theoretical physics and if i cant create formulas then there is no point in doin physics in college.
     
  12. shmoe Registred User Registered Senior Member

    Messages:
    524
    So you 've stuck with the "popsci" physics books? Avoiding textbooks and problem solving? It would be no wonder that you don't think your math skills have developed. Books aimed at the general public usually avoid exposing their readers to any math if possible (even ones about math!!). Without practice, you will never learn.

    What kind of courses have you completed so far, both math and physics?

    By "create formulas", what exactly do you mean? Be able to derive mathematical results like proving theorems? Fit some kind of curve to some test points? Something else? Any examples of what kind of problems you're having?
     
  13. ameda Registered Member

    Messages:
    5
    I said popsci and textbooks but i usually didnt do the problems in the text books.
    Besides thats not the prob, i can take a formula and solve it if i have the info to solve it. Ill try to put this as simply as i can. This is just to try to represent want im trying to ask while being simple yet not to easy. Take the Pythagorean theorem. Say i was Pythagoras and i had a right triangle with one side being 6 and the other 4 then the hypotenuse would be 7.21. With that knowledge how do i figure out the mathematical relationship between the 2 smaller sides and the
    hypotenuse. In other words how do i devise the theorem from the values of the sides.
    Im just asking how do ppl create formulas from data on things that do not already have formulas. Take string theory. String Theorists have to create new formulas because some of the concepts have not been explored yet.
    Hope this is enough, im sorry if im becoming a pain in the ass.
     
  14. shmoe Registred User Registered Senior Member

    Messages:
    524
    With just one triangle, you can't. With a page full of the lengths of the sides of various right triangles, you stare at them for a few hours looking for relations. You realize that only one angle is fixed, and knowing the lengths of the shorter two sides determines your triangle, an old friend from geometry. You also realize that your formula for the length of the hypotenuese, c, should be symmetric in the lengths of the other two sides, a and b. You try the simple cases of degenerate triangles if a=0, then b=c. If b=0 then a=c. Whatever formula you come up with should reduce to these. Then you look for other patterns in the data, if we double a and b, then c is doubled. This gives you further clues about the formula we want. At this point some experience will help you determine what possiblities remain for a formula, guess, check, and try to prove your answer is correct if possible.

    basic steps:
    1. is this related to anything I know already? What does that say about the current problem? Is this really just an old problem? Can we modify our problem so it looks more like an old one?
    2. Gather lots of reliable data
    3. stare at data
    4. drink coffee
    5. Any obvious patterns we can exploit?
    6. Look at the simplest cases, even if they are terribly simple
    7. stare at data
    8. Have nightmares about the problem
    9. More coffee. Data has burned it's image in your retinas, so it's best to work at night.
    10. Make guesses based on the above, especially the nightmare part. test and modify your guesses if needed. Get new data to test your guess. Try to prove your answer is correct.
    11. Try to convince a comitee futher work on your result is worth funding so you can afford more coffee and hopefully a grad student to brew or fetch it for you.

    I'm not certain exactly how Pythagoras and co. came up with their famous little theorem, but I'd expect some combination of the above. You can guarantee that they had plenty of practise working with already solved problems beforehand though. The best way to learn mathematics is by doing mathematics. Go back to the texts, solve the problems.
     
  15. James R Just this guy, you know? Staff Member

    Messages:
    39,397
    There's no systematic way to do that which does not involve at least some intuition about the problem. Suppose the two smaller sides are a and b, and c is the hypotenuse. You suspect there is some relationship between a,b and c. But what kind of relationship? Well, the easiest first assumption is that there is a linear relationship, such as:

    c = Aa + Bb

    where A and B are unknown constants. You have the following data from one triangle:

    a=4, b=6, c=7.21

    So, it would be possible, for example, that for all right-angled triangles:

    c=(0.3025)a + (1)b

    which works just fine for the one triangle you have. But if you try that formula for a different triangle (e.g. one with a=3,b=4,c=5), it doesn't work. In fact, with these two triangles, you could find another linear formula which would work, but you would find that it might not work once you introduced a third triangle. Once you discovered that, you'd have to throw the simple linear formula out the window and try something more complicated. So, perhaps:

    c<sup>2</sup> = Aa<sup>2</sup> + Bb<sup>2</sup> + Cab

    where, now, A, B and C must be determined using actual data. This exhausts the possibilities of a quadratic polynomial formula, since a,b and c must all have the same physical dimension of length.

    How do you find A,B and C, given a set of data? Well, there are a number of systematic methods which do not involve trial and error for doing that (e.g. the "least squares" optimization method). Using one of these methods you will discover that the following formula works for all right-angled triangles:

    c<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup>.

    This is Pythagoras's theorem. Of course, this is NOT how Pythagoras arrived at this formula. He did it using arguments based on geometry, an existing mathematical discipline.

    Similarly, modern mathematicians and physicists don't usually pluck formulas out of the air. They have a good idea, and then derive their formulae from already-known maths and/or physics. You asked about String Theory. String theorists use concepts already well-known in mathematics, but attempt to apply them to create a new physical model of the world. The idea came first, and it was quite a simple one: what if particles are not points, but loops? Then came the question: how could we describe the physics of these loops? Only then did people turn to the mathematics, and so string theory started to develop.

    To be a good physicist, first and foremost you need a good physical intuition, and the ability to form mental pictures of reasonably complex concepts. You also need to have some skill in mathematics, and the ability to translate ideas into mathematically rigorous forms. Some of these skills can be learned, but you generally need some aptitude to start with, along with an interest in the subject.
     
  16. MacM Registered Senior Member

    Messages:
    10,104
    I am not a mathematician but I have used polynomials numerous times to fit a curve. While the solution can do a very acceptable job for most pragmatic purposes you will find that ultimately once you extend your example beyond the applied limits of data in your solution that the results quickly falter.

    The most likely solution usually involves some natural sequence i.e. - the v^2/c^2 or mc^2, Pi*r^2, etc.

    I don't want to take this off topic or piss people off, so I won't even use the term, but in my own work I found the solution required a complex calculus integration.

    The encouraging point I want to make is I did so even though I don't perform calculus. So I would have to say the most important thing is the ability to visualize relationships.
     
  17. Fallen Angel life in every breath Registered Senior Member

    Messages:
    189
    yeah, i started a minor in physics and then had to drop the idea because of time constraints. but don't feel you have to have all the answers before you go. the coolest thing was when (under direction of the prof) i finally reduced the position function of an object from its quantum wave equation to a classical picture in a sort of realistic example. it all fits in beautifully together. it hurt my head for a bit, but i had no clue how to do that in high school. i didn't end up being a physicist, but with the background i now have i could figure out how to do it again. but it's all mathematics from now on, if you don't get that, it'll be difficult to figure out the current physical theories. and you can't destroy them if you don't understand them... <insert evil laughter here>... hope you like div, grad, curl

    Please Register or Log in to view the hidden image!

    (all of this coming from a non-physicist,non-mathematician so... basically no authority... but eh, it's my opinion)
     
  18. ameda Registered Member

    Messages:
    5
    I really appreciate all the responses, thank you very much. Im sure you are all right that it just takes practice and alot of deep thinking. I guess that if i dont develop the aptitude for deriving formulas then i can still make good money just plugging numbers into formulas. Although its not really about the money so much as discovering the workings of space and time that interests me. But i would be lying if i said that i dont want a physicists salary.

    Please Register or Log in to view the hidden image!

     
  19. Silas asimovbot Registered Senior Member

    Messages:
    1,116
    You want a physicist's salary?! What the hell do you think they earn?? Non-practical science is where you go for intellectual fulfillment, not a large bank balance.

    You can't do physics without the math. If you got straight As in math, I really wouldn't worry about it.
     
  20. Brandon9000 Registered Senior Member

    Messages:
    172
    Having gotten a couple of degrees in Physics, I suspect that your problem is coming from having only looked at popular treatments, rather than the real thing. I think that if you major in Physics, which will involve taking quite a large amount of math too, your concern here will become a non-issue. Honestly, I wouldn't worry about it. If you're interested in the subject, then study it, but do be aware that a major in Physics will require you to do your homework faithfully, both when you're in the mood and when you aren't.
     
  21. Pete It's not rocket surgery Registered Senior Member

    Messages:
    10,167
    Since when is physics not practical? Perhaps you're thinking of theoretical physicist academics?
     
  22. shrubby pegasus Registered Senior Member

    Messages:
    454
    physicists are the 14th highest paying profession here in colorado at something like an average between 81 and 83000 a year. tahts not too bad.

    as long as you are willing to put the effort in, you can be a physicist.
     
  23. Epsilon Prime Over Epsilon Registered Senior Member

    Messages:
    60
    therefore, we should all be CHEMISTS! WOOT!

    i mean, physicsists.


    anyway......
    (sorry for this random post -_-)
     

Share This Page