Relationship between maths and physics

[paralleloscope]

Thanks mkrnhr, had a browse through it on google books and first impression was that even this seemed too complicated. Part of that may be that is in english and translation of terms in this area makes it extra steep. But perhaps english->danish comprehension may even be the way to go about it. As I uttered yesterday when asked why I wasn't speaking danish to the examinators (on an english spoken multimedia course I'm in where the teachers are danish); "My IQ drops like 25 points when I speak danish". :D , which may actually be true, that the danish thinking "I's" really do comprehend in a very different way. (hope that made sense)

My secret hope has been to find material produced by someone who understands the mathematical learning disabilities that 'artistic' people may suffer, and so can construct better explained examples. As for example substantiating between math<->physics. (which some books do but in a sort of detached and logically strict way)

 

[StrangeCaptain]

Thanks mkrnhr, had a browse through it on google books and first impression was that even this seemed too complicated. Part of that may be that is in english and translation of terms in this area makes it extra steep. But perhaps english->danish comprehension may even be the way to go about it. As I uttered yesterday when asked why I wasn't speaking danish to the examinators (on an english spoken multimedia course I'm in where the teachers are danish); "My IQ drops like 25 points when I speak danish". :D , which may actually be true, that the danish thinking "I's" really do comprehend in a very different way. (hope that made sense)

My secret hope has been to find material produced by someone who understands the mathematical learning disabilities that 'artistic' people may suffer, and so can construct better explained examples. As for example substantiating between math<->physics. (which some books do but in a sort of detached and logically strict way)

I am not a strictly artistic sort of thinker, but it is an aspect of my personality even though I come to appreciate more and more what solid analytical thought can do for me and my various daily tasks. As it is a part of my personality, I sometimes find a visual image or idea helps me give flesh to an abstract idea in math/physics. That visual image then helps me be mroe comfortable with the situation. Then I still may not understand all of the manipulations I may be doing to solve problems, but that comfort level helps me move one.

Example: Years ago when I first saw derivatives, they were terrifying. My teacher told me to memorize one line and think about it until I understand it:

"The derivative of a function at a point is the slope of the tangent at that point."

I memorized it and looked at about 20 pictures illustrating that concept and made sure I understood what each word in the sentence above means. Then I made my little visual image. I am standing on a hill. There is a function that describes the surface of that hill, and there is a derivative at each point where I could be standing on that hill. The derivative tells me how steep that hill is where I am standing.

So... Two ideas... Making a verbal description of the math you are trying to understand it if that appeals to you... Making a visual image of the math you are trying to understand if that appeals to you...

If you can not do this, then there may very well be a more primordial concept that you have not grasped that is stopping you. That is one thing tricky about math and about phyics. Sometimes you can not move on until you improve your understanding of something that was basic to what you are now trying to work on. It can feel like a loss of time to go back to something that you already did in the past, but if you can not move on without it, the quicker you go back to it, the quicker you can move on.

Then there is trying to identify what that primordial idea is that is lacking... That can be tricky, and that can be where a teacher can help save some time.

 

[paralleloscope]

Thanks alot for you thoughts Patience, those are great examples both your derivative imagery and comprehension methods. I think both doing a visual and a verbal discription in tandem at each step will help a lot compiling a vocabulary in aid of understanding.

If you can not do this, then there may very well be a more primordial concept that you have not grasped that is stopping you. That is one thing tricky about math and about phyics. Sometimes you can not move on until you improve your understanding of something that was basic to what you are now trying to work on. It can feel like a loss of time to go back to something that you already did in the past, but if you can not move on without it, the quicker you go back to it, the quicker you can move on.

That's definitly true, and a step you have to be vigilant about if your adaptive mind is running the impatience loops or is feeling sorry for itself not grasping something that seems simple.

 

[ec1968]

Hi Parallel

Are there specific topics in physics that you struggle with more than others, or is it a generalised difficulty with differential calacuus?

The reason I ask is that, extending my earlier comments, there are some very good texts which explain some physics topics without the use of maths. If you could use those as your starting point and really get to grips with the underlying scientific principles of a topic before you even look at the mathematics, you could then move on to introducing the maths. Because you know the concepts, following the maths line by line will be easier, as you'd know what it is representing.

Sounds so easy when written down like that. As I said, I failed my astrophysics final, so I know how difficult it is in reality. Some of my classmates were able to learn the maths by rote. One friend in particular didn't understand any of the physics, but he knew all of the maths, and always did really well in exams. For example, ask him to explain mass energy equivalence in relativity and he couldn't do it, but he could prove E=MC^2 from first principals because he had memorised the maths line-by-line. I was the exact opposite. I could explain concepts in written English, but the proofs, and solving problems, were always really difficult for me. I don't know what it is like now, or at other Universities, but at QUB in the late 80s/early 90s the physics exams were slanted towards the maths side of things which didn't suit me at all!

It sounds arrogant to say it but I found my Master's degree in electron microscopy much easier than my BSc in physics. I still read physics journals and textbooks, but am quite content to skip over the maths as I don't need to know it when I'm doing it for recreation!

 

[paralleloscope]

Hi Parallel
Are there specific topics in physics that you struggle with more than others, or is it a generalised difficulty with differential calacuus?

The reason I ask is that, extending my earlier comments, there are some very good texts which explain some physics topics without the use of maths. If you could use those as your starting point and really get to grips with the underlying scientific principles of a topic before you even look at the mathematics, you could then move on to introducing the maths. Because you know the concepts, following the maths line by line will be easier, as you'd know what it is representing.

Hi ec1968
In general I am confused and daunted by long proofs (which I haven't seen with good written explanation other than about the mathematical operations) and formula chains. In physics my main difficulty would be visualizing the story told in formulas (as Patience nailed above), not so much understanding the physical relationships when written out in words, but to reconnect that with formulas.

Sounds so easy when written down like that. As I said, I failed my astrophysics final, so I know how difficult it is in reality. Some of my classmates were able to learn the maths by rote. One friend in particular didn't understand any of the physics, but he knew all of the maths, and always did really well in exams. For example, ask him to explain mass energy equivalence in relativity and he couldn't do it, but he could prove E=MC^2 from first principals because he had memorised the maths line-by-line. I was the exact opposite. I could explain concepts in written English, but the proofs, and solving problems, were always really difficult for me.

This tendency towards rote learning is quite frustrating; it's a divorce of putting things in relation and hinders real teaching and learning. Can't find the quote from the C's that says something like; '4D StS have made precautions against many of us learning algebra' and I guess that also goes for many of those who have flair for algebra connecting it's relationships the other way.

 

[mkrnhr]

Maybe I'm from an old school, but I think that the study of physics requires mathematics. Physics describe phenomena (but usually do not explain them, that's the role of philosophy) and even the relationship between physical phenomena and mathematics is a philosophical question.
Physics are based upon measurements, and how those measurements relate to other measurements. And the way you describe that relationship is through mathematics. For instance, a quantity A is the rate of change of a quantity B relatively to a quantity C. C can be time, position and so on. This means that dB/dC=A.
This little equation describes a behavior of your measurables relative to each others. Then, in order to find B if you are given the variation of A through C, you can transform this equation into an integral and deduce B(C). Here is were calculus plays a role. Mathematics are a language after all, and that language describes what is observed. If you understand what a derivative is, that an integral is a continuous sum, it becomes a tool to express what happens between your measurables.
Why mathematical deduction allows to anticipate measurements is what defines our reality as we observe it so far. Why it is so is IMHO a mystery :)
My subjective view on the matter is that you can know about some physical phenomena by what happens during experiments (what happens in the Young slits experiments for example) but in order to describe the measurements you need some mathematics (for instance complex numbers to describe the spatial distribution of the diffraction pattern in the detector plane).
Feynman lectures are a good example on how to translate mathematical phenomena into spoken words. However, without mathematics there is nothing to translate, OSIT.

 

[darksai]

I am wondering if anybody can help me; hopefully this topic may help inform others also.

In my school days I was relatively gifted at maths (nothing special) and I did enjoy it. I enjoyed other subjects more, however, and pursued philosophy for my degree.

Now I am trying to get myself up to a level in maths and physics from where I can try to understand some of the more difficult concepts and the maths.

The approach I have been considering is just to work my way up in terms of maths so I can start to get to University level. In terms of physics I have bought one or two 'popular science' books which were rated very highly just so that I can start to have a background into some of the topics (.e. relativity).

I wondered if anyone can give me some advice regarding whether this is a good route to go down or if there may be a more fruitful avenue to go down in terms of really developing my understanding of the subjects.

Also, I am particularly interested in understanding how maths relates to physics, so might anyone recommend me a good way to start understanding this also?

Thanks in advance.

If I may ask, why exactly do you want to study maths and physics? Do you want to know the subjects to be able do complex calculations or understand them to apply to everyday life?

 

[ec1968]

Maybe I'm from an old school, but I think that the study of physics requires mathematics. Physics describe phenomena (but usually do not explain them, that's the role of philosophy) and even the relationship between physical phenomena and mathematics is a philosophical question.

Mkrnhr, I don't think that you are from any 'old school' at all - you are absolutely correct imho. In fact not only does the study of physics require mathematics, but mathematics is absolutely essential to the study of physics. The problem that arises, however, that made studying for my degree in physics so difficult for me when I was in college, is that some lecturers and textbooks race ahead with the mathematics with little or no explanation of the physical concepts underpinning the formulae. So you'd get a page and a half of equations leading to E=MC^2 and one little comment like 'and there we have Einstein's famous mass-energy equivalence formula'.

Describing mathematics as a language is hitting the nail on the head. Some of us, however, need a lot more help in translating the language than is often given in class. The teachers on my postgraduate degree were much better at that translation that the teachers on my BSc(Hons) course.

 

[mkrnhr]

Describing mathematics as a language is hitting the nail on the head. Some of us, however, need a lot more help in translating the language than is often given in class. The teachers on my postgraduate degree were much better at that translation that the teachers on my BSc(Hons) course.

I agree that when the teaching is not balanced enough, the whole thing becomes difficult to follow. I personally gave up theoretical physics (quantum field theories) because of very annoying lecturers who didn't seem to understand what they were talking about. And I hated solid states physics because I hated a nazi-type teacher as well :P

Joke aside, there is a new thread on the relationship between physical sciences, philosophy and consciousness, that may be pertinent to the subject of the actual thread: http://cassiopaea.org/forum/index.php/topic,30378.0.html