- 01 Sep '09 15:12 / 1 editIn another thread this issue has come and I already given some of my views on it. But as I feel that it is somewhat marginal in that context I decided to start a new thread.

Ever since Galileo we know (loaded term so bomb away at this notion that I'm willing to argument on it) that the right way to do physics is with mathematics. There is no denying, there is no discussion and there is no single shred of controversy in this point. If you think you do, once again just bomb away that I'm willing to discuss things in this point too.

The problem is that a lot of people that this is an elitist, snobbish approach to Physics and so try to contest it. Most of these people, from my personal experience, are armed with the very dangerous weapon of pop science and/or some courses physics trimmed down to people that won't follow a career in physics. Since they are relatively smart in their area of expertise, and with good probability they got good grades in those two or three trimmed down versions of physics they feel they got a feel for the subject.But the hard truth is that they don't have a feel for the subject (I'm not counting highly exceptional people on this analysis).

Physics is basically modeling real world events (this is an oversimplification to which I don't fully agree but it's enough for our current discussion I think. But if you feel like arguing about this too I'm all for it.) and this modeling is done in 99.999999999999% of the cases using differential equations. Ordinary, partial, linear, nonlinear, scalar, vectorial, tensorial are the kinds of equations that appear and if you do have a feel for physics you should have a feel for those types of equations (this is a necessary but not sufficient affirmation). So if you can't understand solutions of ordinary differential linear equations you certainly don't know much about physics. Of course you can have some notions, and solve some textbook exercises of physics (nevermind the fact the real world isn't very much like the textbook world) but in what concerns real physics you are very much lacking if you can't even do that highly simple thing: to interpret the solution of an ordinary linear differential equation. As an example I leave this:

Given y=y(x) solve py''=-qy where y'' denotes the second derivative of y in order of x and p, and q are constants.

Can you see what that problem is about? Can you solve that problem even without knowing what it is about? Of course you can. Just consult any elementary book on ODEs. After arriving at the solution can you understand the why of the solution?

Answer truthfully to those questions and then ring me a bell. When I propose this I'm not proposing it with an elitist flavor (at least not that I'm aware of), but I do it to urge people to have a knowledge that is informed, formed, responsible, and self-critical. Of course I know we don't have time to do everything we like and some things just have to be done in a more superficial way, but what I'm arguing for in here is that at the very least people do have the conscious of superficiality of some areas of their knowledge.

To finalize I'll just leave three links that stress the need of Math in Physics:

http://math.ucr.edu/home/baez/crackpot.html

http://insti.physics.sunysb.edu/~siegel/quack.html

http://insti.physics.sunysb.edu/~siegel/warning.html

Siegel's page also have some other interesting articles:

http://insti.physics.sunysb.edu/~siegel/history.html

http://insti.physics.sunysb.edu/~siegel/mine.html

http://insti.physics.sunysb.edu/~siegel/curriculum.html - 01 Sep '09 16:24

I don't agree.*Originally posted by adam warlock***So if you can't understand solutions of ordinary differential linear equations you certainly don't know much about physics.**

I've met too many physicists who know the equations, anderstands the maths, but cannot make the connection to everyday world.

I've also met people without much math that can see things in perspective, make parallels, and understand why things in the world behave like they do.

But of course, without math, physics cannot progress. But without common sense, it's just equations, nothing more. Yet, how many of us progress physics?

And remember, how much physics are taught in school to pupils not yet knowing anything of ODE? - 01 Sep '09 16:47

I think the main difference between physics and economics is the relative ease and the precision with which physicists can measure the things they are describing. It's much harder to "experiment" with a society.*Originally posted by Palynka***You think that's bad, you should try economics. Everybody is an expert and we also have dynamic models.**

I expect, however, that with increasing computing power numerical simulations will become increasingly relevant for economics and may provide a reliable model of real societies much akin to a laboratory for a physicist. - 01 Sep '09 16:47

Common sense is a way of coping with things we do not understand very well. It's also a way of justifying an opinion by picking the best sounding metaphor.*Originally posted by FabianFnas***I don't agree.**

I've met too many physicists who know the equations, anderstands the maths, but cannot make the connection to everyday world.

I've also met people without much math that can see things in perspective, make parallels, and understand why things in the world behave like they do.

But of course, without math, physics cannot progress. B ...[text shortened]... d remember, how much physics are taught in school to pupils not yet knowing anything of ODE? - 01 Sep '09 16:54 / 2 edits

I certainly agree that economics cannot be a 'hard' science in a very strict sense. At least, not with the current level of technology, as you mention. That said, it's interesting how much economics has evolved since it's attempts to move towards harder sciences and, especially, how much it was able to*Originally posted by KazetNagorra***I think the main difference between physics and economics is the relative ease and the precision with which physicists can measure the things they are describing. It's much harder to "experiment" with a society.**

I expect, however, that with increasing computing power numerical simulations will become increasingly relevant for economics and may provide a reliable model of real societies much akin to a laboratory for a physicist.*reject*. I think the way can only be forward.

But physics has long ago left the philosophical approach while economics only very recently (by other hard sciences standards) did. This means that we still have generations of economics graduates who think in the old-school way and 'common sense' (as I defined it before) still rules the day in politics and the media when talking about economics. - 01 Sep '09 17:12

My experience is that I'm usually quite successful in explaining how things are, but when I am asked*Originally posted by Palynka***So, to get back to physics, I think a physicist MUST know the math. Hopefully, some will also know how to explain it using 'common sense' so that the non-physicists can have an idea about what's going on.***why*things are so I often end up saying "you need some math for that". - 01 Sep '09 20:15 / 1 editI'm still not convinced that math is everything in physics. Math in physics describes things in an ideal world.

A mathematical sphere is easily described in an equation, but still there are no mathematical spheres in nature, only close. With this I say, that no mathematics can exactly describe real phenomena, only close.

Does this matter? Newton described gravitation in a sole equation. Good enough. Einstein described it better. Good enough Where's next step to exactness? Can it be described exact? In my opinion no, only close.

In singularities, there are no math. The BigBang when t=0 the math of relativity and math of quantum theory gives different results, yet it is the same singularity. Same with a BlackHole singularity. Close but not exact.

Math is important, but we can describe much in physics without math. In my lectures to young people, they understand difficult things without math. But do they understand everything to 100%? No. Can math describe everything with 100%? No. Can things precisely described with math be understood by these young people? No.

The question asked by so many physicists: "What if...?" is needed more than math to begin nyw branches in physics. Math isn't everything.

IMHO - 02 Sep '09 00:17

I only have a couple semesters of calculus under my belt which isn't much and has long been forgotten. My hat is off to the mathamajicians that are able to use math to prove and even predict things in the quantum world. It is a discipline I wish I had kept up on.*Originally posted by KazetNagorra***My experience is that I'm usually quite successful in explaining how things are, but when I am asked***why*things are so I often end up saying "you need some math for that". - 02 Sep '09 02:25 / 2 edits

I believe that mathematics is everything, the rest is just nomenclature.*Originally posted by joe beyser***I only have a couple semesters of calculus under my belt which isn't much and has long been forgotten. My hat is off to the mathamajicians that are able to use math to prove and even predict things in the quantum world. It is a discipline I wish I had kept up on.**

and having said that ,I feel that you all should know ( and probably do) that I am but a court jester in both disiplines... - 02 Sep '09 21:38

Wanting to learn and thinking (and thinking about thinking) are very important things. From what I read from you the posers forum you certainly don't lack the drive in both. Thus never count yourself out.*Originally posted by joe shmo***I feel that you all should know ( and probably do) that I am but a court jester in both disiplines...**

[shamelessplug]

By the way check these two blogs of mine (the first will certainly be helpful to you):

http://climbingthemountain.wordpress.com

http://physicsfromthebottomup.blogspot.com

[/shamelessplug] - 02 Sep '09 21:45

But you still can keep up on it if you have the time. Just check this out: http://farside.ph.utexas.edu/teaching.html*Originally posted by joe beyser***I only have a couple semesters of calculus under my belt which isn't much and has long been forgotten. My hat is off to the mathamajicians that are able to use math to prove and even predict things in the quantum world. It is a discipline I wish I had kept up on.**

Besides the two texts on quantum mechanics you can also find texts by this author on almost every major field of Physics.

If you feel that you don't like this author you can always check http://www.theassayer.org/cgi-bin/asbrowsesubject.cgi?class=Q and browse the sections of maths and physics and feel any gaps that you feel.