# Nobody complains about physicists' math?

1. Nov 9, 2007

### jostpuur

One might think that you can find anything on the internet, but I haven't found any site where somebody would be complaining about physicists' way of using mathematics. I wonder why. Wouldn't physicists math be an easy thing to make fun of?

2. Nov 9, 2007

### Mororvia

If it describes reality, why would it be made fun of?

3. Nov 9, 2007

### zoobyshoe

"What do ya mean, funny? Let me understand this cause, I don't know maybe it's me, I'm a little ****ed up maybe, but I'm funny how? I mean, funny like I'm a clown, I amuse you? I make you laugh... I'm here to ****in' amuse you? What do you mean funny, funny how? How am I funny?"

4. Nov 9, 2007

### Jimmy Snyder

You mean like 'Quantum physics is classical physics in the limit as zero approaches h?'

5. Nov 9, 2007

### mgb_phys

In physics 0/0 or infinity/infinity cancels - it's obvious!

6. Nov 9, 2007

### jostpuur

This (or things like this) happened often in physics lectures. A physicists wants to use the derivative rule of composite functions

$$D_u f(x_1(u), x_2(u)) = (\partial_1 f) x'_1(u) + (\partial_2 f) x'_2(u)$$

but of course he wouldn't use already proven simple rigorous theorem. Instead he does this with with "differentials". First the lecturer assumes that this is clear

$$d f = \frac{\partial f}{\partial x_1} dx_1 + \frac{\partial f}{\partial x_2} dx_2$$

and then divides by du, and gets

$$\frac{df}{du} = \frac{\partial f}{\partial x_1}\frac{dx_1}{du} + \frac{\partial f}{\partial x_2} \frac{dx_2}{du}$$

which is the desired result.

Q: What precisely is the dx and du?

A: Well they are some kind of infinitesimal quantities, but there's no need to be rigorous here, because this is physics.

Q: Why was the result derived like that?

A: Well mathematicians would have probably done this more complicatedly with epsilons and deltas, but a simpler proof such as this is sufficient for us, because this is physics.

7. Nov 9, 2007

### Gilligan08

Goodfellas? What movie is that from?

8. Nov 9, 2007

### jostpuur

The conclusion

$$f(x)=1+Ax+O(x^2)\quad\implies\quad f(x)=e^{Ax}$$

is among the most unbelievable ones.

For example when you solve a quadratic equation, you can write the expression

$$x^2 + Ax$$

in a form

$$(x+A/2)^2 - A^2/4.$$

Here you write the old expression in a different new form. Similarly, once a particle physicist is given a function

$$f(x)=1 + Ax+O(x^2),$$

he can write it in a form

$$f(x)=e^{Ax}.$$

9. Nov 9, 2007

### ZapperZ

Staff Emeritus
1. Does this violate any part of mathematics, within the confines of what it is being used for?

2. Does this give a consistently correct description of the system it is describing?

Zz.

10. Nov 9, 2007

### jim mcnamara

I think somebody's cage got rattled, hmm, Zz?

11. Nov 9, 2007

### ZapperZ

Staff Emeritus
Someone is in a cage?

Zz.

12. Nov 9, 2007

### Integral

Staff Emeritus
AFAIK nearly all mathematicians laugh at the way Physicists do math. Of course, not nearly as hard as they laugh at the way engineers do math.
But this is so unsurprising that it is not discussed outside of Math dept coffee rooms. :rofl:

13. Nov 9, 2007

### Mk

Hey, physicists are the ones that always have to draw pictures before they can understand a problem :yuck:

14. Nov 9, 2007

### zoobyshoe

Yeah, That's Newton doing the Joe Pesci line from "Goodfellas".

15. Nov 9, 2007

### robphy

Maybe that's why some of us are physicists.
Somehow... maybe with luck or maybe with physical intuition... in spite of the physicist's sloppy and impatient mathematics, the physicist often gets the answer correct. (Certainly there are cases when the mathematics is just plain wrong and leads to nonsense... for [almost] everybody.)

I have encountered [overly-]mathematical colleagues who are too wrapped up in the math that they miss the physics under discussion.

I certainly appreciate the mathematical physicist who can use enough mathematics to show the physics [and its abstract structure]... but who is able [when pressed] to deliver the mathematical details.

16. Nov 10, 2007

### FredGarvin

Yeah. And we laugh at mathematicians at the way they try to talk to girls.

17. Nov 10, 2007

### Chi Meson

Wow, Newton's pretty good. Has he been in any movies himself? Didn't he host SNL way back?

18. Nov 10, 2007

### zoobyshoe

He used to work the Catskills every summer, and had an off-Broadway one man show one season that Johnathan Demme was interested in translating to film, but the deal fell apart in negotiation due to Newton's temper.

He does a great Brando, too:

"Bonasera. Bonasera. What have I ever done to make you treat me so disrespectfully? If you had come to me in friendship then this scum that ruined your daughter would be suffering this very day. And if by chance a man like yourself should makes enemies then they would become my enemies. And then they would fear you."

19. Nov 10, 2007

### G01

:rofl: I think I actually canceled infinity over infinity once on a optics test, and got full credit! :rofl:

20. Nov 10, 2007

### NeoDevin

to find a flux per unit area through an infinite plane we can do

$$\frac{1}{A}\int_S\Phi da$$

Where $S$ is the entire infinite plane, and $A$ is it's area.