What are your favourite physics/mathematics misconceptions?

[PeroK]

Sure buddy. Whatever you say.

I've just worked out that you were talking about his law of gravity, not the speed of light.

That's then a grander version of the misconception, which I think used to be in the UK A-level physics syllabus. Which assumes, wrongly, that Newton undersood the connection between the propagation of gravitational attraction and the speed of light.

Newton had no conception that his action at a distance was related to the speed of light. That took until 1905.

 

[Hornbein]

Adolph Hitler believed the stars were made of ice.

 

[BWV]

unless you have a sample size >= 30, you can't do any statistics

 

[fresh_42]

unless you have a sample size >= 30, you can't do any statistics

I have heard from a med student who solved this problem with a scalpel!

 

[Frabjous]

Adolph Hitler believed the stars were made of ice.

And once again Godwin’s law stands

 

[berkeman]

And once again Godwin’s law stands

TIL (I had to look it up).

 

[Bystander]

TIL (I had to look it up).

TIL(me too).

 

[JT Smith]

TIL(me too).

Maybe this is an age/generation discriminator. Godwin's Law dates back to the era of Usenet forums.

I'm kind of surprised there is still a Physics forum. Hasn't pretty much everything transitioned to face book and the like?

 

[berkeman]

I'm kind of surprised there is still a Physics forum. Hasn't pretty much everything transitioned to face book and the like?

There is no LaTeX Guide on Facebook. QED.

 

[phinds]

Hasn't pretty much everything transitioned to face book and the like?

NO, NO, and NO. Well, OK, maybe a lot has but some of us have NOT.

 

[OCR]

Hasn't pretty much everything transitioned to face book. . .

Facebook. . . ??I'll have to look that up. . . .

.

 

[BWV]

I'm kind of surprised there is still a Physics forum. Hasn't pretty much everything transitioned to face book and the like?

Me too, perhaps people here feel threatened by their brother-in-law’s deep scientific insights

 

[Eclair_de_XII]

Yay, you are a physicist! although the second one ought to be $\dfrac{1}{2}R^2 \sin{2\theta}$
(the alternative answer was $r\theta$ )

Is the alternative just some value that $f$ approximates for sufficiently small values of $\theta$?

Like, is $r\theta$ just some other way to express $R(R\theta)$ when $\theta$ is small?

 

[ergospherical]

@Eclair_de_XII you're thinking too hard ... when there's a change of variables $\tilde{f}(\mathbf{u}) = f(\mathbf{x}(\mathbf{u}))$, it's common (at least in applied mathematics...) to not distinguish notationally between $f$ and $\tilde{f}$

(for example... the chain rule should be written $\dfrac{\partial \tilde{f}}{\partial u_i} = \dfrac{\partial f}{\partial x_j} \dfrac{\partial x_j}{\partial u_i}$, but is usually abbreviated to $\dfrac{\partial f}{\partial u_i} = \dfrac{\partial f}{\partial x_j} \dfrac{\partial x_j}{\partial u_i}$)

 

[Hornbein]

Maybe this is an age/generation discriminator. Godwin's Law dates back to the era of Usenet forums.

I'm kind of surprised there is still a Physics forum. Hasn't pretty much everything transitioned to face book and the like?

I remember Usenet. Every unmoderated group degenerated into a cesspool. The first of many disappointing discoveries about the nature of some people.

FAcebook? No face value.

 

[phinds]

FAcebook? No face value.

+1 on that. For keeping up w/ remote grandkids it's great. For science it's just a joke.

 

[Bystander]

Facebook. . . ??

"Farcebook?"

 

[robphy]

Not a misconception but a confusion. We were taught r theta phi in math. But American physics now uses the r phi theta convention to be in sync with European physics.

Possibly interesting reading:

https://bridge.math.oregonstate.edu/papers/CMJspherical.pdf

Spherical Coordinates

Tevian Dray and Corinne A. Manogue (Oregon State University, tevian@math.orst.edu and corinne@physics.orst.edu) have a proposal.

The problem. Nearly everybody uses r and θ to denote polar coordinates. Most
American calculus texts also utilize θ in spherical coordinates for the angle in the
equatorial plane (the azimuth or longitude), φ for the angle from the positive z-axis
(the zenith or colatitude), and ρ for the radial coordinate. Virtually all other scientists
and engineers—as well as mathematicians in many other countries—reverse the roles
of θ and φ (and use some other letter, such as R, for the radial coordinate).

Why is this a problem?...

 

[robphy]

That reminds me, here's a test to see whether you're a physicist or a mathematician at heart...
if $f(x,y) = xy$, what is $f(r,\theta)$?

Possibly interesting reading...
https://bridge.math.oregonstate.edu/papers/bridge.pdf

Bridging the Gap between
Mathematics and the Physical Sciences
Tevian Dray and Corinne A. Manogue

...
Here’s our favorite example:
Suppose $T(x, y) = k(x^2 + y^2)$. What is $T(r, θ)$?
We often ask this question of mathematicians and other scientists. Some mathematicians
say “$k(r^2+\theta^2)$”. Many mathematicians refuse to answer, claiming that the question is
ambiguous. Everyone else, including some mathematicians, says “$kr^2$”. One colleague, who
holds a split appointment in mathematics and physics, simply laughed, then asked which
hat he should wear when answering the question. What’s going on here?
...

 

[gmax137]

here's a test to see whether you're a physicist or a mathematician

Just to take a tangent, do you know how to tell if someone is a plumber or a chemist?

Ask them to pronounce "unionized"

 

[DaveE]

That reminds me, here's a test to see whether you're a physicist or a mathematician at heart...
if $f(x,y) = xy$, what is $f(r,\theta)$?

Exactly. The difference between mathematics and physics is not so much in what is taught, and even less in the instruments, they use. The main difference is simply that it is another language.

Yes, a perfect illustration. Once again the Mathematicians are correct, exactly, precisely correct. But the people that need to use the math to solve problems leave out the tedious rigour only retaining the essence that is useful and tailored to their particular field. Then they add in, but don't talk about, some jargon or assumptions that are always made by their peers. Which is why none of us find it easy (or possible) to read the papers from the "other guys". I think it's actually a pretty efficient system. There are good reasons that people take shortcuts, you know, the good ones anyway.

This is often what leads to misconceptions. Someone threw out some useful stuff because it was easier that way. Like me; I do this all the time.

 

[vela]

Favorite misconception: The short version of mathematics is maths.

 

[vela]

Actually, I was going to go with favorite doesn't have a u in it.

 

[Eclair_de_XII]

thinking too hard

Oh, I get it. In the case of $\tilde{\mathbf{f}}$, you use the substitution $x=r\cos\theta,y=r\sin\theta$, but in the case of $\mathbf{f}$, you just substitute $x=r,y=\theta$ without making any allusions whatsoever to polar coordinates.

 

[fresh_42]

Actually, I was going to go with favorite doesn't have a u in it.

My spell checker is set on "American". You cannot imagine how many "u"s I've deleted thru the years. I'd say there is a u in it, at least as long as you don't clean up the more important mess. Otherwise, we may start calling it Pittsborough.

And here is my legitimation.

Favorite misconception: The short version of mathematics is maths.

You mean there are no shortcuts to mathematics?

 

[jedishrfu]

Interesting that for the f(x,y)=xy question, when I saw the r, $\theta$ I immediately and implicitly thought polar coordinates as that was our training. Certain variable names x,y,z,t or $r,\theta,\phi$ or m,a,f,e, … all had physical meanings in physics.

Whereas a mathematician may see patterns beyond the meanings.

 

[Jarvis323]

Possibly interesting reading...
https://bridge.math.oregonstate.edu/papers/bridge.pdf

Bridging the Gap between
Mathematics and the Physical Sciences
Tevian Dray and Corinne A. Manogue

How about $f(\pi, \tau)$? I think some will assume $\pi$ is just a symbol.

 

[OCR]

"Farcebook?"

Well, of course. . . . Damn, I now feel so foolish. . .

.

 

[valenumr]

Exchanging the roles of $\phi$ and $\theta$ in my use of spherical coordinates was a seminal moment in my transition from amateur hack mathematician to amateur hack physicist

So wait, is the spherical coordinate system I learned in engineering calculus different than what physicists use? We learned $\rho$ $\phi$ $\theta$.

 

[Office_Shredder]

This is madness. The x-y plane is defined by $r$ and $\theta$, adding a third dimension doesn't change that. If you switch polar coordinates to $r$ and $\phi$ then I have no problem with this convention.