The h Bar

12:05 AM

@heather That's tricky, and I don't have a really good answer for you. The best I can suggest is if you can get some data on where its graduates get admitted for grad schools, and see how it compares to other undergrad institutions of higher and lower reputation.

heather

hmm, okay.

David Z

@Lozansky I think "relative rate of change" might be something I've heard. "relative time derivative" could work too. Maybe also "logarithmic derivative" because $\dot{T}/T = \frac{\mathrm{d}}{\mathrm{d}t}\ln T$. But I'm not sure that any of these will be universally recognized.

GPhys

I went to a much smaller place than Iowa State, but managed to get into Stony Brook

Admittedly I had to bend my back over at times

David Z

@heather This is kind of what I was saying before, that the advantage of top-tier schools like MIT is that everyone knows they will prepare you well for grad school, but Iowa State is not such a big name that the same claim can be made about it. So it's hard to tell without having specific detailed information about that particular school.

heather

right.

::sighs::

GPhys

12:10 AM

I did make sure to go out of my way academically since I was aware my undergraduate was not so well known

David Z

Honestly, from what little I see of you here, I think there's a good chance you would do well at a bigger-name undergrad institution and in particular that you might feel constrained at Iowa State.

heather

...and that's what makes it difficult, unfortunately.

my dad wants me to go to iowa state.

which, i don't know. i think i want to go there, but i might also want to go to one of those "bigger-name" institutions.

David Z

Yeah... well, it should be your decision where you go to college, but in practice it doesn't always work out that way. If your dad is willing to go so far as refusing to pay for you to go to any other university, refusing to sign admission forms, and so on, he could make it very difficult for you to go anywhere else. (Not impossible, but very difficult)

At least, if you do go to ISU, it's not going to kill your hopes of further study in physics (if that's what you want to do). So I wouldn't worry too much.

Lozansky

@DavidZ Yes relative rate of change (wrt time) is probably the most universal/sensible way to put it

heather

@DavidZ well my dad said I will basically have to pay my own way through university - iowa state or not. which is what really is semi-stressful about the whole college thing. both my parents say not to worry about it, but i ask for specific advice and i don't get much - just that i'll "get enough scholarships" and "get a free ride" which is a bit to magical for me.

i doubt he'd refuse to sign admission forms, though.

David Z

12:18 AM

Well that's good at least.

heather

i suppose i just need to talk to a counselor at school or someone about how to start saving for college.

maybe go to a bank/read up on the internet and inquire about 529 plans.

David Z

Yeah, that might be a good idea. Granted, it really should be your parents who are thinking about that stuff on your behalf; you shouldn't have to worry about it, but it does help to be prepared.

I don't know you as your parents do but in general, I would recommend against anyone counting on getting a full scholarship. If you do get a full-tuition merit-based scholarship to any university, then you're probably also qualified to get into a higher ranked university where you would likely have a better experience.

heather

hmm, that makes sense.

David Z

BTW in case you didn't know, don't count out the top schools on financial grounds, at least. They often have some pretty generous financial aid packages (bluntly, because they're so rich).

heather

question: when do you fill out the FAFSA? senior year of highschool? or can you fill it out earlier/update it?

David Z

12:23 AM

Yeah, I believe it's senior year of high school.

fafsa.ed.gov/deadlines.htm#

heather

hmm, okay.

David Z

Each individual university will have their own deadlines, but they typically come toward the end of the last year of high school. IIRC you should plan on filling out FAFSA forms in... February-ish?

heather

okay, so i don't have to worry about that for a bit.

David Z

Yeah

I'm pretty sure it's not something you can do before senior year of high school, although you really should check with a guidance counselor or someone at your school if you want to be sure

heather

maybe i can get some sort of job, to start saving, hmm.

David Z

12:34 AM

Yeah.I'm not sure if you can save enough to make a significant dent in the cost of college, but having a job is good experience if nothing else.

heather

i guess it's possible to get a none-McDonalds like job because i have some programming experience...let's see.

David Z

(And even if it's not a significant dent, it is something)

heather

hmm...i wonder if i could go to Iowa State (it's not that far away) and put up posters with an offer to get documents/notes/whatever put into LaTeX for some cost.

i bet there'd be people who want that. and i could do that over the summer/on the weekends during the school year.

David Z

Interesting idea. I'd be curious to know if it works out.

Kenshin

1:09 AM

MCdonalds is awesome

heather

@DavidZ, well, whether it does or doesn't, i'm having fun making a poster in LaTeX =P

Kenshin

Hi @JaimeGallego

Jaime Gallego

Doing an all-nighter here

Kenshin

u serious brah

y tho

ur SAT is over

Jaime Gallego

Philosophy and math

Kenshin

1:21 AM

what is your philosophy

Jaime Gallego

Dunno

The one we are studying, however, is business philosophy

Kenshin

The philosophy of business?

profit maximisation

suitable return on capital

Jaime Gallego

That and some more BS

Kenshin

My view is that an enterprise is defined by a series of contracts between stakeholders, each stakeholder having an individual interest

r u still at school @JaimeGallego despite having done the SAT?

Jaime Gallego

Well, of course, the Spanish schedule and the American one are mismatched

I finish in two weeks

Kenshin

1:28 AM

breaking news Teresa May is likely to lose the brittish election

all good as long as brexit isn't set bakc

Jaime Gallego

I think I am not capable of having any intelligent conversation right now :P

bolbteppa

1:55 AM

@ACuriousMind chapter 10 of Freedman gives a derivation of wikimedia.org/api/rest_v1/media/math/render/svg/… I guess is the best one can get

Shing

2:43 AM

I am a but confused, and would like some helps here:
in Lagrange, we pretty much take $q$ independent of $\dot q$,
however, in Hamilton, $\dot q$ depends on $q$; and is a function of form: $\dot q( q, p)$
so are they independent or not?

Kenshin

if x= t, and y = t are x and y independent?

Shing

$x$ and $y$ should be dependent

Kenshin

yes one should note the difference between explicit and implicit dependence

Shing

what exactly is the difference between explicit and implicit dependence?

I mean in Lagrange:

$\frac {\partial q}{\partial \dot q} = 0$

in Hamiltion however it is not true, we cannot take that as zero.

Shing

3:12 AM

damn, I think I figure it out...

two partial differentiations are different.

$f(x) = x + x^2$

and if I let $u=x^2$

and doing $\frac{\partial}{\partial x}$ while I fix everything else. I will get $f'(x)=1$

but if I don't fix anything, I should get $f'(x)=1+2x$

um.... I am still a bit confused. I didn't convince myself.

David Z

Think of it like this: on a two-dimensional plane, with $x$ and $y$ axes, you can parametrize the plane using the two vectors $\hat{u}_1 = \hat{x}$ and $\hat{v}_1 = \hat{y}$, or using the different set of two vectors $\hat{u}_2 = \hat{x}$ and $\hat{v}_2 = \frac{1}{\sqrt{5}}\hat{x} + \frac{2}{\sqrt{5}}\hat{y}$.

Any point on the plane can be represented as a unique linear combination of $\hat{u}_1$ and $\hat{v_1}$, so those are a valid basis, and can also be represented as a unique linear combination of $\hat{u}_2$ and $\hat{v}_2$, so those are a valid basis.

So are $\hat{u}_1$ and $\hat{v}_1$ independent or not?

Shing

3:30 AM

@DavidZ $\hat u_1$ and $\hat v_1$ are independent, as there is no way (not a linear combination) to get $\hat u_1$ from $\hat v_1$ , vice versa

David Z

Oh... well yes. But I really meant it as a rhetorical question. (Sorry) Asking whether $q$ and $\dot{q}$ are independent is analogous to asking whether $\hat{u}_1$ and $\hat{v}_1$ are independent.

And asking whether $q$ and $p$ are independent is analogous to asking whether $\hat{u}_2$ and $\hat{v}_2$ are independent.

It might actually help to think of two different "versions" of $q$, namely $q_{\text{Lagrangian}}$ and $q_{\text{Hamiltonian}}$

Shing

@DavidZ what exactly are their difference? Are their numerical values also different (given a same point mass at same location in space)?

David Z

Between the two versions of $q$, you mean? Well, if you're asking that question, then it is probably not going to help you to think of two different versions.

They are exactly the same, just as $\hat{u}_1$ and $\hat{u}_2$ are the same in my analogy above.

Shing

@DavidZ yeah I mean two versions of $q$

perhaps, my major confusion comes from this:
$\frac{\partial L(q,\dot q(q,p))}{\partial q} = \frac{\partial L(q,\dot q)}{\partial q}+\frac{\partial L(q,\dot q)}{\partial \dot q}\frac{\partial \dot q(q, p)}{\partial q}$

David Z

Was that supposed to be $\dot{q}(q, p)$ in the top of the last factor?

Shing

3:45 AM

yeah

my bad

David Z

np

So, the reason to write $\dot{q}(q, p)$ there instead of just $\dot{q}$ is that you're switching what are thought of as the linearly independent coordinates, basically performing the generalized version of a shear transformation on phase space. In the analogy I used before, it's as if you shear the plane so that $\hat{u}_2$ and $\hat{v}_2$ are now perpendicular, which means that $\hat{v}_1$ (the former $\hat{y}$) is slanted off a little to the left.

After you do this transformation (which is a shear in the analogy, but in a real Lagrangian can be something more complicated), $\dot{q}$ itself has some "component" of $q$ in it, whereas it didn't before. So this introduces an extra way in which $L$ depends on $q$.

Or in other words, in the Lagrangian approach, when you vary $q$ you keep $\dot{q}$ constant. But after the transformation, in the Hamiltonian approach, when you vary $q$ you keep $p$ constant, not $\dot{q}$. So the way $L$ changes in response to a variation in $q$ is going to be a little different.

The second term in that expression you wrote there accounts for the "extra" change in $L$ that comes from the "component" of $q$ that is now in $\dot{q}$ - or in other words, it accounts for the "extra" variation in $L$ that comes from holding $p$ constant instead of holding $\dot{q}$ constant. It lets you calculate that variation even though your formula for $L$ might be written in terms of $\dot{q}$ instead of $p$.

Shing

4:00 AM

@DavidZ so basely, we choose a "coordinate/phase space", such that varying ,say, $q$ will make $p$ constant?

and choosing another "coordinate", s.t. varying $q$ will not affect $\dot q$ ?

David Z

It's phase space, not coordinate space. Coordinate space is the space of all possible values of the $q$'s, whereas phase space is the space of all possible values of the $q$'s and $p$'s (or equivalently, $q$'s and $\dot{q}$'s)

Shing

oh, right, thanks.

David Z

Anyway, it's a fairly general principle of multivariable calculus that whenever you vary one variable (or, really, perturb a system in some way), you have to make some choices about what is held constant while you do your varying.

The way multivariable calc is usually taught, they choose variables so that when you vary one variable (e.g. $x$), the others ($y$, $z$, etc.) stay constant. But it doesn't have to be that way.

With Lagrangians and Hamiltonians, this is a case where you have some flexibility in what you choose to keep constant while you vary $q$.

Mathematically, it's two different ways of parametrizing the same phase space.

Shing

I see

Thank you so much, David.

I can see the big picture now.

David Z

Cool, glad to help

FWIW, thermodynamics is another case where this pops up. You can vary temperature while holding pressure constant, or you can vary temperature while holding volume constant. And so on.

user228700

5:52 AM

@JohnR: Morning! :-) How'd the checkup go?