@rob, that happens to me

@rob That problem has come and gone a few times over the years.

At oeast once is was something begin done wrong on the SE end and ant least once it was a bug on the MathJax end.

I am having two problems with git/linux/me: 1. I cloned my calculus-notes github repository onto my computer, which includes the picture files, but when I try to compile the main tex file, it gives an error, saying it can't find the images. 2. I made an update to the main tex file to fix a typographic error, and I added it to the staging area and commited it, but I think I need to merge it with the online master branch or something, because it isn't showing up online.

I'm not sure what the problem is with either, if anyone wouldn't mind helping.

I don't think I've noticed either the five-second delay or the "disable preview" link under the text box for a while now, but for whatever reason the rendering lag was particularly slow just now.

I been having pages on the main site simply not render from time to time for a few weeks. A reload usually fixes it, but it might share a root cause.

Sure. What's up?

It's a self-cite but clearly labeled as such. It's related enough to the question that I would decline an "not an answer" flag on it. So sure. I don't see anything wrong with it from a moderation point of view.

I think it is possible that some other users will think that offering a "simplest way to do the same thing" kind of answer isn't helpful enough and down-vote it, but that is a different thing.

Well. If the question is "How does this instrument in particular do it?" then your answer isn't that great. If the question is "How can this be done?" then your answer is bang on.

Depends how people interpret the intent of the question.

@Nullarbor I don't think so. You don't always need big words or intimidating equations to write a very professional answer.

In any case, most people are charitable on such matters.

I'm not suggesting removing it or anything.

Just be aware that people can read the question in a way that would make downvoting a plausible course of action.

BTW, f you were worried about the timing, we encourage answer to old questions. There are even a couple of badges for that.

Hi, everybody.

Revival and Necromancer.

@heather Still need help?

@Nullarbor It's pretty long for that.

@DanielSank, if you don't mind, yes. =)

@heather Ok, what's the deal?

You cloned your repo and you have no images?

Link to repo, please.

github.com/physicsnerd/calculus-notes

I have the images appearing in my file manager, but when I try to compile the main tex file, it says images not found.

That's because the paths are wrong.

where did I misreference them/what do I need to do to fix it?

Hi @Daniel

I'm reasonably sure the problem is that you \input, say, limits.tex, then in that file you try to grab an image images.png, but that image file is in the parent directory.

Try using ../images.png and see if that works.

@Danu yo

@heather, the deeper you get into this, the more that blog post of mine will make sense.

And actually, if I were you I'd move the image files to the same directory as the .tex file that uses them.

@Danu wrote a chat server in python3.

So next week I'll have to explain a bit to my tutee's about tensor products and such. I'm wondering what'd be the best way to do it. My feeling is that it might not be so bad to go for the actual definition of a tensor product (free groups over generators quotiented by relations...), but perhaps there are good alternatives. Suggestions?

Bernardo ran it on some server of his in London and we were able to chat. Pretty cool. He tried to break it by sending Chinese characters but it worked because utf-8 is cool.

@Danu Is the student a math student?

I have strong opinion about how to teach tensors, and it differs from what all the physicists do :\

@DanielSank No, they're all physicists. Do you have a nice way of defining stuff? :P

I don't mean index notation stuff---more like the stuff you need in intro to QM

(it's related, of course)

@Danu I do it the algebraic way and introduce coordinates/bases afterwards. The usual business about a tensor being a bunch of numbers that transforms a certain way was always very confusing to me.

@DanielSank, yes, that worked! =D

@Danu Yeah, but even there the algebraic approach is waaaay better IMHO.

@DanielSank So quotient of free group over generators?

@DanielSank That's what I was gonna do

I would start with vectors. Everyone knows what a vector is. Then define covectors as a thingy that eats one vector and produces a number. This is easy to understand because everyone knows what a dot product is.

Then point out that the dot product itself is a linear function that eats one vector and one covector and spits out a number, so it's a 1-1 tensor.

Go from there?

That's how I'd do it.

I was gonna go a bit more mathematical

Then you can point out that bras are covectors etc. etc. and everything is hunky-dory.

@Danu Up to you, of course.

But I'm afraid I'll scare them too much

For my part, I really like to explain math with the minimum of new ideas.

A good rule is to introduce the fewest new words per unit time as possible.

Their background is a bit varied---some are from Spain where they do a bit less math stuff in undergrad.

The German ones have heard a lot of terminology before

If you can get people to understand the structure of the math without using the new words, that's really helpful.

Get them to "do tensors" and then name it.

Point out that a matrix eats a column vector and a row vector and spits out a number. Then say "ok that's called a tensor".

and I committed the change. Now I just need to figure out how to merge. =)

So I was thinking about the general definition (third subsection here).

Then point out that if you feed the matrix a column vector, you have something left over that wants to each one vector to produce a number. Therefore, feeding a 1-1 tensor a covector gives you a covector.

Easy-peasey

But the concept of free vector spaces is probably a bit high powered

@Danu Not sure what that means, actually.

@DanielSank Right... Because in physics nobody really does the basis-independent definition of tensor products :P

@Danu Eh?

Just don't really need it in physics---but for me the construction was quite insightful.

@heather What you want is called "push".

@heather, in git, the repository on your computer and the one on github are each independent, fully functional repositories.

@DanielSank So the way you define tensor products is as follows

Consider vector spaces $V,W$. Now you can form the set of ordered pairs $V\times W$

When you make a new commit on the master branch, your repository is fully up to date. If you want to tell another repository about that change, you "push" your commits from your local repo to the remote (i.e. github) repo.

"merge" means to update a branch with new commits from another branch. You're not doing that here.

@Danu ok

oh, okay @DanielSank, I looked it up and it says the syntax is git push <REMOTE NAME> <BRANCH NAME>

would the <REMOTE NAME> be calculus-notes?

Yes, you can do that, but in fact I would recommend this:

Now, you take the free vector space over $V\times W$. What that means is that you take the vector space where each element of $V\times W$ is taken as a basis element. Notice that this space is absolutely enormous (typically infinite-dimensional, in particular)

and then branch name be master?

$ git push

Because you cloned your local repository from the one on github, your local branches are already configured to push to the proper remote ones.

You don't need to explicitly give the remote name and branch name, and in fact I'd advise against it for fear of typos :)

whoa, cool!

it just asked for my username and password, and then did it!

yes'm

::refreshes github page:: and it did it =D

git is magic

Now, you pass to a quotient of this space. The equivalence relation is generated by the relations $(v_1,w)+(v_2,w)\sim (v_1+v_2,w)$, $c(v,w)=(cv,w)$ and similar rules for $w_1,w_2,cw$

well, code, but practically the same thing =P

thank you @DanielSank!

It's pretty cool. You haven't actually seen the awesomeness of it yet though. When you start using branches, then your head will asplode.

Addition and multiplication by scalars are defined via representatives

when is it best to use branches?

@Danu I am embarrassed to say this, but I actually do not understand most of what you just wrote.

@DanielSank Anyways, that's the real definition of the tensor product. Not that you'd need all of that in physics, ever.

Probably best not to go this route for my students, I guess.

@heather When you're making unrelated changes as the same time. Suppose I'm working on my PhD thesis and I need to do two things: 1) Make some figures in chapter 1, and 2) Write some paragraphs in chapter 2. Suppose I do some work on item #1, get bored, and want to work on item #2.

So the thing that you do know is the following

In git, if I do my work on item #1 in a branch, I can commit what I've done, switch to a new branch, work on item #2, and maintain both lines of development separately.

Eventually, I merge those two branches into master, but that can be done in any order.

It's so, so, so useful to work this way. When you have multiple people working on the same project, it's absolutely essential.

so like, if in one branch I wanted to add the formal definition of integrals/derivatives with limits and in the other I wanted to fix latex formatting/typos, I could do that?

Absolutely.

::mind blows up:: ::brain puddle on floor:: ::mom pulls out mop::

Let $V,W$ be vector spaces which are defined as free vector spaces over (basis) sets $S,T$. That just means that each element of $S$ ($T$) spans a direction in $V$ ($W$). Then you can define the tensor product by $V\otimes W=F(S\times T)$, where $F(X)$ denotes "free vector space over set $X$", i.e. the tensor product is the vector space where each combination $(s_j,t_k)\in S\times T$ spans a direction.

That sounds more familiar, doesn't it? :)

This is probably a good enough way to go.

teach me the ways of the force, Obi-Wan! =P

@heather My workflow is like this: 1) Make an issue describing what work is to be done. Suppose that issue is #5, 2) Make a branch whose name is 5-description_of_work, 3) Do work on that branch, making commits. 4) Eventually merge that branch into master, automatically closing the issue by putting Fixes #5 in the commit message.

@Danu Actually, it doesn't. I think you know a lot more math than I do.

@DanielSank But you know that a basis of your tensor product is just given by things like $a\otimes b$ where $a,b$ are basis elements of the original vector spaces... Right? :)

That's what I wrote there, in slightly different notation (and using the word "free vector space") :P

@DanielSank, okay!

In any case, I must admit that this way of phrasing things mostly turns out to be useful when actually trying to prove theorems about things... Since it makes certain properties of the tensor product easier to see

I'd define it like this. Suppose I have a tensor $T$ where $T: U \times V \rightarrow \mathbb{R}$. Suppose I also have $S: W \times Z \rightarrow \mathbb{R}$. Then $A \equiv T \otimes S: U \times V \times W \times Z \rightarrow \mathbb{R}$ such that $A(u, v, w, z) = T(u, v) S(w, z)$.

From there, it's easy enough to prove the stuff you said about bases.

I guess it's just a question of what you want to take as definitions and what you want to derive :)

^ All those $U$, $V$, etc. are either vector spaces or covector spaces (distinguish between those two however you want, you get the point).

But you didn't define what the space was that $T,S$ live in

They're special maps on $U\times V$, $W\times Z$

I did above: $T$ is any linear function on $U \times V$.

I define tensor as a multilinear function on a Cartesian product of (co)vector spaces. That's a very, very good definition for 99.999% of anything your students will ever care about.

Anyways, I appreciate your point about first focusing on the dual spaces (so spaces of linear functions)

Those are very important in quantum theory (bra's)

@Danu Yeah, well, that's the first thing that ever made any sense to me :)

@Danu Indeedy

The funny thing is that until you have a nontrivial metric, the dual space and the vector space really are the same thing.

And I was definitely confused about that back in my QM days

::shrugs::

@DanielSank Or infinite dimensions...

One extremely helpful example for me was the gradient.

(hurr durr quantum mechanics infinite dimensions functional analysis something something)

In a particular coordinate system, the gradient of a scalar field transforms inversely to the vectors. This was a very elucidating example for me, but only made sense after I understood the algebraic approach to tensors.

@Danu hurr durr indeed

@DanielSank Hmm, funny. That example really confused me when I first learned about tensors :P

@heather did you need any more help?

Fucking covectors

@DanielSank :D

@Danu It made sense because I already understood the coordinate independent approach.

Yeah

Dangit... I had an idea for a blog post and now I forgot.

they went good ol' transformation properties on my poor ass

that is a crappy approach

::shudders::

It's a terrible approach.

It's the historically first one though

:D

Yes, like so much of physics the historical approach is awful.

@DanielSank, well, I created the branch, and I figured out that I can use checkout to go between branches and branch to double-check which branch I'm on. So I can now make general edits on the master branch and the "formal definition" adding on the new branch that I added! So for now I think I'm good =D

Thanks for all your help!

To see what branch you're on, use git status or git branch.

I type git status a lot.

okay

oh, that information's helpful

good to know

(i just tried git status)

@heather One more thing: in git, if you try a command that doesn't work, git almost always tells you exactly what to do to fix the problem.

So, if you make a new branch on your local repo, and then make commits, you might want to push that branch to github.

If you just do git push, it probably won't work because git has no idea what branch to push to.

However, if you actually try it, you'll see that git tells you this, and tells you what you probably want to do. Git has surprisingly helpful error messages. Read them.

@DanielSank 'tis a funny thing

In mathematics, sometimes the historical approach is much more down-to-earth, understandable.

@DanielSank, okay, I'll try that (make a small edit).

In physics, it's always completely WTF :P

@Danu yeah

@Danu yeah

hi Null

@Nullarbor Hi

So now I'm trying to look up books on representation theory of Lie algebras for my tutees :P

I think I'm pushing the math agenda pretty hard

Anyone have any suggestions that need a minimum of prerequisites?

It's fine; just leave it as an answer.

@Danu uh oh :P

@DanielSank, hmm, it gave no error when I did that.

@DanielSank I'm honest about it, at least. I tell them it's not that important in physics..... But that I care a lot about it :D

@heather You made a new commit on a new branch and pushed it and it worked?!

@heather Mostly no

@Nullarbor No.

however, it didn't show up on the github site...would it show up in the master branch then, I guess? ::goes to check::

@DanielSank, yep

@Danu Uh, try to remember your job is to teach them physics...

@heather Only go through the trouble of compiling things yourself if you need things you don't have

@heather Uh... what branch are you working on?

@DanielSank Don't worry, I just spend like 10 minutes out of 90 on this kind of stuff... And only when I have left-over time.

I try to maximize how inspirational I sound---which I think I'm better at when talking math.

I tried to wow them by telling them all the SM particles were predicted by studying representation theory

@DanielSank, the new branch "7-formal-def"

@heather You made commits and then did git push and it worked?

Is the new branch on github?

no, it's not showing up, and neither is the push

but it also didn't give any errors

so I don't know what's going on there =)

do i need to add/commit a branch?

What branch are you on?

currently, master (I switched over after I "pushed")

ummmm

Ok, from master, do this:

$ git checkout -b test_branch
$ touch foo
$ git add foo
$ git commit -m "Added file foo"
$ git push

The touch command just makes a new empty file (in this case, called foo).

git commit -m "blah blah" is a shortcut to make a commit with a specified commit message. It's useful for short commit messages.

okay, did that, did git push, then it said "everything up to date" and was done

That can't be right.

that -m "bla" is a useful trick to know, I'll keep that in mind

$ git log

What does that say?

(hit q to quite the log viewer)

a whole bunch of things, let's see...

the very first thing lists a commit that says "added file foo"

then a commit that says "fixed images, fixed quote change" - that one showed up on the github site, that was before I added any branches

Yeah ok that's what I wanted to know.

So you can see the commit you just made, which added foo.

but it doesn't mention my middle commit, adding a line to the main tex file, after adding my first branch

strangely

What happens if you do git status?

Hi @Kaumudi.

on branch test_branch

lists some untracked files

then says nothing to commit but untracked files exist, use git add

the untracked files are, for instance, main-file.aux

main-file.log

etc

@Kaumudi, hello

@heather yeah yeah that's junk that latex made. There is a really nice way to tell git to ignore all that junk, but let's do that later.

okay

sorry, wasn't sure what all you wanted =)

don't apologize

...and git push just does nothing?

you mean, if I type it in now? let me try real quick

well, it asks for username/password, and then i input that, and then it says "everything up to date"

:\

$ git remote show origin

Also

$ git --version

git version: 1.7.9.5

remote origin

ah

urls are right

remote branch: master tracked

okay

how do I update?

Can you paste the entire output from git remote show origin?

unfortunately, no, I can't copy and paste between chromium and linux; I've got two separate clipboards

oh

ok

How did you install git in the first place?

i installed it using apt-get install, I think

weird

I know i installed it to get the github version of vim @BernardMeurer was showing me

hmmmmm

Well anyway, we don't need to update git!

okay

Ouch, actually @heather, your version has a known security vulnerability. Let's upgrade.

okay, I prefer not to have security vulnerabilities =P

be right back, sorry

ok

WOW I got an upvote on the music theory and practice site!

@heather Hello human

heather needs to upgrade git. She's running 1.7, which has a known security problem (and lacks some nice features).

okay, i'm back

What the hell I'm on 2.10.2

@BernardMeurer, hello human (or AI...?)

@BernardMeurer Yeah, exactly. I have no idea how she got an old version.

@heather just install git again and it should update

@BernardMeurer, sudo apt-get install git I assume? that won't mess with my branches or anything?

nope

Nope, that's exactly the command you need

Your branches etc. are all data in your home directory, or wherever you put your repos.

although doing a sudo apt-get update && sudo apt-get upgrade -y might be a good idea

^that first? okay