Oh dear.....

and then for $r$ trying to substitute a vector

@evinda If you add the same constant to all $e_i$ and $d_j$, you don't change the differences. If the constant is a large enough positive value, your modified elements will all be positive, regardless of whether some of the originals were negative.

eg $\frac{1}{r^2} =? \frac{1}{\{x, y, z\}^2}$???

lol

Radius (or distance, if you'd prefer) is a scalar by definition

For me, the difference between the two is that of night and day.

Indeed, but the position of an object, $\vec{r}$ is a vector

Position of an object? Points are one-dimensional and therefore have no length or direction, though?

@DanielFischer So could we add for example the number 1000*K ? Or do we have to add a known number? And how does this helps?

@teadawg1337 That's true, but you define a coordinate system and where that point is relative to the origin of your coordinate system is a vector quantity.

@evinda It doesn't matter. I just illustrated that it's irrelevant whether the $e_i$ and $d_j$ can be negative or not.

@Pedro @Kevin: It's more math than physics here. You want to get a differential equation for the angle at which the front wheel must steer.

Hello Professor @TedShifrin

@DanielF: I actually do use vector symbols in my multivariable and differential geometry courses. Not in just a pure linear algebra class.

Hi @skull.

@Kevin: I don't think forces are relevant. I think it's more about velocity vectors for rear and front wheels :)

@TedShifrin But forces are noting but changes in velocity

But I can believe that I'm oversimplifying the problem in my mind

I understand. But I don't know the accelerations of the front and rear wheels. I do know something about their velocity vectors. Assume, for simplicity, that the rear wheel is proceeding at constant speed.

runs away now that @Kaj is here

Hey everyone

Hi pal

@Kaj: @Kevin and @Pedro are working on the problem you might have worked on briefly last year. Given the path of the rear wheel of the bicycle, find the path of the front.

@Pedro: You are already too much of an algebraist :(

Hey @KajHansen

@TedShifrin I could think about it, but I wouldn't hold high hopes.

Well, @Pedro, you can work on the other problems I've given you :D This is quite elementary if you look at it right, but you need to know what curvature means.

@TedShifrin So, if the bike is front/back symmetric then it seems that the forces perpendicular to the path of the rear wheel have to be the same. If they aren't then there's a torque and the bike will rotate but that would cause the back wheel to slide sideways

No sliding, @Kevin. But it's not symmetric. The front wheel turns; the back does not.

@TedShifrin I never said that mathematicians mustn't. I said they need not.

@Ted So the condition then is slightly more general. They need not be hte same, but they are related.

I say it depends on the course/students, @DanielF :D

Of course they're related, @Kevin ... There's an axle of fixed length connecting the front and rear wheels!

And the bike is not sliding

Yessir.

so the relation is simple $\tau_{front} = \tau_{back}$

What's $\tau$?

@evinda It ought to be $\lvert -1 - (-5)\rvert = 4 > 3$, $\lvert -1 - (-4)\rvert = 3$ etc.

@TedShifrin, @PedroTamaroff , this was a problem I wrote up for last week's complex analysis set. For obvious reasons, I'm unsatisfied with my solution. Do you guys see an easier way of going about this? (I tried working in polar too, but that just passes off the mess you see here into exponents of e) i.imgur.com/QM0uHC5.png

Oh, sorry its torque t the specified point about the center of mass

I haven't thought about torques. I haven't thought about forces.

@KajHansen Yes.

I think there is no torque, or else the back wheel would have to slip.

@PedroTamaroff, a hint?

Right, precisely

The net torque must be zero

Ugh @Kaj

Consider the sum $\sum_{|k|\leqslant n} e^{ikt}$. Pair up negatives and positives to get cosines, use geometric formulas to get sines.

@KajHansen

Even easier, take real parts of both sides.

@TedShifrin Anyway if you have enough information to calculate the curvature of the path, then you have enough to calculate the force on the back wheel

That's morally equivalent to @Pedro's comment.

@TedShifrin, that's basically what I did?

@KajHansen But what you did is too long. =D

No, @Kaj, you tortured me.

LOL

Rather, I tortured our grader.

Just figure out the real part of the right hand side.

You'll find out that, with the exception of me, @Kaj, graders don't read most of what you write. :(

@DanielFischer I see.. But how can we know then till which element we have to look from the second array? :/

@Kevin: I still say forces are irrelevant. You want a differential equation for the steering angle.

Have any of you ever read Kelley's Topology? Is it appropriate for someone who knows some real analysis (i.e., to the level of Bartle and Sherbert)?

@Clarinetist Read it, and you'll find out. =)

=)

@TedShifrin I feel like I don't need that angle if I can just directly figure out where the front wheel is based on where the back wheel is going.

@KajHansen By the way, google Dirichlet kernel.

@evinda Star with $K = 0$. How would you efficiently check whether two sorted arrays contain a common element?

@Clarinetist: It is a masterful book, but very concise, with no pictures. I would suggest Munkres instead.

@OK, @Kevin. My solution is to give a differential equation for the steering angle, as it's clear that that gives the front path ... :)

@TedShifrin Maybe I'm assuming you're giving me too much information. Suppose the back wheel stays in the same spot and the front wheel makes the bike spin in a circle. What would you be giving me in that case?

Oh, well, good, I've trained Jun well, then :) @Kaj

Just that the rear wheel is fixed, @Kevin. So you deduce that either the front wheel is fixed or the front wheel turns at $90^\circ$ constantly.

Thanks @TedShifrin. I have Munkres as well, but... you may want to see this question I had: math.stackexchange.com/questions/1080777/… . I think I may try to find a class that uses Munkres and check out the syllabus (which I imagine wouldn't be too difficult).

@Kaj: Yeah, I'm making my way through 25 papers at the moment.

@DanielFischer We could call the Binary Search that checks for each value of the set D, if it exists in the set E, right?

@evinda We could. What time complexity would you get from that?

@TedShifrin Ah?!

$m \lg n$, right? @DanielFischer

@Clarinetist: My advice for the GRE is very simple. Don't worry about what you do not know. If you've had real analysis and know the topology of metric spaces, don't try to learn a bunch extra. The bulk of the GRE is calculus, multivariable calculus, sequences&series, linear algebra, and then a variety of advanced things like probability, algebra, analysis, topology, differential equations.

You must nail the basics, quickly, and then take the time to do what you do know among the advanced things. They don't expect every student to know everything.

@Pedro: Grading diff geo for my last semester ever :P

@evinda Yes. (Or $n\lg m$ if the array sizes were the other way round, don't remember.) Is that good enough?

@TedShifrin Mixed feelings, I suppose!

Hi, @Alessandro: Du schläfst noch nicht? :)

Yes, @Pedro, very.

@TedShifrin - Would the axiom of choice be something expected on the GRE?

I only had one course which covered it for about 10 minutes.

@DanielFischer I think that it is... Isn't it?

No, @Clarinetist.

@TedShifrin - Thank you. sigh of relief Not that I won't learn it later, but I had no idea.

Who makes up the GRE?

Doesn't GRE put out a thing that says what the relative % of subject on the subject GREs is?

I know they do for physics

@evinda Don't guess, check.

People who work for ETS, @skull, probably some people who have math degrees. I don't know if they ask faculty. I've never heard of it.

I took it back in October and thought it had quite a bit of topology, tbh with you.

CollegeBoard also does AP exams

Basic open sets, closed sets, compactness, continuity, sure, @Clarinetist. But not the product topology on infinite products ...

Sorry, ETS, not College Board. What am i thinking?....

@TedShifrin - Indeed, those terms that I have no idea about. :P

Oh, what kind of analysis class did you have, @Clarinetist?

@TedShifrin Do GREs have physics?

@TedShifrin - A very, very watered down one. Have you read Bartle and Sherbert?

Bartle should have those terms in it.

no, @Pedro

@TedShifrin - Toward the end, yes. But we didn't cover that material.

Conceivably in an applied differential equations question, @Pedro. Skip it.

How does one do analysis without concepts like open sets and such?

Well, you need to learn that stuff, @Clarinetist, but it should be enough in the setting of $\Bbb R^n$ or, at worst, a metric space.

@DanielFischer Isn't the time complexity in this case less than this that we want to have? Our desired time complexity is O((n+m)*lg(n+m)) ? :/

@PedroTamaroff No, they don't.

I don't know, @Kevin, but there are lots of watered-down courses, including some at UGA in recent years.

One can do analysis on $\Bbb R$ without doing analysis on metric spaces...

@TedShifrin I guess I shouldnt be shocked. People still try and teach "algebra-based" physics.

I'm aware.

But one should mention closed, open, compact, even in $\Bbb R$ if it's an analysis course.

More than mention.

How does one do pysics without notions like derivative, dot product, etc? You just fake it.....

@evinda And, can you bound $m\lg n$ by $(n+m)\lg (n+m)$?

You give people formulas to memorize, @Kevin, which to me is totally abhorrent.

Yes, we can bound it by $(n+m)\lg (n+m)$. @DanielFischer

Oh, sure @Ted

That's how I 'learned' 'physics' :)

Pfeh.

@evinda So, is it good enough?

Calculus itself is "algebra-based"

Yes, it is. @DanielFischer

When there's time in my life to spend on such silly things I'll read Spivak's book, @Ted

So calculus-based physics is just adding another layer to the algebra-based

Ya that's basically the whole of it @Ted. My girlfriend still remembers "F is ur ma" but has no concept of what it means or why. So much of that 5 months of her life she spent in a high school physics course.

To really do thermodynamics requires understanding line integrals, path independence and lack thereof. But our "low-level" thermo course for chem majors at UGA requires no multivariable calculus. Fed up

@evinda Right. Now, can you generalise to $K \geqslant 0$?

It should be built on understanding and derivation and solving more interesting problems, @teadawg.

@teadawg1337 In calculus-based physics you do everything you did in "algebra-based" physics but this time you do it right and actually attempt to understand what you're doing.

@teadawg: I can recommend a wonderful serious physics book on mechanics when you're bored.

@TedShifrin and @KevinDriscoll - Think $\inf$, $\sup$, convergence of sequences, $\delta$-$\epsilon$ proofs, uniform continuity, series of functions, and uniform convergence in $\mathbb{R}$ for the first semester. For the second semester... the professor was awful. But we covered some things on differentiation, defining $\ln$, spent a lot of time on triangles (I don't remember that stuff for the life of me... some Jordan thing with triangles that I hated)...

That's one book I'm taking with me cross-country and not giving away :)

Darboux integration, surprisingly not much time on Riemann integration, we looked at $\mathbb{R}^n$ for a little bit and ended with complete metric spaces and a brief intro to the Lebesgue integral. What was depressing (IMO) is that we didn't cover Riemann-Stiltjes.

@TedShifrin We have the same problem sometimes with thermo. Multivariable-calc is at worst a "co-requisite" with thermo. They even have to teach people stuff like Taylor's Theorem.

Woah, I just took AP Physics B for college credit... I would've taken C if I could

What is Darboux integration?

I think Pedro was obsessed with that for a while.

@Clarinetist: If you really know the first semester and know open, closed, compact, connected, you should be fine. Again, you don't need to attempt every problem. You need to nail the 50+% of the exam on calculus/multivariable/linear/series, and then do well on, say, half to three-quarters of what's left.

@MikeMiller It is the nice way to define Riemann integration at least in $\Bbb R$.

You sillypants.

What is the motivation for the Stiltjes integral?

Spivak uses Darboux's approach. Ted should know.

We never used Taylor's Theorem in my thermo course, that I can remember.

@Clarinetist So no like Heine-Borel theorem or anything?

Now that I'm fairly experienced with calculus, I can see a lot of the general ideas behind calculus-based physics

unifying integrals and series is a start, @Kaj

Spivak can go to hell I say

@MikeMiller WOAH.

smacks @Mike hard

WHOA.

WOHA.

I SAID IT.

AND I'D SAY IT AGAIN

@TedShifrin - That is a HUGE relief since I feel that I REALLY know the first semester material and was really hoping I wouldn't have to go through Spivak's Calculus with Manifolds.

@teadawg: Look for Kleppner/Kolenkow's Mechanics book. Fabulous, with wonderful problems.

@KajHansen Well, you can think of it as a way of giving different weighs to intervals Kaj.

@KevinDriscoll - None of that. No topology whatsoever. I don't know what open, closed, compact, connected, any of that stuff means.

@Mike: I teach everything with upper and lower sums, and only mention Riemann sums in passing.

So basically it is a small part of more general measure theory, @Kaj.

@Clarinetist You are preparing for the GRE, yes? You really, really need to know that.

@TedShifrin I think its an integral part of any physics course that you be able to take a taylor series approximation. It helps elucidate intuition about, eg T=0 and T =$\infty$ limits

@Ted Oh, that's fine. My comment was unrelated to integrals.

oh, sure, linear, and occasionally quadratic ... but I never used that in thermo, that I remember, @Kevin

@MikeMiller - Calculus with Manifolds? Looks like I have another book to buy...

Calculus on Manifolds is a terrible book. If that's what @Mike's ranting about, I agree.

If you don't already know the material, it's almost impossible to learn from (sort of like Lang).

@Clarinetist No, basic topology. I'm talking about your statement that you don't know open/closed/compact/connected.

But his other books are fantastic, if somewhat long-winded.

By all means do not buy Calculus on Manifolds.

@MikeMiller - I completely agree that I need to know those.

and I will not buy Calculus on Manifolds.

Great!

@TedShifrin Noch nicht, normaleweise schlafe ich ~6 Stunde pro Tag

If one doesn't already know multivariable calculus quite well, Calculus on Manifolds is way off the deep end. I, of course, prefer my book.

@Alessandro: Gewiß :P

@Clarinetist I think it's a cute book.

@Ted: Me and my colleague are still not satisfied with stuff, but we won't whine right now. We're making coffee and going home to look at Kobayashi. :)

@TedShifrin One example I think I remember is to show that the Fermi-Dirac and Bose-Einstein distributions approach boltzmann in the $T \to \infty$ limit

@MikeMiller Breakfast at Tiffany's?

Another unreadable book unless you know it already @Mike :P

I really don't understand why I shouldn't feel confident about taking calculus-based physics if I have lots of experience with algebra-based physics as well as elementary calculus

OK, @Kevin, sure, with anything probabilistic, the Taylor expansions of $e^x$ show up :)

I didn't do that in thermo. It did show up in my second course, which was statistical thermo

Oh, that's Yunioshi.

You're fine, @teadawg. I'm just recommending a superior book to you.

@TedShifrin OH RIGHT, sorry. I make no mental distinction between thermodynamics and statistical mechanics. The 2 are usually taught as a single course in physics.

@teadawg: However, to do a serious E&M course, you should already have completed multivariable calculus.

Yes, @Kevin, many of my probability students had no knowledge of Taylor expansions, it seems, even though calculus and multivariable calc were a prereq.

Some of them weren't so good at double integrals, what little we did, either.

@TedShifrin I can't recalle when we convered it in my calculus courses. That was 10 years ago now.... UGH

Covered what, @Kevin? Taylor stuff? Almost surely second semester.

OK, I need to go back to grading. Fun, fun :(

@Ted I'm starting with a semester of mechanics, then taking E&M next semester.

@TedShifrin You're probably right be we spent a LOT of that 2nd sesmeter covering integration techniques so that clouds my memory

Ideally, mechanics should have Calc II as a corequisite, @teadawg, and E&M should have at the very least a co-requisite of Calc III. But schools mess it up and don't use as much calculus as they should.

I've taught myself multivariable calculus up to Stoke's Theorem

They don't normally says "Stoke's Theorem" in an intro E&M class

OK, E&M is full of flux and line integrals, @teadawg, and Divergence and Stokes's Theorem, if done right. But I will bet $100 the course you take doesn't do it right.

Stokes's Theorem, guys!

no, most E&M ends up being low-level and trying to do everything with just single integrals. Pfeh.

@Ted: Yes, it takes some work. On the other hand, he defines everything (which the authors I'm reading don't like to) and everything is meticulously proven.

that's what I need today :)

@TedShifrin Stokesies!

By the way, for the record, I imagine some of you here are professors. If you know anyone who loves math (I'm talking intro real analysis and beyond), I would suggest that they DO NOT go the actuarial route. The field is extremely boring and really only requires high school algebra I and a competency at Microsoft Excel. The exams are just a hurdle you are supposed to jump to move up in the field. I somewhat regret not having pursued the graduate school route immediately.

I agree, @Mike. I adore Kobayashi. Sadly, he's now dead :(

Considering how much I've learned in the past four months, I have no worries about taking E&M six months from now

@TedShifrin We put much less emphasis on gauss's law and ampere's law for exactly that reason. They don't want to re-teach all the calc 3 stuff. So they kinda half-ass it.

@Clarinetist: Actuarial stuff used to be far more math-based. (There was an exam specifically on numerical analysis.) They changed it 10 years ago. Now it's entirely business-based, with a bit of stat.

@teadawg1337 Every year, for the rest of your life, you will realize how much stupider you were the year before.

@Kevin: See, dumbing down, dumbing down ... :P

Until one day you get old and the arc starts falling.

Thanks @Mike

No problem @Ted

@evinda Well, at most one time. Just remember that you're not (necessarily) looking for equality, but for closeness.

I've been old for 25 years, @Mike.

@TedShifrin They reason that these things aren't really useful for engineers anyway and so spend that time on other things.

Sorry about your arc, @Ted

I guess I'm no longer even arc-connected, @Mike.

Pfeh @Kevin.

@TedShifrin - I graduated with a statistics degree. There are some statistics, but considering that the great majority of actuaries don't even know what a hypothesis test is, I would say that actuaries don't know statistics at all from the exam process. The whole exam process is just a matter of having done so many problems that you see a problem on the exam and know the process to solve it. No understanding whatsoever. I wish I were around back when they still had that numerical analysis exam.

My physics course at MIT was much more math-intensive. We used Kleppner/Kolenkow and then Purcell, @Kevin.

Wait, nvm. I have learned Stoke's Theorem and the Divergence Theorem.

@Ted I'm with you. I think sweeping it under the rug only makes it worse when they have to do actual engineering and solve some coupled DEs using finite-element method or something and can't figure it out

You get no argument from me, @clarinetist. I just taught probability and had some students in there working on their actuarial certificate. But I had fun doing the conditional variance formula and applications :P

Yes, @teadawg, and your course won't use any of it.

Well, one day you'll really learn Stokes' theorem (his name is Stokes, not Stoke). And it'll be grand.

But I'll give you hard problems on that stuff :P

@TedShifrin - Yep, that stuff is fun... even better: learning probability with measures. I wish they put that stuff on exams. :P

Note: I'm not claiming you haven't learned Stokes' theorem. But one can really really learn Stokes' theorem. :)

@Clarinetist: As it was, a third of my probability class got Ds and Fs.

@MikeMiller I've never learned the generalized Stokes Theorem so :-P

Watch my lectures on video, @Kevin :P

Oh, it IS Stokes' Theorem. I made an error when I was writing my notes....

why not?

@TedShifrin Perks of retiring soon? DGAF what the department thinks of all your failing students?

90% of math people don't know it, @Mike, not to mention physicists and engineers.

I know that, @Ted. But I think it's astonishingly beautiful, and they should. :)

@Kevin: Even our probability expert who's taught the course a dozen times and taught it last year had grades like mine. I'm not out of line.

Oh, and he is a notorious easy grader.

@Ted Ah okay, thats good then.

@TedShifrin - Haha, really? O_o I've graded for a few probability classes... so maybe that's not as surprising as it sounds, now that I think about it. I was a bit cruel. If there was a probability question for which the answer was outside of $[0, 1]$, I gave the person a 0 automatically.

@Kevin: I had 11 A's and A-'s out of 30, I believe.

Fair enough, @Clarinetist. No common sense. You fail.

@MikeMiller The machinery to learn it seems to require some knowledge of Real Analysis 2, forms and such and I just have no idea about these things

On the homework, or the question @Clarinetist?

@MikeMiller, on the question.

@Kevin: As I said, watch my videos. You'll learn it surprisingly quickly :P

@Clarinetist I would do the same.

I've learned about Stokes' Theorem, but I need another book to learn it more in-depth

@Ted Whats the prereq? Real Analysis 1?

OK, I'm going to try to finish grading. Night.

I would rather they show the work and say something like "I thought I did it right but the probability won't come out correctly" on their homework, haha.

Stewart's Calc: ET is pathetically short in the vector calc section

No, @Kevin. Less. I do prove the inverse and implicit function theorems in there and define derivatives rigorously. But you can jump into the differential forms and line/surface integral stuff and make sense of most of it.

@evinda No, you should search for D[i] itself.

@Clarinetist We do the same thing for people who gives answers which are, say, a speed greater than $c$

@teadawg: Most people who write calculus books don't understand multivariable stuff worth a f***.

@teadawg1337 The thing we're talking about is a different sort of Stokes' theorem, much more general than what you're learning about. (But yes, Stewart's calculus is not the best source.)

@TedShifrin have fun with that. I just finished my grading

Heya, @JMoravitz. Well, come do mine. :)

Alright @Ted, it's going on my list then. Good luck grading.

110 quizzes was enough for one day, thanks.

LOL, you might not know undergrad diff geo, @JMoravitz, but you could learn :)

Unfortunately you have to sit through the crappy university calculus class before you can take other stuff.

Well, I learned using what I already have. Stewart's Calc: ET was given to me as a high school graduation present

I tried to teach myself using vector calc using Stewart when I took the Math GRE last time. Awful, awful exposition, I hate to admit. I feel like I was just memorizing a list of equations.

If you truly know Stewart's book and can work 70% of the problems, you should try to place out of calculus courses, @teadawg.

Shoulda asked for an amazon gift card. ::)

@DanielFischer But if it doesn't exist the Binary Search algorithm will return the value 0. How can we find in this case the difference with the desired property?

I didn't ask for it, Mike :P

But then there'd be nothing for you to take to get high grades in, @teadawg.

That's how almost every standard calc book is on that stuff, @Clarinetist. It takes a good teacher who understands the stuff deeply.

OK, I'm gone.

@evinda Modify the binary search so that it doesn't return 0 but something useful, whether or not the target exists in the array.

Btw, I don't know if you all heard, but I think there's a new version of Stewart's text coming out in 2015/2016.

Do you have Spivak's book?

@TedShifrin I went through all of Stewart and made sure to do every single problem with red numbering, and then some

TedShifrin, he's the professor we all need right now, but not the one we want

I've also done about 70% of the Problems Plus following every chapter

I despise that book.

Have any of you read Apostol? What's so good about it? [It just seems so expensive...]

@Clarinetist Apostol's Calculus I/II?

I've read Apostol's Mathematical Analysis

@teadawg1337 - Yep, that's it.

Calculus I/II.

Nope, too damn expensive.

I'd much rather not spend $400 on two books

@teadawg1337 - Haha, I know, right?!

There are high school books going for $200

I got lucky and found Apostol's Mathematical Analysis at a garage sale for $2.50

It's in really good condition, too

Now THAT's a deal. I got Stewart at Half-Price Books for $72. Not perfect condition, but it holds up and I can read it. :)

and I'm talking about the current edition (7E).

@Clarinetist Stewart's Calculus: ET (7E)?

Yep.

I got it new as a graduation present, I'm spoiled

Welp, back to using my results from earlier today to evaluate $\sin{(\frac{3\pi}5)}$

Cya guys later

I'll be going too. See you all later!

Phew, I've finally arrived at $\displaystyle \Gamma\left(\frac35\right)=\frac{\pi}{\Gamma\left(\frac25\right)}\sqrt{2-\frac2{‌​\sqrt5}}$

That was MUCH more trouble than it was worth...

Hello!! Is someone here who is familiar with measure theory??

I have a copy of Apostol I,II I will give away to anyone who pays shipping :P Finally done grading papers. Whew. @Kevin: Not at all sure what your earlier remark meant.

That didn't take too long @Ted. How many papers total?

@TedShifrin, In all seriousness, I'd be happy to take a few books off your hands.

@JMoravitz: 25, 5 problems each, but I did some grading last night and a fair amount earlier today. :)

OK, @Kaj. Absolutely.

@TedShifrin You were leaving, so I adapted a quote from The Dark Knight for your departure. Basically, I'm saying you're Batman.

Hey there @skullpatrol

Hi pal @KajHansen how are you?

Not too bad.

Big day in the NFL tomorrow.

haha, I don't watch football myself.

Isn't your username after something about the 49'ers or some such?

The raiders.

Ahhh

Do you @KajHansen lift weights to train for a sport?

@skullpatrol, nope. Just for fun.

And for confidence + warding off depression

I'll repost this here, in case somebody can offer some advice:

Hey Jasper

Hi, I am feeling bad. Bad things just keep happening.

Lots of small bad things? Or big bad things?

Well, my OCD. Every time I try to deal with some obsessions, new ones pop up, for example. It's like never ending.

I'm sorry to hear that man

To normal people, these things are nothing. But to me, they affect me a lot. So normal people can never understand.

I wish I were normal. I might have won the Fields medal by now. But as it is, I can only do 1+1=2.

By the way, you should be going to bed.

I hope you find a girlfriend soon, let me know what it happens.

I really like the actor Justin Long, lol. Also another JL.

Last night, I watched his Drag Me To Hell.

Certainly. I met a girl the other day at the gym and we hit it off well. I'll get her number next time I see her.

Was it a good movie?

Yup, just an old movie. If I were not sick, I would have finished my PhD and gotten married by now, that makes me sad too.

:/

youtube.com/watch?v=yNzi9gXV-5U I am listening to this, does not say much about OCD, but for one who has it, can be encouraging.

What are you doing right now Kaj? Math?

Indeed @JasperLoy. Nothing too intense. Just starting my complex analysis homework that's due on Thursday.