Mathematics - 2012-05-18 (page 2 of 3)

8:01 AM

i wrote an answer on another site about some recursively-defined series, and i read it the other day (i wrote my answer 3 years ago). i was like: "i wrote that? heck, i don't even understand what i did there." i suppose remembering my address will be the next thing to go (the phone number is already a lost cause).

J. M.

@DavidWheeler How many digits are there in your phone number?

David Wheeler

10 (if you count the area code)

Brian M. Scott

I remember phone numbers from Berkeley (we left when I was just seven) and Amherst, Mass. (we left when I was just 12), but I’ve lost most of the ones in between.

J. M.

@DavidWheeler Ech, and I thought eight digits was troublesome...

David Wheeler

i'm good for the area code and the exchange prefix, but the last 4 digits, i'm like: "it's got a 30 in it somewhere"

Brian M. Scott

8:04 AM

@JM Around here you need ten: we have at least two area codes, and they don’t determine what’s long distance for you.

David Wheeler

oh, true story: i was watching this show called "touch" which has this mystical mumbo-jumbo about the "amelia sequence", part of which is the 4 digit sequence 1188

Matt N.

@BrianMScott I don't like the idea that one cannot remember stuff learned after a certain age : (

Brian M. Scott

@MattN It does seem to disappear faster.

David Wheeler

and i thought "1188" that means something to me...and i tried to remember what. a phone number? pin number? guitar chord? i couldn't place it, but it was bugging the heck out of me.

J. M.

@MattN Yes, but when you're juggling so many stuff at around the 30's and 40's, things will tend to blur.

David Wheeler

8:06 AM

it finally hit me...it was the plan number of a tract house i had designed trusses for, many times.

Matt N.

@JM So you're saying it's not age it's quantity?

Brian M. Scott

@DavidWheeler !!!

@MattN Both, I think.

J. M.

@MattN Also, the Internet made me lazy. I know I can look stuff up, so all I actually remember for a good portion of things is how to look them up...

"I forgot the exact wording, but it should be in that book somewhere... let me check Google Books."

Matt N.

I'm planning to fight it.

J. M.

So that's my dirty secret behind answering stuff here. :) I need to review for a bit before writing.

Matt N.

8:10 AM

: )

David Wheeler

@MattN it's not so much memory, as "allotted memory space". one's brain is no longer "the quicker-picker-upper".

Zhen Lin

Make room in your memory palace!

Matt N.

By drinking? Or what? : D

I am doing actually: I don't remember people's names and I also can't remember history and geography for very long.

(not by drinking, I'm a natural)

Brian M. Scott

So you have an excellent forgettery?

David Wheeler

i'm not a neuro-biologist, but i think what happens is that once neural connections are made, they're there. so it's almost impossible to "forget how you knew what you used to know". even if the details are gone, the pathways remain. so older facts "stay better" because the neural pathways of access are well-worn

Matt N.

8:14 AM

Yes. But I hope it only deletes boring and irrelevant things.

I'm not quite sure.

Brian M. Scott

Mine deletes more than I’d like, but the really annoying thing is the increasing difficulty in accessing information that actually is there.

J. M.

@DavidWheeler Well, I find I can "go through the motions" with an appropriate prompt...

Matt N.

@BrianMScott : / I guess the more you access one thing the easier it is.

J. M.

If I exert myself, I can't remember it, but when somebody supplies a trigger, things rush out all of a sudden...

Brian M. Scott

@MattN Oh, definitely. But there are some street names, for instance, that I know perfectly well from cycling yet often have trouble calling to mind when I want them. Of course, then I remember them three hours later.

David Wheeler

8:18 AM

it's weird though...like, i still remember first-year calculus, clear as day. i've forgotten a LOT of multi-variate calculus, and a good deal of topology. i remember a lot more algebra.

J. M.

It's also happened to me that the thing I try so hard to remember on, say, Wednesday, I remember upon waking up at Friday morning. It's always that time... no idea why. That's probably the only way I remember things I forgot without a prompt.

David Wheeler

i wanted to do my undergraduate thesis on the rubik's cube, which was a new thing at the time. but the only competent algebraist on the faculty, was also the most popular, so i got stuck with this guy who forced me to study fundamental groups instead. at the time, i was pissed.

Brian M. Scott

@DavidWheeler Fundamental groups always made me want to get drunk, too. :-)

Matt N.

@JM Funny!

Brian M. Scott

@JM It can be any time for me, but it’s always when I haven’t been thinking about whatever it was.

J. M.

8:23 AM

@MattN Well, at least I can laugh at it now... :)

David Wheeler

to this day, i have a "mental block" regarding covering spaces because of it. we had to give an oral presentation. mine started with: we take the loop. we loop-de-loop and get the group-de-loops.

Brian M. Scott

@JM Have you noticed that your coil has a little human figure in it, legs to the right, head to the left?

Matt N.

@JM I meant "funny" as in "weird" : )

J. M.

@MattN Works both ways.

Brian M. Scott

@DavidWheeler Oops.

J. M.

8:24 AM

@BrianMScott Yes, must have been an artifact of the grid I used... it wasn't intentional. :)

David Wheeler

for a proof that the punctured sphere was homeomorphic to the plane, i popped a balloon.

3

J. M.

@DavidWheeler That's the most vigorous way to demonstrate it, I suppose. :)

Matt N.

@BrianMScott Actually, I had a headache for about 8 days last week and I've been feeling sick. I'm quite sure it's not the flu but rather the fact that I'm stressed about the two looming exams in august.

David Wheeler

i illustrated the fundamental group of the torus with a bagel i bought at the local coffeeshop.

Brian M. Scott

@DavidWheeler Sounds like the sort of thing that Jearl Walker would have done if he’d been a mathematician instead of physicist.

@MattN That’s still some way off; what are they?

J. M.

8:26 AM

@BrianMScott You know Jearl Walker personally, by any chance? :)

Matt N.

@BrianMScott Commutative algebra and functional analysis.

Brian M. Scott

@JM We’ve spoken, but only a few times.

Matt N.

The commutative algebra one consist of homological algebra (about 20%) which I'm looking forward to learning but I'm just not suitable to take exams.

Brian M. Scott

@MattN I know nothing about the first; I was dragged into a bit of the second, thanks to a couple of colleagues.

David Wheeler

i should have brought some fishnet stockings to illustrate the lattice property of the covering space...did not think of it at the time....

J. M.

8:28 AM

@BrianMScott Oh, okay. I loved his Sci. Am. articles...

@DavidWheeler I'm not sure you can get away with buying those without a few weird looks from the shop... :)

Brian M. Scott

@JM Most students thought him a very good teacher, too.

David Wheeler

at my school, yes. i could have.

Matt N.

@JM Jearl Walker Texas Ranger?

Brian M. Scott

Though some would be very happy never to meet another damned penguin on ice.

Matt N.

Excuse my silliness. It's not even funny.

@BrianMScott So tell me: you don't know about tensor products?

Brian M. Scott

8:31 AM

Absolutely nothing.

J. M.

@MattN Well, should you be able to spare some time, try looking up a copy of The Flying Circus of Physics. Absolutely fascinating.

Matt N.

@BrianMScott Interesting!

@JM Thanks for the book recommendation. It has an excellent rating on amazon.

David Wallace

@DavidWheeler Didn't your mother tell you not to play with your food?

David Wheeler

i STILL play with my food. for example, when i eat green beans. i only eat the top-most bean that is touching an odd number of other beans. this is very important to me.

Brian M. Scott

Does that make you an odd human bean?

David Wheeler

8:41 AM

even so.

David Wallace

@DavidWheeler Don't you have to move some of them to count how many it's touching; and that would potentially change the count.

And what happens if all the beans are touching an even number of others? Do you go without your veges?

David Wheeler

such are the philosophical debates that lead to my well-trimmed physique.

Matt N.

PG tips claims to be "England's No 1 tea" but I think Sainsbury's red label is much better. I think people shouldn't be allowed to make false and / or random claims.

David Wallace

@MattN It may be true, but you're just different from the mode.

Brian M. Scott

@MattN There are several possible definitions of England’s No 1 tea.

Matt N.

8:44 AM

It's quite outrageous that there is an ad campaign by Lipton claiming that it's "typically British" when Lipton is an American brand and considered undrinkable by people with taste buds.

@BrianMScott I know, I just wanted to complain : )

David Wallace

@MattN I take it you're British?

Matt N.

And I don't know anyone with UK citizenship who would drink Lipton tea.

David Wheeler

the only english brand widely available in the US is twinings.

Matt N.

But then "typically British" probably also has many definitions...

J. M.

Maybe I'm biased, but Twinings $\approx$ Sainsbury's $\gg$ Lipton

David Wheeler

8:48 AM

Lipton's is AWFUL.

Brian M. Scott

I quite like Twining’s English Breakfast. I don’t care for anyone’s Earl Grey.

@MattN I’ve drunk worse, though I’ve mercifully forgotten whose.

Matt N.

@JM I think if you drink it with milk then that's probably true. : )

David Wheeler

but most americans would not know the difference between a darjeeling or assam or english breakfast if you hit them over the head with it

Matt N.

@BrianMScott I like that too.

@BrianMScott : D I haven't. At uni they only have Lipton and the coffee equivalent of it.

David Wheeler

i like earl grey, but i prefer the bergamot flavor to be a bit stronger than it is in twinings blend

J. M.

8:52 AM

@MattN Not really; I don't care for chai. Only a teaspoon of sugar on mine.

Brian M. Scott

@MattN I can manage bad tea better than bad coffee, I think; for one thing, if they give me teabags, I can always make it stronger.

@DavidWheeler And I’m pretty sure that it’s the bergamot flavor that I just don’t care for.

David Wheeler

i like chai...but i make it differently than the stuff you buy

Matt N.

@BrianMScott Right. But if I take two bags they charge me double : )

Brian M. Scott

@MattN Tsk. Most tea needs two bags!

David Wheeler

i cook the spices with the milk and honey, and then pour that over the tea leaves through a strainer

David Wallace

8:54 AM

@BrianMScott Leaves, people, not bags!

Brian M. Scott

mutter, mutter What good is tea if it doesn’t dissolve the spoon?! mutter, mutter

David Wallace

My grandmother used to say "why would I want my tea wrapped in toilet paper?"

Matt N.

@BrianMScott You should try Sainsbury's red label as soon as you get a chance. You'll love it.

Brian M. Scott

The only acceptable adulterant in tea is a little lemon juice, and I can do nicely without that, too.

David Wheeler

@BrianMScott yes, some people find the bergamot flavor "too floral"

Brian M. Scott

8:55 AM

@DavidWheeler I don’t perceive it as floral; it’s just unpleasant.

Faintly medicinal, perhaps.

David Wheeler

lemon is to take the bitterness out, a good tea shouldn't be bitter (you steeped it too long)

Matt N.

I vary the add-ons. Sometimes milk, sometimes sugar, sometimes both, sometimes neither.

But coffee has to be dark and strong.

J. M.

@BrianMScott My friend put it this way: "it smells more like something I'd rub on a sore arm than something I'd drink..."

Matt N.

: D

Brian M. Scott

@MattN I can’t stand either in tea. (Do you know how hard it is $-$ or at least used to be $-$ go get a native English(wo)man to pour a cup of tea without first putting a huge dollop of milk in the cup?)

@JM :-) I can see that!

David Wheeler

8:57 AM

darjeeling is especially good "straight", as it is a fairly mellow tea

Matt N.

@BrianMScott No, no idea. : D

Brian M. Scott

@MattN I once had a lovely woman fail twice in a row to pour me a cup of black tea. She succeeded on the third try. Fortunately, there were other guests.

Matt N.

@BrianMScott : )

Brian M. Scott

And she was so dreadfully concerned that I was unwittingly making a mistake, because she always brewed the tea very strong, knowing that she’d be diluting it; I thought that it was just approaching just about right.

@JM: I love Iverson notation, but I rather suspected that the OP would prefer something very straightforward.

Rajesh D

9:10 AM

@JM : now this is interesting (gravatar)

Hi @David

David Wheeler

@BrianMScott i think you still have that numerator wrong

should be (a-2)(a+1) + other term

Brian M. Scott

@DavidWheeler I didn’t give him the correct numerator: I told him what was wrong with the last step in the calculation that he actually made.

David Wheeler

i understand, but it makes for a confusing read

@RajeshD you realize you ping 2 Davids don't you?

Rajesh D

yes that was intentional

two at one go

Brian M. Scott

@DavidWheeler How so? It’s clearly introduced as a counterfactual (‘If your first step had been right’), and I maintained the subjunctive throughout.

David Wheeler

9:15 AM

i suppose the two of us will have to duke it out to see which one of us has your affections. so be it.

Matt N.

Wow, Brian, I want this badge too : )

David Wheeler

@BrianMScott i'm impressed that you know what the subjunctive is.

Brian M. Scott

@MattN I’ll be damned! Talk about an exclusive club.

Matt N.

@BrianMScott : )

Brian M. Scott

@DavidWheeler It’s even a natural part of my idiolect.

Matt N.

9:16 AM

And this : )

No surprise of course in both cases.

I better start doing some work towards those.

Brian M. Scott

I’m certainly not surprised that Theo has it; I am a little surprised that no one else does.

Matt N.

(i.e. study, not answering question)

Rajesh D

@DavidWheeler lol

Matt N.

@BrianMScott No one else is awesome enough : )

Brian M. Scott

I’ll bet that Martin could have either one if he really wanted to.

Matt N.

9:18 AM

Are there gold equivalent ones for these?

Brian M. Scott

Dunno.

Matt N.

@BrianMScott Sleziak? Or which?

Brian M. Scott

@MattN Yes, Sleziak.

David Wheeler

@BrianMScott idiolect is almost certainly a 20-dollar word

Matt N.

@BrianMScott The most likely person to have one if they exist is Arturo.

And yes, they do!

Brian M. Scott

9:21 AM

@MattN There apparently are gold equivalents. I just checked Arturo’s badges, and he has gold badges in linear algebra, homework, abstract algebra, group theory, and calculus.

And yes, I wrote that before you posted. :-)

Matt N.

Yes. : )

Brian M. Scott

@DavidWheeler Well, linguistics is my major hobby.

David Wheeler

how nice! i speak english better than my typography might indicate, all personal issues with capitalization aside.

Brian M. Scott

@MattN BD has them in elem. nr. th. and abstr. alg. Which is also no real surprise.

J. M.

@BrianMScott Oh well... :)

Brian M. Scott

9:27 AM

@JM I first encountered the notation in the IBM journal in which he used it to describe the machine instructions of the IBM 360.

J. M.

@BrianMScott Ah yes, pre-APL...

Brian M. Scott

Yep.

But I thought that the notation was really neat.

J. M.

Iverson used parentheses first, if memory serves.

David Wheeler

are you guys talking about the bracket?

J. M.

@DavidWheeler Yes, those brackets.

David Wheeler

9:30 AM

like the kronecker delta is [i = j]?

J. M.

@DavidWheeler Yes, like that.

Now that you mention it, I'm rather fickle with Kronecker's. Almost always I only use it when I'm dealing with orthogonal functions...

I know I can use Iverson to indicate an orthogonality condition, but somehow I can't shake off the Kronecker habit there.

Matt N.

9:51 AM

@BrianMScott The Zariski topology is exactly the same as the cofinite topology, right?

Brian M. Scott

I think so, yes.

I always have to look it up, since it doesn’t normally come up (under that name) in general topology.

Matt N.

Zariski doesn't, I assume.

I prefer cofinite topology.

Because the name contains information.

Brian M. Scott

That would be true in $\Bbb R^n$; once you get into the serious stuff, things get more complicated, and the topologies aren’t necessarily even $T_1$.

Matt N.

@BrianMScott So they're not the same!

Brian M. Scott

@MattN Not by definition, no.

That’s just the one setting in which I’ve most often run into it.

Zhen Lin

10:02 AM

If you are only working with the closed points of an irreducible curve over an infinite field, then the Zariski topology is the cofinite topology.

Otherwise it's a little bit more sophisticated.

Even in $\mathbb{R}^n$.

Brian M. Scott

Fortunately, I’ve only ever had to try to answer questions (not here) about the simplest settings.

t.b.

10:46 AM

@MattN By definition the (non-empty) closed sets of the Zariski topology are the zero sets of polynomials. Since a polynomial in one variable over R or C only has finitely many zeros the Zariski topology there is the cofinite topology. But already in two dimensions the situation is entirely different.

Matt N.

Teddy bear!!

t.b.

Hi Matt!

Matt N.

runs at teddy and hugs him

t.b.

heh :)

Matt N.

Thought you'd be gone for at least a week again.

t.b.

10:47 AM

No, but I'm only here for a few minutes. I probably won't be able to come back till Monday I guess.

Brian M. Scott

You have managed to pop in to make a few comments on questions.

Matt N.

No worries. Missed you like monkeys last week but shouldn't say that because don't want to make you more likely to appear here since don't want to make you waste time.

J. M.

@tb In which case: hello, and nice to see you for a short while. :)

t.b.

@JM Hi J.M. Nice new Gravatar you have there.

J. M.

@tb Thanks! It took some amount of thought and work to make. :)

Brian M. Scott

10:51 AM

@JM How big a collection of them do you have now?

t.b.

@BrianMScott Yes I have. I guess I should be answering that topological group thing, but I'm still looking for a good reference for that user to learn more. Unfortunately, the only ones I know (like Weil or Hewitt-Ross or Bourbaki) are quite dated and difficult by many of my students or otherwise just plain unreadable (like Stroppel's thing).

J. M.

@BrianMScott Didn't count, but the pictures and code for all the artwork I've done take about 3 GB on my hard drive.

...and I've only released about a quarter of them.

Brian M. Scott

@JM 3 GB? That's quite a chunk!

J. M.

@BrianMScott Not counting the failed experiments, of course. :D

Brian M. Scott

@tb Never learnt much about topological groups. I’m not sure why.

Matt N.

10:54 AM

@tb Did you manage to show sleep who's boss? (at least a little bit?)

t.b.

@MattN me too, I've got enough votes but I still have about a dozen questions to answer in that tag. But Brian's just too darn quick at those questions that spark my interest.

Matt N.

: )

t.b.

@MattN Yes, finally. I was like a walking dead yesterday evening, but I managed eight hours last night, so that's good :)

Matt N.

@tb That is awesome!!! I'm so glad!

David Wheeler

@tb! quick! tell me a topological group that isn't hausdorff!

t.b.

10:57 AM

Take any one with the trivial topology.

Zhen Lin

Probably some algebraic group with the Zariski topology...

t.b.

@ZhenLin An algebraic group is a topological group only if it is finite, that's a nice exercise.

David Wheeler

ok, that works, because then {e} isn't closed.

J. M.

@tb Congratulations. :)

Matt N.

@tb Now you do that every day. : )

Zhen Lin

10:58 AM

@tb Ah, the product does something stupid.

t.b.

@DavidWheeler Well, the fact that $T_0$ implies $T_{3 \tfrac{1}{2}}$ for topological groups doesn't make it easy to come up with interesting examples.

So the really interesting question is to find $T_{3 \tfrac{1}{2}}$-groups that aren't $T_4$.

J. M.

Since there's a sizable crowd now: do any of you guys have a good grasp of the differential geometry of minimal surfaces?

t.b.

@MattN I'll try my best :) I'm being more modest, though, 8 hours is a whole lot for the likes of me.

Zhen Lin

I did a little bit about minimal surfaces last year. I forget what I did.

Or, indeed, what the definition is...

J. M.

@ZhenLin surfaces with zero mean curvature. :) You know, soap bubbles...

Matt N.

11:02 AM

@tb Never mind trying your best and being modest: do it! : ) Otherwise Matt will be sad.

t.b.

@JM Enneper's surface might be a nice thing to draw textures on...

But more seriously, what are you looking for?

J. M.

@tb Yeah, that was already one thing I did. I'm actually looking at genus-1 surfaces now. In particular, I'm having trouble applying what I know about the Weierstrass elliptic function to building things like the Chen-Gackstatter surface.

Matt N.

@JM I'd like it if you looked like one of these.

J. M.

(or maybe I'm just misusing the Enneper-Weierstrass parametrization)

Zhen Lin

Mmm... I remember that name.

There was some weird algebra that showed that the Cauchy–Riemann equations were satisfied.

J. M.

11:08 AM

Anyway, just in case: it sounds like something I can ask on MO, no?

(The troubles I take just for producing fine artwork... :D)

@MattN I can fake most of those, I think, but I'd have trouble with making convincing-looking sprinkles.

t.b.

@JM The only reasonable presentation of the Weierstrass parameterization I know off the top of my head is in this German Vorlesungsskript by Struwe.

(section 1.17)

Brian M. Scott

@MattN That green one front and centre would be cute.

Matt N.

Oh well. : )

t.b.

@MattN notes might be an exaggeration...

J. M.

@tb Apparently so. I'll need to read this deeply. Thanks!

Matt N.

11:12 AM

@JM I'll eat all sorts of donuts, even without sprinkles : )

@BrianMScott Are you saying that because it has got a beard? (= subliminal message because I said beards were for monkeys? : ))

Brian M. Scott

This is the second time I’ve had someone here complain about using l’Hospital’s rule on sequences. Grr.

@MattN Not in particular. It’s just very vivid, and the ‘eyes’ amuse me too.

t.b.

@JM I guess you want to play with the formula in Satz 1.17.3 (page 47) and the example there. It's not much, but maybe it gives an idea.

J. M.

@BrianMScott Do you think they'd still bitch if you had used Stolz-Cesàro instead? :)

@tb Just got to that formula. It's a long way from an actual program, but I can chew on that.

t.b.

@BrianMScott well, at least it's not the usual complaint about circularity...

J. M.

I've already tried searching at Google Books, but the nice refs that discuss both elliptic functions and minimal surfaces aren't accessible for me. :(

Brian M. Scott

11:17 AM

@tb Oddly enough, I’d never heard the complaint in any form until I ran into it here a while back.

J. M.

I only managed to figure out Costa's surface after much thought and some guessing, for instance.

Hello, Ilya.

t.b.

@JM Did you try Kühnel's book? The chapter on mimimal surfaces starts here.

and it contains a seemingly detailed discussion of the Weierstrass parameterization.

J. M.

Tsk, no preview here. :( It looks good, based on the table of contents...

t.b.

Google wants you to work, not read :/

Matt N.

It's actually not because of Google that not every single book is freely available on Google Books...

J. M.

11:24 AM

@MattN I know, but it's no less annoying when a section you can read can't be seen by somebody halfway around the world...

Brian M. Scott

Reshetikhin-Turaev TQFT is quite a mouthful.

Matt N.

@JM Sure.

J. M.

@tb Maybe some other day, it'll become accessible. I've bookmarked it, thanks.

At least, the catenoid was easy to do...

Brian M. Scott

That’s quite nice. Hm; could you give it a twist?

J. M.

@BrianMScott I've tried the helicoid already; unfortunately the result looked... noisy. I haven't figured out how to reparametrize so that it agrees with a hexagonal mesh.

Brian M. Scott

11:34 AM

@JM Too bad: it would remind me even more strongly of an interesting toy that I had years and years ago!

J. M.

What's it called?

Brian M. Scott

@JM No idea. It was two disks with parallel strings running between them around the edge so as to make a cylinder. But then you could rotate one end relative to the other to get pretty shapes, until you worked it down to a cone.

Sorry: that wasn’t very coherent. But it’s about time for me to head for bed.

J. M.

See you later!

Matt N.

@BrianMScott Good night!

Brian M. Scott

G’night, all!

t.b.

11:41 AM

@JM a few screen grabs with parameterizations from Kühnel's book: part 1, part 2, part 3, part 4. Hope those help.

@BrianMScott Good night, Brian, see you soon!

Brian M. Scott

@tb Likewise! Take care of yourself.

J. M.

@tb Not surprised the catenoid was the very first example. :) Thanks for taking the time!

robjohn

11:56 AM

@BrianMScott Good night!

as I get back :-)

J. M.

Hey rob.

robjohn

@JM howdy!

t.b.

@robjohn Hi, robjohn!

robjohn

I finally came across a problem that really uses inversive-geometry. @anon looked at it earlier and had some difficulty interpreting it, so I tried to clarify it. I don't konw if anyone else cares about that topic. There are only 12 questions so tagged, so it is not very popular

@tb How's it going?

t.b.

@robjohn pretty busy these days. And as usual when you show up, I'm on the verge of leaving...

Chris

12:01 PM

Hello all!

Is there a linear map $ f: \mathbb{R^{4}} \rightarrow \mathbb{R^{4}} $ with a basis a, whose matrix is diagonal?

Would this linear map f be this:
$ f(x) = x_{ij}$, if i ==j or 0, if i != j ?

t.b.

I saw the answer but I'll have to look closer another time.

robjohn

@JM are those going to become future gravatars?

@tb that happens with various time zones :-(

J. M.

@robjohn Had a quick look; looked good!

robjohn

@Chris what are you considering the basis of a linear map?

Matt N.

@robjohn Hello ~~resident numerologist~~ mean square! : ) Did you see my rep?

J. M.

12:03 PM

@robjohn I did the catenoid already. :)

t.b.

@robjohn I think Srivatsan introduced the tag. I guess these two answers of mine would also qualify as using inversive geometry.

robjohn

@MattN pretty cool!

Matt N.

: )

Chris

@robjohn: The basis a is a basis of $ \mathbb{R^{4}} $ so the matrix is (f : a,a)

t.b.

I only have palindromic rep at the moment. Nothing much to impress the resident numerologists... Unfortunately I missed the moment when I could have adjusted BD's rep to 66'666

Matt N.

12:06 PM

The next one for you will be 44444, I suppose.

t.b.

Yes, Kannappan spoiled the fun with 33'333

and robjohn didn't see enough reason to spoil his zero-downvote clean slate :)

Matt N.

: )

t.b.

Anyway, I really should be going now. Have a nice week-end you all and enjoy your diabolic days, Matt!

Matt N.

@tb Have a nice weekend you too! Bye.

J. M.

See you later, t.b.! Thanks again for the help!

Matt N.

12:11 PM

Nice surprise : )

Matt N.

12:48 PM

@BrianMScott I have a question for when you come back: why do we ever say "open neighbourhood"? It seems to make no sense to me. Of course every open set is a neighbourhood so the only situation where it seems appropriate to me to call a set a neighbourhood is when it's not open.

Chris

I found this theorem after a search:
"Let L be the linear transformation

L(v) = Av

then A is diagonalizable with n linearly independent eigenvectors S = {v1, ... ,vn} if and only if the matrix of L with respect to S is diagonal."

Do you know if it is true the other way around?
What I mean is, if A is diagonalizable with n linearly independent eigenvectors S = {v1, ... ,vn} then the matrix of L is diagonal.
Is that true?

Antonio Vargas

3:26 PM

Hmm, guess he didn't like my edit.

J. M.

@AntonioVargas Eh, at least the proper tags were restored later.

Maybe s/he can use an explanation of why the original tags were irrelevant.

Antonio Vargas

Yeah, I should have included a short note in the reason for editing at least.

Moshe

Anyone here?

Antonio Vargas

I think I am.

By the way, did you know that magnets are awesome?

J. M.

@AntonioVargas I've seen that; quite nice!

Antonio Vargas

3:38 PM

@JM I wonder if it scales well. Need to send supplies down a mine shaft?

Slap an electromagnet on your payload!

robjohn

@AntonioVargas I wonder what kind of current is generated in the pipe by that?

J. M.

@AntonioVargas Well, they do use electromagnets to lift cars, but I'm told the electricity consumption for those is brutal.

robjohn

@AntonioVargas If you isolated the pipe with a diode, you might be able to build up a decent static charge, and then let it discharge :-)

Antonio Vargas

@JM I googled "electromagnet cat lift" with disappointing results.

robjohn

@AntonioVargas how about "car lift" :-)

Antonio Vargas

3:43 PM

@robjohn I'm no physicist but I'm thinking you might build up enough charge to slightly annoy a mouse after a while!

@robjohn "The fingers you have used to dial are too fat..."

J. M.

@AntonioVargas I've seen frogs being levitated, but nothing as big as cats. But they use supercooled magnets for those, not electromagnets.

Antonio Vargas

@JM You have just blown my mind.

J. M.

@AntonioVargas Yes, precisely that. :)

Antonio Vargas

@JM apparently they have done the same (or similar) with mice, but I can't find a video.

J. M.

But keeping things that cold long enough to levitate cars remains impractical, so we still use electromagnets in the junkyard.

@AntonioVargas Well yes, animals of more or less that size. If they ever manage to levitate a cat, that should be journal-worthy...

leo

3:52 PM

hey

J. M.

hello leo.

Antonio Vargas

Hi

leo

@robjohn, what do you think of this?

leo

4:09 PM

See you!

Antonio Vargas

5:20 PM

Is it a common misconception that the comparison test gives the precise radius of convergence?

I've encountered this while tutoring in the help center at my university and just now in a question here.

(context)

robjohn

@leo Looks good (+1)

leo

Thanks!

robjohn

@JM does that mean they levitate frozen frogs?

leo

@AntonioVargas It's the the ratio test what give us the ratio of convergence, right?

crazy frogs

Antonio Vargas

@leo Yes, if it's applicable.

robjohn

5:59 PM

@Bill: I answered a question here that Zev migrated to physics.SE. The question was associated with the OP's account there. I created an account there and flagged my answer asking that the same be done for it. It has been about 5 hours, with no change. I am wondering if it might not be possible to do this. Do you know?

leo

6:14 PM

The chat must have a playlist so that we all can add some song

it was an idea in chat.TeX.se

by now

good bye

:-)

Bill Dubuque

6:59 PM

@robjohn I'm not aware of any way to do this. Perhaps you should post a question to meta so that mods with migration experience will see it, and so others can learn from the experience.

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$Mathematics$ Mathematics