The h Bar

0celo7

11:00 PM

@ACuriousMind my drive home is bigger than your country

ACuriousMind

@0celo7 So it is. Why does that make it insane that we don't all own cars?

peterh

@BernardMeurer Hehe, also to me is hard to say on English everything :-) Yeah, it can be hard, but it only around the cities. If you travel between the cities, it is ok, even if you don't have a GPS.

Bernard Meurer

@ACuriousMind I have actually entered and had lunch at Bielefeld

Lots of actors pretending to be residents

0celo7

@ACuriousMind just...how do you get around?

Bernard Meurer

@0celo7 Bahn, bus, tram, horse

ACuriousMind

11:03 PM

@0celo7 As I said, public transportation! Or by feet, or by bike.

peterh

@BernardMeurer You are in Brazil? Or in .de?

0celo7

Horse is probably more expensive than a car

@ACuriousMind By feet?

Bernard Meurer

@peterh Brazil, last week here

0celo7

I haven't walked anywhere in a while

why bother?

Bernard Meurer

@0celo7 Loosing the fupa

0celo7

11:04 PM

I don't have a fupa

Bernard Meurer

Right

0celo7

@ACuriousMind Something I was working on: Let $B$ be $\tilde g$-bounded. Fix $x\in B$ and let $(y_n)$ be a sequence. Connect $x$ to each $y_n$ with a curve $\gamma_n$. Each curve can be made to have finite length, in fact, one can bound them above. Then the sequence $L_{\tilde g}(\gamma_n)$ has a convergent subsequence.

Now the goal is to get $f$ to blow up along this sequence, and somehow get a contradiction

i.e. choose $y_n$ so that $f(y_n)>n$.

DanielSank

What's going on in here?

@BernardMeurer, back to work!

0celo7

Riemannian geometry.

Bernard Meurer

@DanielSank Yessir! ::opens larson::

DanielSank

11:15 PM

::throws tomato, mozzarella, and basil at @ACuriousMind::

::leaves::

ACuriousMind

::munches happily::

0celo7

@BernardMeurer is the fupa the roll right above the dick but below the gut

ACuriousMind

@BernardMeurer What is a "larson"?

0celo7

@ACuriousMind Calculus book I told him to read

I was tempted to tell him to read Global Calculus but I figured sheaf/categorical diff geo isn't what he was looking for.

peterh

Also @count_to_10 has gone

0celo7

11:20 PM

@ACuriousMind Aha

I figured something out.

The functional $h$ of $f$ has to be less than one, definitely.

Because (please correct me if I'm wrong) if one metric is always as large as another and is complete, then the smaller one is complete.

Because they share Cauchy sequences.

And a convergent Cauchy sequence for the big one is also one for the small one.

But our manifold was not assumed to be complete, so if the $\tilde g$ metric is larger and complete, then we have a contradiction

So it has to be something like $\mathrm e^{-2f}$.

but that makes the blowup strategy unviable.

ACuriousMind

@0celo7 You say "always as large", but why can't $h$ then be in some places larger than one?

I'm also not sure what you want to do with the "blowup" - wasn't the point to show that $f$ is bounded on $\tilde{g}$-bounded sets?

0celo7

@ACuriousMind The way I've been trained to prove something is bounded is to assume the opposite and go for a contradiction.

ACuriousMind

Ah

0celo7

going directly for a bound works sometimes.

i.e. "Cauchy sequences are bounded"

ACuriousMind

But then you don't "need to get " $f$ to blow up, you just assume it.

0celo7

11:26 PM

right, but $\sup\mathrm{e}^{-2f}$ will always be 1, so there's nothing to blow up!

@ACuriousMind Hmm.

That would be a more sophisticated functional

Bernard Meurer

@ACuriousMind Yep, it's the calc book

It seems quite good

ACuriousMind

@0celo7 Well...isn't that the proof, then?

I'm not following you really. If you're saying that $f$ cannot blow up because of the choice of $h$, then you're done

I'm not sure what the sup of $h$ has to do with $f$ blowing up, though

0celo7

I'm not saying that.

The problem is linking the boundednes of the set to the blowup of f

and prove a contradiction in there

Sir Cumference

Can anyone tell me what the partial derivative symbol ∂ is called?

I'd imagine there's a name for it

ACuriousMind

It's a "del".

0celo7

11:38 PM

@ACuriousMind huh

That's the gradient operator

ACuriousMind

Hm

Sir Cumference

@ACuriousMind One person called it "doh", another told me it was "dee"

The hell?

0celo7

It's Dee.

Sir Cumference

Sigh...

ACuriousMind

@0celo7 In German, we do at least pronounce it "del", and I've never heard anyone call the nabla "del".

Although Wikipedia agrees with you on that usage

peterh

11:40 PM

delta

NeuroFuzzy

@peterh nope! $\partial$ vs $\delta$

Sir Cumference

@peterh ∂ looks nothing like Δ or δ

NeuroFuzzy

@SirCumference it looks a little like it...

peterh

well, really

Sir Cumference

@NeuroFuzzy I guess...sorta

0celo7

11:41 PM

Makes me so mad

2

ACuriousMind

@SirCumference It's obviously derived from the delta, and in Greek handwriting both $\partial$ and $\delta$ could conceivably stand for a delta.

Sir Cumference

@ACuriousMind I thought it was derived from the latin letter d?

It honestly looks more like a curly d

0celo7

Why would anyone star that

Sir Cumference

Star what?

0celo7

Curly d is also an acceptable name

Sir Cumference

11:42 PM

Wait really?

0celo7

I cannot believe you googled this and found nothing though.

Bernard Meurer

Curly D sounds like a rapper name

0celo7

You read partial derivatives with a regular d

Sir Cumference

All right, then what is the integral symbol called?

ACuriousMind

"The integral symbol"

NeuroFuzzy

11:43 PM

@SirCumference The correct pronunciation is "slash int"

Sir Cumference

D:

ACuriousMind

It's derived from a $\Sigma$, btw.

Sir Cumference

Looks more like it was derived from this

Esh (letter)

Esh (majuscule: Ʃ Unicode U+01A9, minuscule: ʃ Unicode U+0283) is a character used in conjunction with the Latin script. Its lowercase form ʃ is similar to a long s ſ  or an integral sign ∫; in 1928 the Africa Alphabet borrowed the Greek letter Sigma for the uppercase form Ʃ, but more recently the African reference alphabet discontinued it, using the lowercase esh only. The lowercase form was introduced by Isaac Pitman in his 1847 Phonotypic Alphabet to represent the voiceless postalveolar fricative (English sh). It is today used in the International Phonetic Alphabet, as well as in the alphabets...

ACuriousMind

@SirCumference It's derived from the $\Sigma$ because of the integral's definition as the limit of a Riemann sum.

0celo7

@ACuriousMind huh? Integral is defined in terms of primitives

ACuriousMind

11:45 PM

@0celo7 Stop trolling :P

Sir Cumference

@ACuriousMind Dude, sigma looks nothing like that

0celo7

@ACuriousMind ...

ACuriousMind

@SirCumference So?

0celo7

I thought Riemann sums were heuristics

Sir Cumference

@ACuriousMind It looks more like that Esh letter

More likely it's derived from the esh

0celo7

11:46 PM

No it's from S.

ACuriousMind

@SirCumference lol, certainly not,

0celo7

It's a big S

ACuriousMind

The old way of writing s inside a word looks pretty similar

"The notation was introduced by the German mathematician Gottfried Wilhelm Leibniz towards the end of the 17th century. The symbol was based on the ſ (long s) character, and was chosen because Leibniz thought of the integral as an infinite sum of infinitesimal summands."

0celo7

@ACuriousMind serious question, how does one know that the Riemann sum converges

Sir Cumference

Well it looks a bit more like an s depending on what region you are from

ACuriousMind

11:47 PM

@0celo7 By, uh, checking it?

Sir Cumference

That's English, German and Russian, respectively

0celo7

There are general theorems on integration though

Sir Cumference

So I guess the Russian version of the integral sign looks like an S

ACuriousMind

@0celo7 You have to ask a more specific question if you want an actual answer

peterh

The German version is the best compressable. It has the smallest Kolmogorov-complexity.

Sir Cumference

11:50 PM

Well in Germany and Russia, definite integrals look more like this

$\int\limits_0^T f(t)\;\mathrm{d}t$

With the range on top and bottom

Unlike $\int_0^T f(t)\;dt$

So that's some interesting trivia

ACuriousMind

Uh, that will differ depending on the person typesetting the thing. That the "German" and "Russian" typographic traditions would have it that way doesn't mean it looks that way "in Germany" or "in Russia"

Bernard Meurer

You guys are insane

Sir Cumference

Oye, made a mistake

That's right, ACM

ACuriousMind

However, sampling a few German versions of books I can access, it appears they indeed seem to mostly follow the German tradition

0celo7

@ACuriousMind I don't really want an answer.

We did integration via primitives in my RA class because "Riemann sums are much harder to make precise"

ACuriousMind

11:55 PM