Mathematics - 2021-08-03 (page 2 of 2)

Ted Shifrin

5:03 PM

I used to call that baseball addition of fractions when I taught math for (future) elementary school teachers.

user178758

Nice name, sir.

robjohn

@TedShifrin perhaps a bit too weighty for the average elementary school teacher ;-)

Ted Shifrin

Well, not to be sexist, but some women are into baseball. But that is the only situation I can think of "in real life" where we add by adding numerators and adding denominators.

leslie townes

ted, this morning, my daughter, once disrobed from her pajamas, began yelling "YOU CAN'T CATCH ME!" and ran around the house. it was imperative that she be dressed. we were 20 minutes late to day care.

copper.hat

baseball is beyond my understanding.

Ted Shifrin

5:08 PM

I don't know how your wife puts up with you and the mini-you.

leslie townes

i love baseball. i don't watch it very often. i need to see it live to be interested in it.

user178758

Cricket?

robjohn

@TedShifrin i do that sometimes to get a fraction between two others.

Ted Shifrin

@copper In this case, it's not too tough. If you batted 2/3 in one game and 3/6 in the next game, it's pretty clear you've got 5 hits out of 9 at-bats.

copper.hat

rounders, cricket, baseball. too complicated for me.

the maths i can handle...

leslie townes

5:09 PM

she also has a new epithet. "you're poo-poo." she said this to my wife at least ten times.

Ted Shifrin

Even live it is mostly boring.

robjohn

@TedShifrin it also helps that they never reduce the fractions

leslie townes

the boringness is part of the fun. you can have a conversation. who cares what is happening.

Ted Shifrin

Well, that's important, of course!! This isn't a well-defined operation on $\Bbb Q$ :P

copper.hat

when ireland decimalised currency in 1971 it considerably reduced the number of fractions used in elementary school, much to the relief of pupils.

robjohn

5:11 PM

@leslietownes my wife and I often refer to people of questionable motives as poo-poo-heads, from some cartoon we saw a long time ago.

leslie townes

where else can you get 4 hours of inconclusive sporting accompanied by a hot dog that you probably paid at least $8 for.

robjohn

@leslietownes it makes it possible to go get dogs & suds.

copper.hat

a friend invited me to some expensive box at a baseball game. i called him up and said, look why don't you invite a friend who actually understands the game? his reply, this is not about baseball, its about drinking.

leslie townes

baseball stadia are also the last place where trough-style urinals seem to be a thing.

user178758

@copper.hat wow, 1971? Why so late?

copper.hat

5:13 PM

ireland & the uk converted from LSD (yes) to a decimal system then.

leslie townes

wasn't it the same for the whole UK? who did it earlier?

copper.hat

i thought it was the same time, but never actually chekced

leslie townes

i mean the americans in their infinite wisdom did it earlier.

copper.hat

15 feb 1971

robjohn

@leslietownes but left everything else fractions

copper.hat

5:14 PM

still using inches, etc, gallons, etc

robjohn

yep

leslie townes

it's funny that many US stock markets didn't decimalize until about 20 years ago

user178758

Buffet broke the stock market.

copper.hat

was it fixed beforehand?

leslie townes

i like inches and gallons. although every time i cook i have to ask my wife "how many cups in a quart?" the answer is in the name but i can never remember.

user178758

5:16 PM

Calculation wise, I mean.

Ted Shifrin

How many recipes call for quarts of things?

copper.hat

true, much nicer than 25g of something

old units have some physical meaning

leslie townes

ted, it's the "give the cook a quart of gin so he can tolerate cooking." it might not be written down, but it's there.

Ted Shifrin

Well, in that case, grab the biggest gin bottle you can find. And be done with it.

copper.hat

furlong, acre, rood, etc

Ted Shifrin

5:17 PM

(That'll be 1.75 L, not quarts.)

copper.hat

just that not many people plough a field with a horse any more

litres/100km is a funny one to convert to

leslie townes

my wife detected that i'd had a drink in between scheduled drinking sessions. i got to deploy one of my favorite sayings from horace rumpole. a man's gin bottle is his castle.

copper.hat

:-)

rumpole is wonderful

user178758

(-:

lol

Ted Shifrin

Since I'm a gin snob, it had better be top-flight gin.

leslie townes

5:19 PM

it was bombay dry, i don't know where that fits in.

copper.hat

i just take it for malaria

leslie townes

my wife just constantly opposes my ongoing campaign against malaria

Ted Shifrin

Bombay is my every-day gin.

leslie townes

bombay sapphire is too nuanced for my taste.

copper.hat

actually, i do not fit the stereotype of my birthplace, my main imbibement is wine, with a sporadic beer.

my integrated lifetime consumption of guinness is less than a pint (a real pint, of course).

Ted Shifrin

5:21 PM

is "imbibement" really a word?

copper.hat

it is now

leslie townes

i'll allow it.

copper.hat

i'm following wilde, joyce, beckett

Ted Shifrin

I would appeal to the Supreme Court, but that's an abomination.

leslie townes

i've had quite a bit of guinness although usually not draught.

copper.hat

5:22 PM

stream of unconsciousness

user178758

@copper.hat actually, the fix could have been in before hand; but, that's a different story.

copper.hat

at least one brother has consumed a pint/hr over a 24 hr period

leslie townes

probably more jameson than guinness, integrated over lifetime.

guinness is basically a meal and i don't want a meal from liquid.

copper.hat

@user178758 the fix? (i'm still accumulating caffeine while on a boring slack meeting)

the liquid lunch

actually, from a social perspective i liked that my companions consumed so much

leslie townes

i've had a three-martini lunch, per the stereotype. it kicked my ass.

copper.hat

5:23 PM

it gave me time to think

leslie townes

i met up with a former coworker and she could expense it as 'business development.' we got absolutely plastered and had to lie down in my hotel room.

copper.hat

i wasn't exactly a lightweight but certainly not in the tyson grade

i have expensed a few drinks

Ted Shifrin

@leslietownes You just said we had to lie down in "my hotel room"!!!

copper.hat

unfortunately silicon vallet is pretty lightweight in that regard

leslie townes

well, that's where we were. no funny business.

copper.hat

5:25 PM

except (excuse the stereotype) the japanese customers

if the irish use drink to open up, then they took it to an extreme

leslie townes

just two attorneys needing a break from the real world.

she moved away and we don't do that any more. i have grown.

copper.hat

@user178758 ahh, just figured it out. the market is continually broken.

user178758

Yup.

Ted Shifrin

I think someone would have fun drafting a Leslie confessional tract based on the posts here.

leslie townes

i could probably be incarcerated on the basis of what i've said here.

the equities markets have been crazy lately. i was hoping for a crash so i could dive back in.

copper.hat

5:29 PM

me too

i am getting some whiplash from the market as we speak

leslie townes

everything i invest in is aggregate, index funds and the like. my job makes it really hard to invest in single companies.

copper.hat

just a suggestion for younger folks, make your money when you are younger :-)

user178758

Labor shortages are rampant.

leslie townes

i think the sp500 is overvalued right now and am not going to buy the index at this point.

copper.hat

don't take time off to be with kids or travel the world

leslie townes

5:31 PM

Family. Religion. Friendship. These are the three demons you must slay if you wish to succeed in business.

When opportunity knocks you don't want to be driving to the maternity ward, or sitting in some phoney-baloney church. Or synagogue.

this is a quote from the simpsons, lest anybody think i am being more offensive than usual.

copper.hat

early on i dismissed the simpsons. fool me.

user178758

me too

leslie townes

i don't watch it anymore but from its inception to about 2003 i was there every week.

if bart simpson had aged naturally from his first appearance, he would be my age, which is frightening. so would calvin from calvin and hobbes.

copper.hat

a lovely dublin inner city lady used to look after my sis's kids. one day she came home and they were watching the simpsons. my sis raised her eyebrow, the minder replied "its ok, its just the cartoon version..."

leslie townes

it's a very smart show, although my high school calculus teacher (!) weirdly wrote a good column once in our local newspaper about how some of the things you love aren't easily shareable with children. he decided that he loved the simpsons but it was too much for his kids. it was a great piece.

there is a lot of nihilism in the humor and there's definitely an age threshold for that.

one of my then-friends once said, i liked the simpsons but they are putting too much gay stuff in the scripts now. it is true they were putting very gay stuff into the scripts. but this was more a reason for dropping the friend than dropping the simpsons.

i can handle it.

user178758

5:38 PM

(¿) in response to your (!)

leslie townes

how do you even make that character?

Ted Shifrin

¿

Easy peasy on a Mac keyboard.

leslie townes

¿ i can cut-paste it.

user178758

press. and hold ?

leslie townes

yeah, not on pc.

Ted Shifrin

5:40 PM

Press and hold sounds like iPad or iPhone.

user178758

yes sir

leslie townes

i was on the phone with IT the other day about a technical issue relating to my inbox. they asked what phone i had. i said samsung galaxy s5. there was a long pause. the phone was released in 2014.

Ted Shifrin

Your antique phone is dual to your immature behavior?

copper.hat

i hate the need for updates every 15 mins. sad for a tech guy

shintuku

centralize investment

Ted Shifrin

5:44 PM

Well, that is beyond excessive.

user178758

updates suck

leslie townes

yes, it's another form of me acting out

copper.hat

i wish my old nokia e51 still worked

ahh, that's why my son hates me. i gave him my nokia for while

beautiful phone

leslie townes

that is a good phone.

he should not resent you for that

Ted Shifrin

I had a Nokia in the pre-dinosaur era.

AMDG

5:47 PM

Have a phone that lasts long and is easy to service? We can't be having that!

leslie townes

my first cell phone was a nokia brick phone with no independent keys. it was a rubber mat over an array of pressable things. it cost $30.

AMDG

How else are trillionaires going to make more money than they need?

leslie townes

my second phone is the one i have now. there will be no third phone.

user178758

Hard core.

shintuku

centralize investment damnit

leslie townes

5:49 PM

if you wanna get in touch with me, it's gotta be through this 2014 phone.

if i'm not a priority, i feel bad for you.

my friends will text me stuff with emojis that don't render and all kinds of other things. i pretend to be in the loop.

copper.hat

i do like that i can make calls as if from an irish number on my phone. could not do that on my nokia

you know for when i need to pretext

user178758

Once you get the loop of tech around your neck, it will not let go.

leslie townes

when you need more gunpowder for your projects. or new bell bottoms.

copper.hat

i spent the weekend unwinding my incredibly complicated it home setup

now the russian guy has a chance, i have removed the fortress

i'm using cheap off the shelf stuff now. usb drives from costso

nothing hardened

since i'm off the no fly list now...

user178758

congrats

copper.hat

6:04 PM

just got a downvote on an answer math.stackexchange.com/a/3734831/27978 and can't imagine a reason why.

i'm not looking for upvotes. just whining

shintuku

behold

i am now in possession of a first-order logic deductive system

fear me, for now i can take full responsability for my shitty real analysis proofs

copper.hat

remember that formalising a proof is the last step...

shintuku

that's what the government wants you to believe

user178758

In these times of coV; what the government wants is what the government gets.

copper.hat

the government has its citizens best interests at heart

shintuku

6:20 PM

ofc, if by citizens you mean, whoever is buying the most real estate shares

copper.hat

well, of course. important citizens.

Vrouvrou

6:35 PM

hello

copper.hat

yellow

Vrouvrou

please i need help in calculus :math.stackexchange.com/questions/4215988/…

2

copper.hat

why not wait for an answer?

Vrouvrou

6:49 PM

maybe there is here someone who have a good idea

robjohn

7:04 PM

@TedShifrin I had Nokia SLVR before I had an iPhone

flipless flip phone

copper.hat

slvr was moto?

robjohn

It was the name of the phone

Sorry, it was a Motorola... SLVR L7

copper.hat

7:20 PM

i'm trying to remember my first cell phone, back in analog days...

robjohn

7:36 PM

@copper.hat My first one was a Motorola brick. got it in 1989

This is what it looked like. LA Cellular was my carrier.

Then I had a Nokia 3310, a Motorola SLVR L7, then an iPhone 4

now I have an iPhone 6 Plus that I am going to upgrade soon.

shintuku

@Terry you must quantify over the interlocutors

copper.hat

@robjohn i don't remember, it was a little smaller than the brick. i have a photo somewhere, but that's another job to find...

robjohn

@shintuku universal or existential?

shintuku

7:54 PM

universal: for all persons, person is here

Balarka Sen

Hi @Ted.

Ted Shifrin

Hi, a Bakarka.

robjohn

is there more than one Balarka?

Balarka Sen

Not that I'm aware of

Ted Shifrin

That’s a deep philosophical query.

Balarka Sen

8:04 PM

Oh, and hi @SayanChattopadhyay.

robjohn

Ted seemed to be addressing "a" Ba[k]arka

Balarka Sen

Ted has generalized me by only using indefinite articles to refer to me.

I have no specificity

robjohn

that makes sense for some Balarka.

Sayan Chattopadhyay

Hi @BalarkaSen What stuff you upto?

Also, Howdy @Ted

Balarka Sen

@SayanChattopadhyay: I have been thinking briefly about Poisson manifolds.

Sayan Chattopadhyay

8:15 PM

Damn, what's the story there?

Ted Shifrin

8:32 PM

Fishy story …

Howdy, Sayan.

Sayan Chattopadhyay

Pretty stressful@Ted. I have to give this very long talk on spectral sequences in my algebraic geometry/complex geometry reading group, and I remember why I had not paid much attention to these before.

Balarka Sen

@SayanChattopadhyay: Nothing in particular, I was trying to understand them.

Sayan Chattopadhyay

They are weird man. I never built much intuition for them except the foliation theorem using symplectic leaves, and there's this moment map construction on it, which I don't remember

Michael Albanese

Hi @TedShifrin

Ted Shifrin

Hi, @Michael.

Balarka Sen

8:37 PM

@SayanChattopadhyay If $(M, \omega)$ is a symplectic manifold, $\pi : E \to M$ is a vector bundle, $\pi^* \omega$ is a degenerate $2$-form on $E$. But it should correspond to some Poisson structure on $C^\infty(E)$, nevertheless, yes? The symplectic leaves description makes me think this is true only if $E$ is a flat bundle.

Michael Albanese

Can I attempt to ask you a question again?

Ted Shifrin

My brain is not working well — maybe slight COVID, not sure yet.

Michael Albanese

That's no good.

Balarka Sen

Oh, did you test, @Ted?

Michael Albanese

I'm pretty sure it is something you know/care about, unlike my recent attempts. Also, its pretty basic.

Ted Shifrin

8:40 PM

These anti-science right-wingers are gonna kill us all.

Yes, yesterday. Waiting.

Balarka Sen

Let us know how it turns out.

Ted Shifrin

Basic? I doubt it, but go ahead.

Sayan Chattopadhyay

Interesting @BalarkaSen, I never thought of this. I will give it sometime.

Michael Albanese

Let X be a Riemann surface of genus 1. Is it possible to show it has Kodaira dimension 0 without using the fact that the canonical bundle is trivial?

Sayan Chattopadhyay

@Ted How are you feeling? Do take care btw

Ted Shifrin

8:44 PM

What does genus 1 mean if not trivial $K$?

Michael Albanese

A line bundle can't have a one-dimensional space of sections without being trivial?

Ted Shifrin

Um …

Michael Albanese

I mean $g = h^{1,0}(X) = h^0(X, K_X) = \Gamma(X, K_X)$.

Balarka Sen

@SayanChattopadhyay Given any smooth function $f \in C^\infty(E)$, you can restrict $f$ to $M$ and take the $\omega$-gradient of $f$, $Hf \in \mathfrak{X}(M)$. Now you can choose a horizontal $\pi$-lift of $Hf$ on $E$.

Let this be your "symplectic gradient" $Hf \in \mathfrak{X}(E)$. Define $\{f, g\} = \pi^*\omega(Hf, Hg)$. I assume this is not a Poisson bracket? Why?

Well, in my construction I don't have to define a lift at all. You can just define $\{f, g\} = \omega(Hf, Hg)$, where $Hf, Hg$ are the symplectic gradients along $M$ or something. This is just by chugging the $\pi^*$ inside $\omega$.

This should be a perfectly valid Poisson structure.

AKA this is just pulling back the Poisson bracket on $C^\infty(M)$ by the restriction map $C^\infty(E) \to C^\infty(M)$. No problem.

So I expect that germinally all Poisson manifolds must look like this. The Poisson structure is induced from a degenerate 2-form, obtained by pulling back a symplectic form by a submersion.

Ah ok (1) the symplectic leaves description isnt actually a foliation, the distribution is singular (2) my expectation is true, this is Weinstein splitting theorem I think

leslie townes

9:31 PM

weinstein is/was a nice guy. i liked his class a lot although i remember nothing from it

Ted Shifrin

10:08 PM

@MichaelAlbanese OK, so this is obviously false. But do we forget Riemann-Roch too?

leslie townes

ted, good to see you. what i thought might have been a breakthrough case turned out to be food poisoning.

leaning more heavily on food prepared outside of the home in recent months, lots of rolls of the dice. can't win every time.

Ted Shifrin

Oh, separate from your spoiled sushi episode?

leslie townes

yes. spoiled turkey sandwich.

Thorgott

so the question is why $\Gamma(X,K_X^{\otimes k})$ is generated by the $k$-th tensor power of a generator of $\Gamma(X,K_X)$

leslie townes

i can't win with these places.

i think it's a conspiracy to prop up the market for toilet paper.

Ted Shifrin

10:21 PM

Hi,Thor.

leslie townes

my fever was alarming because that is a covid symptom and not normally something you get with food poisoning.

Ted Shifrin

Or flu symptom .

leslie townes

i had a high fever and didn't eat anything or sleep for two days. not a great time in my life.

i think the quality of my lawyering may have dropped a little bit.

Balarka Sen

yikes, sucks. i dread food poisoning so try to never eat outside

leslie townes

this week we've made a vegetable soup that ought to last us until friday.

Thorgott

10:24 PM

hey Ted

Ted Shifrin

Hard to drop from 0? runs away

leslie townes

ted you will be pleased to know that i was recognized among the "best lawyers: ones to watch" of 2021. it's like who's who in high school students. you can buy a plaque.

i didn't but i could have. so yeah, i'm the best attorney on the planet.

there's better call saul, and then there's me.

Ted Shifrin

@Thor So, in general, that’s a positivity question. It’s like projective normality, which we’ve discussed before.

Best on planet. Your epitaph, no doubt.

@BalarkaSen I think my only cases of food poisoning were almost 50 years ago twice at McDonalds.

I have never been back.

leslie townes

i last ate at mcdonalds in copenhagen in 2000. no poisoning!

Ted Shifrin

I have survived Wendy’s and BK and Subway on long drives.

leslie townes

10:29 PM

i think my last fast food experience was a carls jr. no poisoning there either, although they did give me somebody else's order.

it was a more expensive order, so i didn't complain

robjohn

I got sick at BK, so I don't go there, but I only get the Filet'o'Fish an McD's

I will eat at Carl's Jr

even though the old, dead owner had bad political views.

leslie townes

subway to me is synonymous with depositions. when you do a depo and get 60 minutes for lunch, there's always a subway within a block. it's depressing but it's food. that should be their slogan.

robjohn

the daughter seems better

Ted Shifrin

No Chick FilA, obviously.

leslie townes

oh, i didn't know of that.

robjohn

10:31 PM

Nope

leslie townes

there was a person at my firm who would take summer interns to chick-fil-a and i said, do you think that's the best idea, and she said "what?"

and i said "stop doing that, if someone wants to go there, i guess, but wait until they ask for it." nobody asks for it.

robjohn

They are popping up all over the place. Chick FilA hopes none of the young'uns remember

Ted Shifrin

I have gay friends who patronize them, and I say bullshit.

leslie townes

she simply had no idea. lots of blinders up.

i have never eaten there. it looks delicious, but a huge nope from me

robjohn

If the food tastes good, and I hear it does, people will overlook history

Ted Shifrin

10:33 PM

You can marinate chicken breast in pickle juice yourself.

robjohn

Pickle juice? I've never eaten there

Ted Shifrin

Chicken breast is dry and uninteresting most of the time.

robjohn

yep

unless I BBQ it. I can make it nice

leslie townes

chicken breast needs a lot of work or it is just protein

Ted Shifrin

I can make most food top notch.

robjohn

10:35 PM

@leslietownes protein that sucks all the moisture from your mouth

leslie townes

dessicating protein.

it's the only kind of chicken that my wife will eat, so we have to compromise on this stuff sometimes. she is largely pescatarian and sometimes i do want chicken.

robjohn

My wife and I prefer dark meat poultry, but I like fish and worry about the mercury

Thorgott

no clue why it's true, though

leslie townes

that's why we don't eat fish that often.

robjohn

yeah

leslie townes

10:37 PM

if you keep it to every couple of weeks and aren't giving birth it's probably fine. we're all half plutonium anyway.

robjohn

I can read by my own glow most of the time

Michael Albanese

@TedShifrin: I wanted to use Riemann-Roch only, but I realise now that you can use Riemann-Roch to show $h^0(X, K_X^{-1}) = 1$. As $h^0(X, K_X) = 1$, it follows that $K_X$ is trivial anyway.

Ted Shifrin

Yes, precisely.

Do you know any theorems addressing Thor’s question?

I’m wondering if it’s somewhere in Griffiths’s positivity of v.b. Stuff.

Michael Albanese

Maybe I'm missing something, but if you take $X$ to be an Enriques surface, then $\Gamma(X, K_X) = \{0\}$ and $\Gamma(X, K_X^2) \cong \mathbb{C}$. So I don't think it's true.

Ted Shifrin

I think you need very ampleness …

Thorgott

10:51 PM

that's a very cool example

Michael Albanese

I would be tempted to agree with you. I think Lazarsfeld's books on positivity may be a good place to look.

Ted Shifrin

I have virtually no books …

It’s like a cohomological criterion for projective normality.

robjohn

virtual books save space

Ted Shifrin

I wanted to look at kodaira’s original proof of K embedding . No longer have complete works. No electronic access.

10 Replies

11:21 PM

what does the i,j mean underneath the sum?

The equation is supposed to represent the amplitude^2 of the sum of different phase and amplitude sin waves

Akiva Weinberger

Add up for all possible values of i and j

Not sure the context so I can't actually tell how high and low i and j can be

but the result shouldn't have any $i$s or $j$s in it anymore (they are "dummy" or "bound" variables)

10 Replies

List of trigonometric identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle. These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non...

its the equation for more than two sinusoids

I'm not sure it is the equation I want though... I'm trying to get the equation for arbitrary phase shift that I can use to sum all the waves that are pi radians out of phase to pi+n radians out of phase.

10 Replies

11:40 PM

The wikipedia equation might not be quite right mathworld.wolfram.com/HarmonicAdditionTheorem.html

although the equation 26 isn't a function of frequency? and I think it should be

oh wait nvm

ok, any thoughts on how to turn equation 26 into an integral so I can calculate the frequency response of a solid line of phase shifted waves?

Transcript for

$Mathematics$ Mathematics