@vzn i think it is odd that programming really has not progressed from sequential.

US manages to have more/ create more conflicts than many even when many have conflicts! o_O

@copper.hat it is more multithreaded. parallel. but you can do a lot of sequential stuff in the threads.

@vzn it is people. the us just happens to have a lot of resource and thankfully a populace/leadership that is broadly for the good.

@vzn my comment was broader. almost all software bugs i hit are timing bugs.

@copper.hat US is very srsly messed up post-Orange-entity o_O ... lets see if it can get back together into something semi coherent, hopefully that we have "hit bottom" recently o_O

I have an interesting math problem for you two: Solve $$\int_{0}^{\infty}\sin(x)\sin(2x)...\sin(2021x)\frac{dx}{x}$$

@vzn def. not a fan of the orange haired baboon. but he represents a lot of people (probably not as many as a week ago).

@MiloMoses expand the $\sin$s as exponentials.

am hoping this is him "going out with a bang" later followed by "a (long) whimper" (aka real legal prosecutions!)

Yeah, but then there's the fun step you need to do after that

@vzn it ain't over until it's over.

Since you get a sum with $2^{2021}$ that you can't solve with a calculator

long 4yr natl ordeal seems to finally be over.

*$2^{2021}$ terms

@vzn i think you are mistaken :-(.

@copper.hat cant imagine anything worse than storming the capital. they are coming down like a ton of bricks on his cohorts in crime wrt legal investigation/ prosecution. think there will be multiple felony convictions. it will take a long time though.

@vzn if we were having this convo 3 years ago maybe. they have not all gone.

a lot of republicans sat there and said nothing.

for a long time.

@copper.hat you mean 3yr into future?

@copper.hat Do you know a quick proof off the top of your head that if $T$ is a self-adjoint operator on a Hilbert space, the the spectral radius of $T$ is $\lim \|T^n\|_{op}^{1/n}$?

meanwhile the dems are busy leaping to the left.

@BalarkaSen unfortunately there is a wine thing going on right now :-).

Ah no worries

but let me think..

Balarka, I think what youre asking for is on the wiki for it

Like en.wikipedia.org/wiki/Spectral_radius contains a proof

That's for matrices. That's ok

I want a fully general proof for self-adjoint operators and I don't want to think too much :)

Oh, sorry

not thinking too much? this is a wannabe mathematician? lol j/k

$\rho \le \lim_n$ is straightforward.

Yeah.

Try $\|T^n v\|^{1/n} = \langle T^{2n} v, v \rangle^{1/(2n)}$ where $v$ is supported on finitely many coordinates, maybe.

A normal operator has a spectral decomposition.

Oh yeah ok that's all

But it is not what I could call a quick proof...

It's ok, this is helpful :) I won't distract you from the wine anymore.

Still digging :-).

lol so courteous :)

my "library" is downstairs...

the book cellar

← found a very fruity sangria recently, its almost like fruit punch... alas, now a fading memory o_O it was from costco lol :P

@user2103480 Tetra-pak Sangria mmm

Glühwein season is almost over here :(

The best drink

← still digging thru bal's musings on QM+QC... maybe need more wine for that :P

creepazoid

lol that would make a good video game title ;)

@copper.hat I was wondering what your reputation was on Math.SE, and I couldn't help but to read your bio and see that you went to EECS at UC Berkeley. That's where my brother is right now!

wow, somebody wrote a SE profile and somebody else read it! o_O

@MiloMoses Thanks Milo, you are the second person to read it ;-).

Somebody please explain horizontal and non horizontal inflection points

lol. It was very long, and I'm not sure how to feel about that Feynman quote...

I am sitting a few miles away from UCB at the moment. What does your brother study in EECS?

@MiloMoses It seems apropos for MSE :-).

He studies computer science! Its one of the top schools for it so I'm super proud of him

← Apparently, this user prefers to keep an air of mystery about them. o_O

I used to know a lot of faculty there but that was a long time ago. Still a few more in EE than CS.

@copper.hat What did you study there?

← <3 <3 <3 feynman

Continuous parameter optimization under the guise of control systems.

@MiloMoses cool any idea what languages?

And yeah, I totally agree that the quote is apropos. I'm just not sure I'm happy about what it ways about me as a person

:-)

@vzn Do you mean what languages he likes to code in on his own time or what languages he uses for school?

feynman, such a jokester, really miss him :) ;'(

@MiloMoses either

I like Feynman but he is not the arbiter :-).

who says hes the arbiter? arbiter of what? lol

He's a huge rust fanboy right now, seeing as its one of the only new low-level languages to pop up and it does things very different

Berkeley is a hard place for UG.

hmmm rust, have a family member working in that... alas hes very quiet ;'(

I discouraged my daughter from going there.

Not that she needed my input.

you mean hard academicly? high courseload?

Oh, interesting. Where did she end up going?

Hard in that you do not have access to the minds that brought you there.

Oxford.

She is an independent girl.

That's really cool

I'm hoping to go to MIT or CalTech

she tells me "dad, you are the best dad. but you are also my only dad."

That's so funny omg

She knows how to work me.

I think college is a lonely place at the moment. All the fun non work stuff is gone.

^

Are you happy with your choice to go to University College in Cork?

Different world Milo.

It's also kind of a bummer time to be in High School

My decision was based on closeness to my mother's cooking not subject.

But it does give me more time to work on making fun math problems (like the $\int_0^1\sin(x)\sin(2x)...\sin(2021x)\frac{dx}{x}$ one)

Going to college in Ireland is an entirely different experience to the USA.

In what way?

Money, complicated applications process, expense, etc.

Plus 50% of time is spent in breath.

re the feynman ("the arbiter"?) quote, remember thinking it sounded like him but it might be hard to attribute. sometimes look up quotes for amusement. all over net without attribution, but a little poking, this pg says it comes from In Fear of Physics by Lawrence M. Krauss (1993). so yeah guess genuine. todayinsci.com/F/Feynman_Richard/…

still poking around functional analysis...

rudin is soo opaque.

Are you enjoying it learning functional analysis?

it is rudin's book of the same title.

i do not enjoy learning from rudin. i use other sources when i need to learn.

i see you are local to me. i am in albany

Oh cool! Yeah, I'm in Berkeley

I guess my brother also wanted proximity to his mother's cooking

:-)

in my naïve way i thought berkeley was representative of the usa when i moved here first :-).

oh boy...

@copper.hat wonder what exactly she meant by that. it is probably better than "you are only my dad" :)

There should be some proof by holomorphic functional calculus or whatever. Take $(I - z T)^{-1} = \sum_{n = 0}^\infty z^n T^n$. The radius of convergence must be $1/\lim_n \|T^n\|^{1/n}$

@vzn she meant i am also her worst dad.

@BalarkaSen yeah, but the details are grinding.

Yeah

give no quarter - my daughter'smotto.

It's pretty crazy how lefty my high school (the local public school) is. Like, we read this one article where they said that the Bolshevik revolution brought upon utopia to the Russian state, and my teacher was like "yeah, I guess that violent revolution probably wasn't the best choice there and there might have been better ways to reform the system"

spelling is a monotonicaly decreasing function of time & wine.

But like on the whole I think it's a cool place

there is no such thing as lefty in US

@MiloMoses i think that reflects more that just BHS.

its a myth

@BalarkaSen ooohhhhh....

have i stories for you :-)

union friends who had fbi move into the house next door.

@MiloMoses where is that?

mccarthy era stuff

@vzn berkeley hs

dude, berkeley is one of the most left cities in entire US. its legendary. 60s. etc

@vzn berkeley today is a shadow of its past...

"one of the most left cities in entire US" not saying much imo

one of the earliest vietnam protests was at berkeley, its credited as starting the wave/ movement.

a lot of wealth foreign students paying nrt

protesting the lack of good boba

I feel like BHS still carries that legacy today though a bit. Like, in my one-and-a-half in person years at the school we've done all sorts of different strikes and walkouts and stuff

Like against rape culture at the school and stuff

@BalarkaSen it is saying a lot, haha you have a lot of opinions on US politics and have never visited. :) ps try also some US history :)

some stuff is good but can be carried a bit too far.

i think it could be hard to go to school there if you are not onboard with it all

Thank god I will never visit US

why never? that's a long time. where are you?

nrt? boba? ?

@BalarkaSen I feel like on the whole the US is still a pretty cool country

non resident tuition. boba is a sort of tapioca drink

no country for old men let me tell you

that's me btw

Boba is so good I love it

@copper.hat a lot of cities are "shadows of their past." have you heard of "neoliberalism"? o_O

never adapted :-)

@vzn i grew up in a country split by historical differences.

@copper.hat i'll probably just stick around in india (which is where i live). its pretty bad but at least we havent started bombing people

@BalarkaSen lol missing out :)

i lived about as far from the norther troubles as one can yet was living in an ira stronghold.

@copper.hat do you have a historically charged prejudice against the English?

@EdwardEvans me? none whatseoever.

@BalarkaSen Are we bombing people in the US?

there is history there., but it is history.

@copper.hat ?!? why not?

@copper.hat haha okay, it was meant tongue-in-cheek. I am an Englishman myself

Though I loathe to admit it

my great grandfather was an mp to the british empire :-)

@MiloMoses 7 different countries in the middle east to be precise

will remove momentarily :-)

How cool

@MiloMoses lol only outside! so dont worry about it :P

Oh, I thought you were referring to us bombing each other

The overseas bombing is an atrocity, yeah

@EdwardEvans however, my dad disowned a sister because she went to work for the crown!

my daughter studies there. however.

as long as its OUTSIDE the US, its not an atrocity IN the US right? spoken like a true american... almost like something Orange Entity would say :) :) :)

every country has its dark side. every country.

I thought that Balarka was saying that she was scared to go to the US since she thought she might get bombed on the streets

lol

the irish and british are much closer than the commpn narrative would suggest.

@copper.hat I'm frankly embarrassed by my nationality at the moment. I identify as European, but unfortunately carry the passport of a Brit. People actually wince when I take my passport out.

US is bad but we dont bomb people (in our own streets). we just shoot em :)

why? brexit? blame cameron.

Right, the arrogance of the pig f*cker

here is a bit of gossip:

If you'll excuse my French

@EdwardEvans lmao

the last bomb the unabomber set was beside my computer terminal in berkeley.

No way!!!!!!

cool claim to fame

unfortunately it got my colleague

i hate that guy he sucks

Not so cool

yup. had my fbi/usps/polics interview etc.

@BalarkaSen what did his colleague ever do to you?

@copper.hat florence is my neighborhood o_O

the unabomber was a uc berkeley math professor before

great story. wow that reminds me.

← went to school with awlacki o_O

That really is a great story, yeah

@Balarka I updated that piece of garbage midi I sent last time, feel free to give it a listen, since you're the only person who does

@vzn serious???

Who is Awlack?

@MiloMoses sad for my buddy. very sad.

Yup, I have it open in a tab. I'm writing a talk right now but I'll listen in a bit

*Awlacki

np hahaha

my dad used to do business with gadafi.

not what you are thinking.

Who is Gafadi?

he would walk around the halls with his turban/ white suit on (what do they call those)? my engr friend told me (or whispered!) the "gossip" that "he believes in jihad" o_O iirc he was in the engr college.

libyan leader of past

my dad was literally in the meat business.

Wow

this was before gadafi was the country leader, of course.

you know the sort of dinner time stories in our house were different :-)

I can imagine, yeah

we were/are not wealthy by any means other than a rich store of stories.

and the odd bombing escape.

What field of math do you think is the most beautiful to learn

@copper.hat did you ever hear of his manifesto against technology? it was actually quite erudite. his brother read it in NYT and called the fbi, telling them it sounded like his brother. it was the 1st tip in many years (over a decade?) that cracked the cold case.