Mathematics - 2021-01-16 (page 3 of 4)

Eminem

4:00 PM

Sorry i meant the joint probability density

Joint probability distribution

Astyx

joint with what?

Semiclassical

like, for a while I was appreciating $$\overline{f}(k)=\frac{1}{\sqrt{2\pi}}\int_{\mathbb{R}} e^{-i k x}f(x)\,dx,$$ $$f(x)=\frac{1}{\sqrt{2\pi}}\int_{\mathbb{R}} e^{i k x}\overline{f}(k)\,dk$$

Eminem

Say R is the distance from origin, and X is the raidus of the cricle, what is f_R,X?

Semiclassical

those are conditions

other convo: then i noticed that the convolution theorem is $\overline{(f\star g)}(k)=\sqrt{2\pi}\overline{f}(k)\overline{g}(k)$

which makes me gag

Astyx

lol

can't have it all

Semiclassical

4:03 PM

quite

Thorgott

i like $\int f(x)e^{-2\pi ikx}dx$

Semiclassical

you're not wrong

the trouble is that physicists never want to put the $2\pi$ in there

Thorgott

this one makes the transform an isometry

Semiclassical

i think the one I wrote is also an isometry

but pays for it with the convolution theorem

Thorgott

mine gets the extra 2pi factors when you try to exchange derivatives with multiplying by x

user2103480

4:05 PM

@Semiclassical let's see. When I take the fourier transform of a function defined on [0,1], do I just act as if this is measurable with compact support and defined on $\Bbb R$?

Semiclassical

right @thorgott

could not tell you @user2103480

that sounds plausible but i am not the person to ask that

user2103480

sigh

Eminem

@Semiclassical Any idea how to start?

user2103480

I should have asked my prof from the start instead of bothering all you

Semiclassical

try figuring out the CDF first. i.e., figure out $P(R\leq r)$

@user2103480 that said, I still think what I said earlier has merit. if you focus on the basis functions $\sin (n\pi x)$

then $(-\Delta)\sin(n\pi x)=(n\pi)^2 \sin (n\pi x)$

and I think you find that $(-\Delta )^\gamma \sin(n\pi x)=(n\pi)^{2\gamma} \sin (n\pi x)$

user2103480

4:10 PM

I also thought this sounds good

Semiclassical

that's pretty straightforward to check as well

doing the Fourier transform for $\sin(n\pi x)$ restricted to $[0,1]$ is easy enough

user2103480

That's why I wanted to calculate the stuff exactly, starting from the fourier-transform (there probably is a smarter way)

Semiclassical

what's your convention for fourier transform

user2103480

n o n e

Semiclassical

cool

user2103480

4:11 PM

we have not done a single fourier-transform in that course

Semiclassical

nice

user586228

Someone please reply to my post

Semiclassical

well. let's go with thorgott's preferred case

$\overline{f}(k)=\int_{\mathbb{R}} e^{-2\pi i k x}f(x)\,dx$

Eminem

@Semiclassical well its $\frac{r^2}{x^2}$

Semiclassical

what is $x$?

Eminem

4:13 PM

The radius of the cricle, we know its distributed exponential with 2a

user2103480

@Semiclassical yeah, I only now noticed that it doesn't make sense to distinguish between "extending" the function formally and just calculating the integral from 0 to 1. Dumb me

Gimme a few mins to calculate this myself, I think I'm able to handle all this now

Semiclassical

sure. i'll try it on my end too

polite proofs

What is wrong with this proof: $\forall n \in \mathbb{Z}^+, n! > (n/2)^n$

$1 > 1/2$ is true. Assume that $k! >(k/2)^k$ for some positive int $k$. Then $k!(k+1) > k^k (k+1) / 2^k = \frac{k^{k + 1} + k^k}{2^k} > \frac{k^{k + 1} + k^k}{2^{k+1}} > \frac{k^{k + 1}}{2^{k+1}}$

Astyx

You want $(k+1)^{k+1}$ in the last expression

polite proofs

@Astyx Ah, I couldn't spot the mistake. Haha! Great work

Semiclassical

4:24 PM

@user2103480 hrm. well, mathematica has no trouble with the forward transform (obviously)

the inverse transform, by contrast...not so much

which concerns me

user2103480

@Semiclassical I'm still looking for the right trig identity so that I don't have to do partial integration

Semiclassical

that's smart

user2103480

found it

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...

Thorgott

my favorite wiki page

user2103480

amen

(you gotta click the link to get directly to the identities I meant)

Semiclassical

4:28 PM

amazing how many of those come down to "use Euler's formula"

Thorgott

yup

lots of trig becomes more transparent when you work with complex numbers

Semiclassical

i mean, looking at the front page of that site is enough to justify the lol...

user2103480

post that one more time and I'LL FLAG YOU

Semiclassical

(context, who needs context)

user2103480

jk I found it pretty amusing

Semiclassical

4:30 PM

lol

Astyx

I'm surprised they don't claim trigonometry is part of some deep gov program to control the crowds

Semiclassical

no, no

that's non-euclidean geometry

Thorgott

trigonometry was invented by antifa

Semiclassical

euclid is enshrined in tradition

user2103480

"The Nobel Prize "selection process has become political, as it was not given to Ronald Reagan or Pope John Paul II or to anyone who criticizes the theory of evolution. The Nobel Prizes for literature and peace are mostly given to outspoken liberals, such as Jimmy Carter."[1]"

Ronald reagan peace price???

Astyx

4:31 PM

good ol' days

user2103480

Crazy american take

Semiclassical

well.

as much as i may disagree with ronald reagan on...well, most things

i like the idea of a US president who was genuinely freaked out by the possibility of nuclear warfare

Sayan Chattopadhyay

I mean they gave one to Obama, so they could have thrown one to Reagan as well

Semiclassical

going from "nuclear war cannot be won and must never be fought" to "why do we have the weapons if we won't use them"

is...disturbing

user2103480

true but... funding latin-american right-wing paramilitaries may be a even worse than obama's drone warfare

Eminem

4:34 PM

@Semiclassical Sorry for bothering you, but i cant get my head around this problem...

Semiclassical

oh, no doubt

well

i dunno about no doubt. i'm not enough of an expert on either

but certainly there's pleeeenty of room to critique that brand of foreign policy. but "nuclear warfare is insane" is at least one mindset i can get behind

user2103480

fair enough

Astyx

No one has been saying it isn't though ... right?

Sayan Chattopadhyay

Yeah one could also look at all the destabilization such warfare brings giving fuel to nationalist extremists which later brand an entire religion as one to be hated

user2103480

You mean drone strikes?

Sayan Chattopadhyay

4:37 PM

Yeah

user2103480

Well, giving fuel to nationalist extremists in afghanistan was the literal agenda during the reagan administration though

Sayan Chattopadhyay

Yeah right, but considering Obama came as "the woke candidate" and then went onto do the same thing kinda hits more

Maybe because I fell into the trap :(

user2103480

they funded the mujahideen to fight against the soviets, thats different from obamas actions

Sayan Chattopadhyay

Right but I ain't talking about direct funding, I mean a more general instability that comes with constant warfare which increased through unmanned strikes

Astyx

I knew I shouldn't have posted this link lol

user2103480

4:40 PM

lmao

Sayan Chattopadhyay

Lol yeah

user2103480

@SayanChattopadhyay I don't know if the warfare increased. Weren't there much more troops before?

Semiclassical

quote from a certain then-candidate for president regarding nukes: "“Why can’t we use them. . . then why are we making them? Why do we make them?”"

so...yeah

user2103480

I don't condone the drone strikes, but I also can't really judge the effect they had on the populace

@Semiclassical wonderful bloke. Best presidential candidate in history

Semiclassical

the funny bit, as i think about that quote

user2103480

4:43 PM

It is true

Semiclassical

is that one conclusion that one could draw from that comment would be "we can't use them, so we shouldn't make them"

user2103480

why do we make them? We shouldnt do that

Astyx

The paragraph on the Capitol storming in the US Capitol building page is hilarious

Semiclassical

but i feel like the implication he drew was "we make them, so we should be willing to use them"

user2103480

@Semiclassical Sad!

Semiclassical

4:45 PM

on a less (contemporaneously) politically-charged context, this is one reason I have mixed feelings about von Neumann

a comparison: there has been a lot of ink spilled about Heisenberg's role in Nazi Germany's nuclear program

user2103480

He was very much enthusiastic to use the nuclear weapons, right?

Semiclassical

and justifiably so, because cooperation with Nazi Germany and all that

Sayan Chattopadhyay

@user2103480 There was a troop surge in 2003-2004, which decreased as it came to 2008, but were again increased in the name of ISIS. Plus drone strikes. I would say its almost been the same, though some decrease in the numbers but not significant considering what more has been added, vis-a-vis drones

Semiclassical

but, well...von Neumann wasn't just involved in creating the bomb, he was involved in the selection process for the targets in Japan

user2103480

But I prefer to avoid thinking about the use of fire- and nuclear bombs in japan in WW2

Semiclassical

4:47 PM

and if we're going to judge Heisenberg for his participation in a (failed) nuclear program during WW2, I feel like we should also judge von Neumann for his participation in a successful one

Sayan Chattopadhyay

But yeah its hard to gauge the affect on the populace, without having proper data. Or maybe there is data and I haven't seen it.

Semiclassical

context: "Von Neumann's principal contribution to the Project was the concept and design of the explosive lenses used in the implosion bombs. Von Neumann was also included in the target selection committee responsible for choosing the Japanese cities of Hiroshima and Nagasaki as the first targets for the atomic bomb."

user2103480

I just can't imagine 100 000 people being killed by fire bombs in one night

Semiclassical

yeah

it does remind me of a rule of thumb I have for WW1 vs WW2

in WW1, it sucked to be a soldier. in WW2, it sucked to be a civilian

obviously that's a generalization

user2103480

@SayanChattopadhyay Ah ok. And in contrast there were never troops in pakistan but an increasing number of drone strikes in pakistan. Since I have zero knowledge about the population's opinions in pakistan, I'm clueless regarding the effects of this

Astyx

4:51 PM

@Semiclassical It depends where you lived as well

Semiclassical

yeah

user2103480

@Semiclassical let's talk math again before I cower in the dark for the rest of the evening

Semiclassical

lol

Sayan Chattopadhyay

Yeah it's hard to filter data about Pakistan from Indian sources, and I haven't found any proper foreign source. In India all you get is either bigoted islamophobic rhetoric or literally nothing.

Okay back to math

Mats Granvik

Can someone give me an epsilon of advice or help here:

0

Q: Absolute convergence of a double matrix and of $\frac{1}{\zeta(\frac{1}{2}+\epsilon)} = \sum_{n=1}^{\infty} \frac{\mu(n)}{n^{\frac{1}{2}+\epsilon}}$

According to Wikipedia the convergence of the right hand side of: $$\frac{1}{\zeta(\frac{1}{2}+\epsilon)} = \sum_{n=1}^{\infty} \frac{\mu(n)}{n^{(\frac{1}{2}+\epsilon)}}$$ for $\epsilon$ an arbitrary small number, is equivalent to the Riemann hypothesis. The logarithm of the left hand side with $...

Sayan Chattopadhyay

4:55 PM

Weierstrass preparation is really something amazing. Considering how much machinery one would need to understand things like every regular local ring is a UFD, with WPT it's so easy to show that the local ring is a UFD

vzn

5:18 PM

@copper.hat re QC "models" forgot to ping you on this think youll like this very cutting edge curious what you think about it :) youtube.com/watch?v=j5HyMNNSGqQ

@user2103480 are you comparing nukes to firebombs? its both apt and inapt. but thx for caring :)

@Semiclassical generalizations? WWII was deadly for both civilians and soldiers. how about "war s*cks". to say the least. but we now have new biological/ evolutionary evidence its inherited from apes. surprise! think you have some excellent points about von neumann, was not aware of all that. think theres lots of validity to reimage history through the lens of ethics instead of... "the victors". old expr: "history is written by the ~~victors~~ ~~assassins~~ ~~military industrial complex~~"

@Semiclassical ? lol reagan increasing funding on the MIC and ramped up the cold war rhetoric/ near propaganda in favor substantially, vilified/ demonized the soviets, etc

Semiclassical

well, he definitely didn't start on a "nuclear warfare is absurd" stance

i was under the impression that he proceeded towards that by the time his terms ended tho

for a reference in that vein, see the source here: " In January 1986, Gorbachev countered Reagan’s Star Wars initiative with a three-part plan for nuclear disarmament by the year 2000. Although the proposal was uniformly rejected by his administration, Reagan’s private response to his secretary of state, George Schultz, was, “Why wait until the end of the century for a world free of nuclear weapons?”"

regardless of everything else (and that's a big everything) I have to respect that sentiment

vzn

5:34 PM

reagan was all about "star wars initiative" but it seems like a massive MIC boondoggle to me under the camouflage of "defense"... its hard to distinguish it from military escalation. have you heard of the price tag on it?

lived thru reagan era as a youngster and would have to do some research, but think there was a lot of (disguised) propaganda floating around at the time.

would like to find a citation for your quote about "why use them" am gonna google now

Semiclassical

yeah, they loved their pie-in-the-sky solutions which conveniently let them pump a lot of money to defense contractors

mostly I find it depressing that the phrase "Why wait until the end of the century for a world free of nuclear weapons?" seems unthinkable as a serious political sentiment nowadays

YouKnowMe

Shouldn't it be "$\mathrm d x=$ change in area" instead of "new area" here?Is it trivial..?

Semiclassical

of course, Reagan stating that privately is a lot different context than what he actually did in practice

user2103480

@vzn do you see any comparison in that sentence?

vzn

where are you slinging all these reagan quotes from? hold on a minute lol ok at least found this one Reagan’s private response to his secretary of state, George Schultz, was, “Why wait until the end of the century for a world free of nuclear weapons?”[4] armscontrol.org/act/2004_07-08/Reagan

user2103480

5:39 PM

or the preceding one

Semiclassical

that's the article I sourced it from, yes.

per my earlier comment

vzn

we somehow worked from the same article? found it by googling. you found/ read the article previously?

Semiclassical

8 mins ago, by Semiclassical

for a reference in that vein, see the source here: " In January 1986, Gorbachev countered Reagan’s Star Wars initiative with a three-part plan for nuclear disarmament by the year 2000. Although the proposal was uniformly rejected by his administration, Reagan’s private response to his secretary of state, George Schultz, was, “Why wait until the end of the century for a world free of nuclear weapons?”"

vzn

the point is that quotes can be very tricky to track down sometimes, have long experience on this

Semiclassical

see the [here]

user2103480

5:41 PM

Also, the biological justification through our relationships to apes is shaky. Bonobos do not engage in warfare comparable to chimpanzees

vzn

ok, thx for the actual citation. but cant find your other purported reagan quote right now googling.

@user2103480 bonobos are the "freaks" of monkeys/ apes and have many atypical aspects. such as a preocupation with sex, incl uh "self pleasuring"... sound like someone you know? lol QED :P

Semiclassical

they give it in the article. (the passage I referenced included citation [4] which i scrubbed for copy/paste purposes)

user2103480

Not saying our violent tendencies do not stem from biology, just saying that it's hard to reason by analogy

@vzn fair, fair

Semiclassical

so that's from Schultz's memoir for his time as secretary of state

vzn

@user2103480 what is hard about reasoning from analogy?

Semiclassical

5:43 PM

not the most objective source, I suppose, but it's what they got it from

vzn

@Semiclassical it doesnt sound implausible as a privately cited quote. can you link to something?

Semiclassical

i'll try

they say it's from "Shultz, George P., Turmoil and Triumph: My Years as Secretary of State. New York: Charles Scribner’s Sons, 1993."

dunno if that's on google books

Astyx

I remember a certain US candidate also mentioning using nukes to stop hurricanes

vzn

anyway, do appreciate the (careful, scholarly) focus on history which is rare :)

@Astyx he who will be nameless like voldemort lol :P

Semiclassical

google.com/books/edition/Turmoil_and_Triumph/…

Astyx

5:45 PM

Maybe if we don't name him we'll forget about him soon

Semiclassical

whether or not we treat that as an unbiased account, the mere fact that that's a view that the former secretary of state could credibly assign to Reagan is something I appreciate

I'd like to think that a modern POTUS would be willing to entertain that, but...doesn't seem on the agenda

vzn

searching thru the book, cant quite find the quote yet. however, MAD was a new concept in the 80s. it came from scientific paper(s). maybe reagan was influenced by it.

Semiclassical

hmm, it should be on the page I linked

user2103480

@vzn I think you are able to guess what I mean by that

Semiclassical

hrm, it seems the link i gave wasn't to the page

google.com/books/edition/Turmoil_and_Triumph/…

try that

vzn

5:48 PM

your link brought me to the title page. it has a search field. was looking up "nuclear weapons" etc

Semiclassical

yeah, try the new link. that one should be direct (as long as "some pages aren't shown" doesn't interfere)

the lack of page numbers is irritating :S

vzn

cant find it exactly yet. but it appears there was some gap between his private vs public rhetoric, which ofc is not uncommon esp among presidents.

the page says he was in favor of eliminating nuclear weapons. however the quote about "why use them" has different nuances etcc.

Semiclassical

well, on that same page they do reference a quote which appears in the NYT article here: nytimes.com/1986/01/17/world/…

not to bury the lede:

"President Reagan said today that the Administration was encouraged by the broad arms proposal offered by Mikhail S. Gorbachev. He said the plan was ''different from the things that we have heard in the past from leaders in the Soviet Union.''

''It's just about the first time that anyone has ever proposed actually eliminating nuclear weapons,'' Mr. Reagan said, responding to questions at a civil rights ceremony in the Cabinet Room."

though that's not exactly the same as saying "this is the first time someone has proposed eliminating nukes, and it's a damn good idea"

vzn

the page has this quote. "why wait until the end of the century for a world without nuclear weapons?"

Semiclassical

yeah, and the second link I gave should go directly there: google.com/books/edition/Turmoil_and_Triumph/…

vzn

5:54 PM

it brings me to the same pg

Semiclassical

hrm

that's annoying

i'll screenshot it, at least

vzn

where did you get the links from? googling yourself? or something else?

Semiclassical

searching within the google book preview, yeah

oh, and using the "share" feature in google books

vzn

think the 2 links are the same eyeballing them

Semiclassical

they don't behave the same on my end

i do have to gripe at the lack of page numbers in this book

vzn

6:00 PM

@Semiclassical thx for the effort but am able to read that from the link. it doesnt have the quote. am just interested in tracking it down. where did you get it?

Semiclassical

the quote is right there.

it's the start of the second paragraph

vzn

1 hour ago, by Semiclassical

quote from a certain then-candidate for president regarding nukes: "“Why can’t we use them. . . then why are we making them? Why do we make them?”"

Semiclassical

oh, that one

that's not reagan, to be clear

vzn

oh, ok.

that was my assumption or guess

but where does the quote come from? an article?

Semiclassical

I was talking about the "why wait until the end of the century" quote

vzn

6:02 PM

it is rare for even presidential candidates to question making (nuclear etc) weapons. agree with you thats the basic logical question. my interest in the quote is that, as orwell emphasized, a lot of propaganda is about suppressing (critical) reason/ thinking.

in other words, its a question civilians ask, that children ask, but not one that politicians ask, esp publicly.

BigSocks

when are multiple roots of the derivative of a polynomial in a field of characteristic p>0 also multiple roots of the original polynomial?

vzn

one might say, often politicians are paid not to ask/ answer particular (key) questions.

here is another very interesting semifamous quote along these lines :)

> It Is Difficult to Get a Man to Understand Something When His Salary Depends Upon His Not Understanding It quoteinvestigator.com/2017/11/30/salary

Semiclassical

MSNBC: Town Hall Interview with Donald Trump and Chris Matthews - March 30, 2016

►

the bit starting at 16:11

Govind75

If I want to perform gaussian elimination on the composition of two matrices, can I perform GE on each one individually, multiply them together and then continue with gaussian elimination on the new matrix?

Thorgott

@BigSocks I don't think that's a regular occurrence in any characteristic

BigSocks

6:07 PM

how about characteristic 2

you have the derivative of a polynomial is a square

so all roots are squares

suppose they all have multiplicity $r_i$

or rather the $i^{th}$ one has that multiplicity

Semiclassical

with the relevant quote at 17:20

Thorgott

$x^3+1$ has derivative $3x^2$, which has a repeated root $0$ in any characteristic $\neq3$, but $0$ is not a root of $x^3+1$ at all

Semiclassical

with the context not being "we can't use them, so we shouldn't make them" but "if we make them, it's because we're willing to use them"

BigSocks

I think it has to follow that $((x - b_i)^{r_i})^2 \vert (f(b_i) + f(x))$

well that is a great point.

although I guess I am a bit more confused in a way

vzn

@Semiclassical how did you find that? googling? its a bit obscure but relevant. its trump talking to matthews (not a fan of his interrupting interview style here!) about use of nuclear weapons in middle east/ elsewhere, US policy. matthews says trump has said thing alarming to our allies etc about not taking nuclear weapons "off the table". trump says, then, why do we make them? it is an argument in favor of "not taking nuclear weapons off the table" by trump.

Astyx

6:13 PM

@Semiclassical So deranging

vzn

the phrase "all options are on the table" has a lot of usage wrt (alluding to) nuclear weapons by different state actors, its a typical US phrase.

Semiclassical

google, yeah. think i looked at this old article in particular: bbc.com/news/world-us-canada-40879868

vzn

trumps attitude on nukes is highly relevant to this topic, but its far from reagans. am not an expert here, but do enjoy looking into quotes/ nuance/ the nature of mixed up thinking on nuclear weapons, which is quite bottomless at times. which reminds me of another quote by nietzsche.

Semiclassical

yeah, and it's the distance between trump/reagan's thinking on this which sticks out to me

BigSocks

@Thorgott Yeah I think you have to assume $f$ has no double roots in the algebraic closure of the field $k$ of characteristic $2$

vzn

6:18 PM

"He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you." - Nietzsche (Beyond Good and Evil: Prelude to a Philosophy of the Future (1886), Chapter IV. Apophthegms and Interludes, §146). philosophy.stackexchange.com/questions/55074/…

BigSocks

That might make a difference

vzn

it would be fascinating to compare/ contrast reagan vs trump esp wrt nuclear/ foreign policy. but basically, to trump, nukes are like a "big gun" that can be pulled out of the back pocket to threaten with. trump is largely pro military but anti war. he managed to keep us out of war, deescalate in some rough ways, but he increased military budget substantially, did not really reign in military in any meaningful way... quite to the contrary. the soleimani strike was branded as reckless by many.

Semiclassical

for me the simplest statement on nukes is one which starts with Reagan and was neatly summed up by Gorbachev: "In his 1984 State of the Union address, the president spoke directly to the people of the Soviet Union. He said, "There is only one sane policy, for your country and mine, to preserve our civilization in this modern age: **A nuclear war cannot be won and must never be fought.** The only value in our two nations possessing nuclear weapons is to make sure they will never be used. But then would it not be better to do away with them entirely?"

vzn

you have heard of MAD right?

Thorgott

but $x^3+1$ doesn't have double roots in the algebraic closure?

Semiclassical

6:21 PM

yeah. i want to say it goes all the way back to von Neumann actually

vzn

to say nuclear war "cannot be won" is something of a bizarre understatement. basically, there seems to be no way to have "limited nuclear war" or perhaps the phrase itself does not really make sense, is not coherent, is incoherent.

Semiclassical

right

so the idea of treating it like a "big gun" is...maddening

vzn

MAD revealed the concept of "nuclear winter" on a scientific level. it said that not only would you possibly destroy civilization but also planetary ecology, life support systems. this was before widespread awareness of climate change.

so even "nuclear winter" may have been an understatement at the time.

Semiclassical

ya

one thing that's made me wonder, in that regard

suppose you had some sort of limited nuclear exchange. the sort of india/pakistan nightmare scenario

how would that interact with climate change?

like, the immediate effect would seem to be nuclear winter to some magnitude

vzn

so in a sense, nuclear weapons break down the very concept of war, such that the concept becomes nearly incoherent. wars are fought to be "won." nuclear weaponry means not only do you not win, maybe you only end in total annhilation, us, them, the enemy, all humanity, etc

reagan/ gorbachev were beginning to come to grips with this realization.

Semiclassical

6:25 PM

but when that went away, would that mean that---if you still had carbon emissions going on in the meantime---that global warming would kick in even harder?

vzn

nobody has reexamined (so called) "nuclear winter" from the pov of climate chg to my knowledge.

Semiclassical

you'd think someone would've

vzn

lol 2 horsemen of the apocalypse instead of 1, not riding independent, but maybe together! o_O

Semiclassical

ya

vzn

maybe theyre all hooked up to a carriage lol :P

Semiclassical

6:27 PM

i mean, my main question isn't so much the immediate effects of nuclear winter (which would clearly be dire)

but what the longer-term interaction would be

what got me thinking about that was geoengineering proposals

vzn

this occurs to me, to understand reagan and the MIC, it helps a lot to study iran-contra scandal. think in retrospect, a big piece of the puzzle. (did not understand much at the time, as didnt the whole country either)

Semiclassical

because one big issue with them is that, if you start doing serious geoengineering, you really need to continue it

because otherwise climate change just kicks back in, and even harder if you've continued doing carbon emissions in the meantime

so could you have an 'accidental' instance of that?

Balarka Sen

Quickly: $(x + y)^n \geq x^n + y^n$ if $x, y > 0$, correct?

BigSocks

yea

Semiclassical

that's equivalent to $(1+(y/x))^n\geq 1+(y/x)^n$

so bernoulli

Balarka Sen

6:29 PM

$x^n$ is convex for $n > 1$

OK great

Thorgott

binomial theorem?

vzn

@Semiclassical not totally following "accidental" instance of what? have been thinking about geoengineering myself lately something reminded me of it. was watching a cool interview yesterday with hassabis (deepmind)/ hannah fry you might enjoy it. not short 30+ min but he gets into how A(G)I might help out on the hard problems eg climate change.

Semiclassical

accidental is the wrong word, i guess

a limited nuclear exchange as "unintentional" geoengineering

vzn

so my thinking is, there could be a "limited" nuclear exchange, its conceivable, but whether it stays "limited" is related to a thin thread of human psychology of whether leaders with their hands on the button choose to deescalate or escalate. it would be similar to the cuban missile crisis. part of the "edge" is human psychology which is sometimes unstable in the heat of the moment...

Semiclassical

of course. my question is along the lines of: even if it managed to remain limited, what would the long-term interactions with climate change be

that's a major if, but it sets a ceiling on how bad the short-term effects could be and how long they'd last

vzn

6:35 PM

so ok, 1s with google shows the question (not surprisingly) has indeed been studied. news to me also lol Nuclear weapons worsen the climate crisis theguardian.com/world/2020/jan/16/…

but for me, again, some of this is mixed up thinking, to say the least. in fact, was thinking recently that general ideas about nukes seem to me to constitute a low-grade collective/ societal psychosis.

Semiclassical

that focuses more on the immediate effect of nuclear warfare, though.

it's the long-term interaction which has always bothered me

(the simplest answer is "we don't know, and we sure as hell don't want to find out")

vzn

appreciated this point of the article something that came into my mind immediately on looking at the headline...

> Nuclear weapons destroy the climate even when they are not used.

BigSocks

@Thorgott this is weird. So the paragraph starts out "Let $k$ be a field of char 2. Let $f(x) \in k[x]$ be a polynomial of positive degree without double roots in $\overline{k}$. The extension $L := k(x)(\sqrt{f})$ is not separable over $K := k(x)$ since the min. poly. $y^2 - f $ of $\sqrt{f}$ has a double root in char 2. "(I guess because you could use $\sqrt{f}$ or $- \sqrt{f}$)

So what has gone wrong? Or how do we fit in the $x^3 +1$ example?

vzn

re your quote about "why use them?"

Semiclassical

yeah

vzn

6:39 PM

"why do we make them? why use them?" are like the deep zen questions of the 21st century, which nobody have really thought about much, like a societal/ civilizational zen-psychosis-koan so to speak.

Semiclassical

the trouble is that there's two ways to go with that logic

vzn

Lao Tzu (Taoism) had some sayings/ verses about weaponry over 2M ago... that still apply, more so.

Semiclassical

one is to say "we can't use them, so we shouldn't have them"

which to me is altogether sane and rational

the other is to conclude that, since we have them, that means we should be willing to use them

vzn

the whole entrerprise is not sane, not rational. its insane, and irrational.

Semiclassical

which is...madness

vzn

6:41 PM

its beyond insane (so to speak), it seems to have a large psychopathic side.

Thorgott

I'm not sure how you wanna fit that example, these are simply different scenarios

at no point is it claimed that repeated roots of a derivative imply repeated roots of the original polynomial

vzn

but alas, its a collective insanity.

Balarka Sen

BigSocks

no, and I am sure it's not true now

Semiclassical

@vzn it's one we seem to have settled into now, unfortunately

vzn

6:42 PM

its a quite physical reflection, reality of humanity and its dark side.

the dark side is darker than what we can imagine. o_O

BigSocks

but later on they have that the derivative is a square and they express as the product of all their roots to their multiplicites squared

Semiclassical

the cold war at least made us cognizant of "oh shit, we might use these things"

now it's more like "we have them, but it's not like we'd ever -use- them..."

which lasts right up until someone decides that, if we have them, we might as well be willing to use them

BigSocks

and somehow each root to its multiplicty divides the sum of the roots of the polynomial evaluated at a root + the polynomial in its indeterminate

vzn

cant remember what reminded me of nukes recently, was musing on it recently.

Thorgott

well, it's definitely not true that repeated roots of derivative imply repeated roots of the polynomial, as the counter-example shows

vzn

6:45 PM

there is another school of thought that, they indeed have been used. the public is unaware or mis/ disinformed. its a school of thought, but maligned as unthinkable... its part of the "real dark side"...

Thorgott

but of course the excerpt you quoted is true regardless

BigSocks

right then idk how to justify

$\alpha_i := \frac{\sqrt{f(b_i)} - \sqrt{f(x)}}{(x - b_i)^{r_i}}$ integral over $k[x]$ whenever
$f'(x) := \displaystyle\left(\prod_{i=1}^t (x-b_i)^{r_i}\right)^2$

Semiclassical

of course, you could say that about a lot of stuff. "a pandemic can't happen, and if it does we can handle it"

vzn

speaking of math, some of the worlds greatest thinkers/ mathematicians have worked on nukes... they are incredible feats of engineering/ science, somewhat like drones amplified on a somewhat inconceivable scale o_O appreciate your citing von neumann... our heroes are often... "multisided..." another term is "two faced"... re Janus...

Semiclassical

@vzn yeah, which goes back to the whole von Neumann reference

BigSocks

6:48 PM

$((x - b_i)^{r_i})^2$ has to divide $f(b_i) + f(x)$

Semiclassical

but in fairness it's genuinely hard to get yourself to the mindset that motivated them

BigSocks

but why does it do that? I am not sure

vzn

more quotes, this one always sticks in my mind

Semiclassical

us 80 years after WWII is a lot different than in the midst of it

vzn

> As he witnessed the first detonation of a nuclear weapon on July 16, 1945, a piece of Hindu scripture ran through the mind of Robert Oppenheimer: “Now I am become Death, the destroyer of worlds”. wired.co.uk/article/manhattan-project-robert-oppenheimer

Balarka Sen

6:49 PM

That sentence sounds like a typo lmao

He means "Now I am dead"

Semiclassical

the other quote from that (Kenneth Bainbridge) is "Now we are all sons of bitches."

vzn

bohm was seriously mistreated by the WWII situation a lot in the anti russian hysteria of the 50s. think its a miscarriage of justice thats largely been forgotten...

Semiclassical

yeah, a lot of the reception to Bohm is colored by the surrounding politics

vzn

Turings life can be seen in the light of a tragedy oriented around WWII

user2103480

@Semiclassical smart

Semiclassical

6:52 PM

of course, there were and are genuine reasons why one could hesitate to buy into the pilot wave approach. but it's hard to separate the genuine physical/philosophical issues from the "Bohm isn't welcome, GTFO" attitude

vzn

wow that is roughly/ nearly my thinking exactly. human biases get mixed up that way.

Semiclassical

I think reasonable people can on the one hand prefer Copenhagen over pilot wave, but nevertheless conclude that the way the physics community responded to such was both harsh and counterproductive

even if you still prefer Bohr over Bohm, you can view the attitude towards Bohm as really quite wrong-headed

vzn

dude, we should talk about hidden variables at length sometime when youre in the mood :) am sure theres zillions of new papers in it, and its fun even if theres not :) ... srsly its a revolution in play, youre unknowingly very close to it... plz give it a real chance sometime :)

Semiclassical

eh. right now my main takeaway from the pilot wave theory is that, as a tool for generating interesting visualizations and computations, it's useful. but there are real reasons why reifying it into a physical reality (rather than a convenient picture) is unwise

vzn

its entered the realm of experiment and soon falsifiability... its right on the cusp now, almost nobody realizes it (yet). a 21st century einstein will untangle the ~~mess~~ "entanglement"... soon... its a multicentury science detective story, with the most subtle of clues, soon to be unravelled...

Semiclassical

6:58 PM

What Bell showed, using Bohm, is that you could restore trajectories to non-relativistic QM

the question is whether you -should-

vzn

bell was scratching/ scraping at the Big Picture and the Big Picture is still emerging.

have you ever read any Bohmian philosophy?

Semiclassical

yeah. i got a copy of his "implicate order" in high school

i appreciated it at the time

vzn

100+ pages on "philosophy" mostly about physics + mathematics lol

excellent ok, the implicate order is now literally being uncovered thru experiment.

Semiclassical

nowadays I much more appreciate what bell did with pilot wave as far as the first-order formalism

vzn

its basically "subquantum." (dynamics, mechanics)

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$Mathematics$ Mathematics