The h Bar

antimony

2:51 AM

is there a way to filter out the scifi world building questions

which are crossed with physics

John Rennie

6:00 AM

Do we get that many cross postings from Worldbuilding?

antimony

not sure if i'm doing something wrong, but i see a few a week

and i know its harmless (just ignore them right?) but i don't like how the titles mess my sense of whats real physics and what isn't

a minor quibble i know, just wondered if there was a setting somewhere

John Rennie

I can't think of a way to filter out questions that have been cross posted. As far as SE is concerned they are different questions i.e. the SE software doesn't maintain any link between them.

antimony

ohhh i see

thanks @JohnRennie

John Rennie

@MatthewChristopherBartsh it's dangerously easy to fall into the someone is wrong on the Internet mindset. Many crimes against physics are perpetrated by popular physics books and it's a futile exercise to try and correct them all. At the end of the day it doesn't matter if people believe mass increases with velocity as their opinions carry no weight.

ACuriousMind

7:49 AM

@antimony wait, do you mean WB questions on the site or do you mean the WB questions in the ticker here in the chat?

we added WB questions tagged hard-science to the ticker back when the WB site was new and it wasn't yet quite clear where they were going with it

antimony

oh both i guess, but i was mostly wanting to filter them out of the 'new feed items' thing top left above the chat

here

erm only if it filters them out for me - don't want to mess with the global system

ACuriousMind

there's no way to adjust that ticker individually

antimony

ahh cool no worries

thanks @ACuriousMind

Blind Miner

@geocalc33 very naively, I'd imagine that not interacting means that corresponding string amplitude has a disconnected worldsheet, just like how disconnected Feynman diagrams correspond to particles propagating freely without interacting. Such worldsheets/diagrams are OK and completely legal. So yes, it seems that they can pass through each other and not interact.

sorry I shouldn't have said "freely", I meant self-interacting.

ACuriousMind

I mean, the string amplitude is a sum over worldsheet topologies, not over specific embeddings of the worldsheets, so I don't think there's really any meaning to strings "passing through each other"

there's a path integral over all embeddings, there will be some among them where the strings "cross", but that doesn't really mean anything just like it doesn't mean anything how exactly you choose to draw a Feynman graph in ordinary QFT

@BlindMiner That sounds like a suitable question for the main site (I don't have an answer off the top of my head)

Slereah

8:08 AM

@ACuriousMind It doesn't make sense in a scattering theory sense, but what if you are considering the wavefunction at a given time

I know, no non-scattering string theory :p

ACuriousMind

what wavefunction :P

Slereah

@ACuriousMind Whatever this is I guess

ACuriousMind

I was about to say that you might ask that kind of question in string field theory, but I don't really know enough about string field theory to say anything about that (I don't think it has the same "sum over worldsheets")

Slereah

Well it probably reduces to it in some limit

There are probably "stringy wavepackets" to describes particles

Apparently the string field is literally what the name implies

Just a map from strings to some vector space

Which means that the action is a functional of functional, I guess?

You have your string $X : \Sigma \to M$, you have your string field $\Phi : \Gamma(X) \to \mathbb{R}$, and you have your action $S : \Gamma(\Phi) \to \mathbb{R}$

I'm not sure how it would work out to have a localized object in that theory

But I guess that an object in a given region corresponds to a neighbourhood in "string space"

There is a paper on the classical version of that theory, but it is about what you'd expect in pedagogy : arxiv.org/pdf/hep-th/0112228.pdf

Slereah

9:00 AM

String field theory is extra tricky because the notation doesn't really make it clear if they're talking about quantum theory or classical theory

Because they use angle brackets in the classical theory

and since it's doubly functional I think the action is a path integral

In the same sense that integrals are path integrals in zero dimension, I suppose

Slereah

9:22 AM

Also I'm not 100% sure what the value of the "string field" is at a point

Since there isn't directly a map from target space to the string field

stanri

Hi, I have a question but I don't know if it would be appropriate for the physics stack exchange. Or if it's too simple.
My 4yo wants to know if it's possible for a metal to be transparent. And I got mixed results on google. would it be appropriate for me to ask here?

Is there maybe a better SE site?

because I know this one is for academics

John Rennie

@stanri the reason light interacts with solids is because the light interacts with the electrons in those solids.

In a transparent material like glass the light transfers some energy to the electrons but then the electrons transfer the energy back again so the next effect is that the light is unaffected.

In opaque materials the light transfers energy to the electrons, but then the electrons transfer on that energy to other destinations - typically that energy ends up as heat.

So the way light interacts with a solid depends on the way it interacts with the electrons in that solid.

Does this make sense so far?

ACuriousMind

@stanri We already have that question! See physics.stackexchange.com/q/429308/50583

John Rennie

So we do :-)

stanri

9:43 AM

oh marvellous!

@JohnRennie yes that does make sense

John Rennie

@stanri If you think what we mean by a metal you'll think of something shiny that conducts electricity, and both of these properties are due to metals containing electrons that can move easily.

Metals conduct because a current is the flow of electrons and the electrons can flow easily through a metal.

And it's the fact that the electrons can move freely within the metal that causes the metal to be shiny and opaque. The freely moving electrons interact strongly with the light, and the end result is the light is reflected back away from the metal surface and cannot penetrate through the metal.

Hence, by definition, metals are opaque i.e. the things we think of as metals have properties that necessarily make them opaque.

Though as so often is the case there is a loophole ... :-)

@stanri OK so far?

stanri

so does that mean that transparent materials are by definition bad conductors in their nature?

John Rennie

Ah, I was going to post a link to the Wikipedia article on transparent conductors next, but you obviously already know about them.

I have to confess I'm not an expert in this field, but as I understand it transparent conductors are a type of semiconductor i.e. they conduct electricity in the same sorts of ways that silicon semiconductors do.

stanri

no i don't haha I was just figuring it based on your explanation

but it seems it's more complicated than that

ooh I know about semiconductors

John Rennie

If you take a transparent material like glass it's not a conductor. Indeed various forms of glass are used as electrical insulators.

But in principle (I'm not sure if it can be done in practice) you could convert glass into a semiconductor.

Then you'd have a material that remains transparent but can conduct electricity.

But the conductivity would be a lot lower than that of a metal, so I don't think we'd call a material like this a "transparent metal". We'd call it a "transparent conductor".

Transparent conducting film

Transparent conducting films (TCFs) are thin films of optically transparent and electrically conductive material. They are an important component in a number of electronic devices including liquid-crystal displays, OLEDs, touchscreens and photovoltaics. While indium tin oxide (ITO) is the most widely used, alternatives include wider-spectrum transparent conductive oxides (TCOs), conductive polymers, metal grids and random metallic networks, carbon nanotubes (CNT), graphene, nanowire meshes and ultra thin metal films.TCFs for photovoltaic applications have been fabricated from both inorganic and...

That's the Wikipedia article I was thinking of.

As so often in physics the answer to the question is "No ... but ..." :-)

stanri

10:14 AM

Thanks so much! this is really helpful

Slereah

golem.ph.utexas.edu/string/archives/000338.html

Hm

antimony

10:27 AM

does it mean that basically certain materials become conductors or dielectrics depending on wavelength?

John Rennie

10:48 AM

@antimony Are you asking what happens when we illuminate a material i.e. whether shining light on it affects its conductivity?

antimony

@JohnRennie moreso whether a material might respond like a metal at eg,DC or even RF frequencies but a dielectric at eg. visible light wavelengths?

or the other way around even, for another material

John Rennie

4

Q: What happens when the frequency of A.C becomes infinite?

In an alternating current, the flow of electric charge periodically reverses direction, and the number of times it does that is called the frequency of the current. However, if the frequency of an AC is made infinite, would any current flow? I asked this question to my school teacher and he was u...

Like this?

antimony

ahh lovely thanks

above the plasma frequency, a metal responds to the incident field as if it were a dielectric?

John Rennie

I'm not sure to be honest. I don't know if it's meaningful to describe it as a dielectric at such high frequencies.

antimony

ahh i see

interesting

thanks @JohnRennie :)

JingleBells

2:13 PM

Why is Elon Musk constantly crying about declining birth rates and calling it the biggest existential crisis humanity has faced by far? The population is growing at a declining rate as far as I know and I think it's too early and too extreme to say what he says, am I missing something?

Hi all btw

This is the best place to ask this I know

user4539917

Publicity, for one.

JingleBells

I'm wondering if there really is some merit to what he's saying tho I really can't understand why he is so certain there will be a population collapse

@ACuriousMind Enlighten me please you smart helpful curious mind

user4539917

🤐

JingleBells

I guess he's too busy being awesome

user4539917

2:29 PM

@bolbteppa is just as awesome

JingleBells

ACM is OG

he kinda helped shape my thinking when i was a teen

i was saying some dumb stuff and he explained to me why they're dumb and I learned

now I'm less dumb yay :)

bolbteppa

I'll take all the compliments I can get

JingleBells

@bolbteppa you've helped me too as far as I remember

user4539917

coolio

😎

bolbteppa

@JingleBells Is this comment just a random thought, or referencing the recent story about him

JingleBells

2:35 PM

@bolbteppa referencing recent twitter posts of him

bolbteppa

Yeah but what about the recent story about him and how many kids he has

JingleBells

yeah that's what I'm talking about

he keeps crying about population decline for some reason

bolbteppa

I believe they call it projection

JingleBells

what is it based on, it seems super random to go to such extremes

does he know something we don't

bolbteppa

@Slereah It also might be the coolest thing in physics, but it's very difficult to make sense of even the simplest aspects

ACuriousMind

3:00 PM

@JingleBells There are two things he could be saying and this type of ambiguous rhetoric is very typical for people who don't want to say the second thing out loud:

1. The declining birth rate together with rising life expectancy in many developed countries means a demographic change (more old people supported by fewer young people compared to the past) our current social systems might be poorly equipped for. I wouldn't call that a "threat to civilization", but it is something you can legitimately worry about.

2. When he's saying "population" and "civilization", he's not thinking about humans. He's thinking about "Western" civilization and white populations, and this is a thinly veiled reference to the Great Replacement conspiracy theory.

More Anonymous

Heh! India does not have this problem... We have others :P

ACuriousMind

Sadly, I'm pretty sure your local racists and nationalists will have their own variant of this idea - a fear of being "outbred" by some Other is a very common trope in many ideologies (compare e.g. various eugenic ideas of how poor/stupid/otherwise deemed unworthy people shouldn't be allowed to procreate)

Sir Cumference

it's amazing how much elon musk's been able to ruin his own rep like this

ACuriousMind

@bolbteppa I always had the impression that string field theory was some kind of neat proof of concept that no one actually knows how to use for anything :P

JingleBells

3:32 PM

@ACuriousMind How do you know that? He could be talking about humans or Americans in general?

ACuriousMind

@JingleBells yes, but as you said that doesn't make any sense when you're talking about humans in general ;) (it also doesn't really make a lot of sense in the conspiracy meaning either, but I recognize it as a talking point of these people)

really the only way "we're having too few kids so we're doomed" makes sense in context of a world that is expected to reach 10 or more billion humans in 2100 is if the "we" that is doomed isn't including all these 10 billions :P

as I said there is also a good-faith interpretation where he's just very concerned about the demographic challenge to our social systems, but then it is very strange he's not being more explicit about that, while it's pretty obvious why one wouldn't want to be more explicit about the other interpretation!

JingleBells

@ACuriousMind Yeah I guess that could be the case, or maybe he knows something we don't (like some secret statistic or something xD) but that raises the question why wouldn't he explain why he's so paranoid about this instead of just posting these random tweets

Maybe it's just a marketing exercise intended to create discussions like this so his name goes around

Mlon Eusk

@ACuriousMind How's life?

ACuriousMind

it's alright :)

JingleBells

same here, still husting on Roblox

bolbteppa

The real use of it is just around the corner :p

JingleBells

3:41 PM

it's starting to work out tho

@bolbteppa marketing?

ACuriousMind

no, string field theory :P

easy things to confuse

JingleBells

string field theory means you play a guitar with a single string in the middle of a football field while making theories about it, right?

ACuriousMind

sounds legit; for all I know that's the secret to M theory

JingleBells

M theory = McDonald's Theory

pff i want mcdonalds

it's so expensive in Bulgaria

ACuriousMind

though it probably should also need to involve psychedelics somewhere along the way

JingleBells

3:46 PM

fast food is supposed to be cheap

guys i just united quantum mechanics with general relativity

has anyone ever thought about the possibility of planets actually being atoms of some other body? while in our atoms there are small humans living on them?

ACuriousMind

yes

JingleBells

infinite hierarchy

ACuriousMind

I've heard the "what if the universe is a giant atom?" plenty of times

sometimes as sci-fi, sometimes from very stoned people, sometimes from physicists :P

JingleBells

im neither of those

ig i must be stoned

guys i heard elon musk will buy stackexchange and hbar after Twitter

I wanna discuss something interesting rn but nothing is popping in my head

@ACuriousMind When a kid spends $10 on my Roblox game, after all transactional and governmental taxes, guess how much I have left

Slereah

@bolbteppa They trick you into thinking it's simple by having very barebones notation

ACuriousMind

3:57 PM

@JingleBells probably something around $2, unless you're in that category where they take a 90% cut (I don't remember how that works exactly)

@Slereah I mean, you could say that Weinberg is at least being honest about QFT in that sense :P

Slereah

@ACuriousMind true

The string field action is like maybe 10 symbols tops

You'd think it would be simpler than that

JingleBells

@ACuriousMind First a kid buys 1000 Robux (the Roblox currency) for 10 USD from Roblox, then the kid spends that 1000 Robux in my game, Roblox then takes 30% of that transaction and it becomes 700 Robux for me, then to convert that 700 Robux into USD it equals 2.45 USD (that's right, not 7 USD) and to transfer that 2.45 USD into my PayPal account the service takes 10%, so it becomes 2.2 USD, then the government takes a 30% tax and I'm left with 1.54 USD.

💀

ACuriousMind

aaaand that's unreadable thanks to ChatJax :P

JingleBells

lemme fix

ACuriousMind

I mean, I can just turn it off, it's fine

JingleBells

4:09 PM

10 USD to 1.54 USD

dies inside

if I live at the border, right in the middle so they can't measure on which side I'm on, can I not pay taxes to any of the 2 countries?

i'll just get my laptop and develop from there

ACuriousMind

go on, try it :P

JingleBells

gets shot by border security

oh wait Turkey is right below me, I'mma go there and buy a condo for 100 USD

erdogan be killing that economy

imma go buy a sports car cheaply there and drive it to bulgaria

puts cool glasses on

@ACuriousMind Anything curious (pun intended) going on in ur life?

I mean interesting*

stanri

@JingleBells Wait, why does 10 USD -> 1000, but then 700 -> 2.45? Why not start a black market of robux and sell your 700 for (eg) 5 USD? They get it cheaper, you get more cash?

JingleBells

@stanri People are doing that but you can get permanently banned if Roblox catches you

ACuriousMind

@JingleBells nah, I'm enjoying having a pretty unexciting life :P

JingleBells

4:24 PM

@ACuriousMind As long as you're enjoying it it's fine

@ACuriousMind At least you don't get 1.54 USD for every 10 USD

ACuriousMind

"unexciting" for me involves not having to think too much about money!

Daniel Underwood

@ACuriousMind just thought you should know that I've started playing Disco Elysium, thanks in part due to your profile pictures :D
I feel just as confused as the main character, which is a whole new level of immersion

ACuriousMind

@DanielUnderwood welcome to Revachol! :D

I won't even dare ask any questions because pretty much any question could be a spoiler

JingleBells

@ACuriousMind money is just green pieces of paper (cash) and numbers on a screen (bank) showing your relative control over society's resources compared to other people. As long as you have enough allocative power to satisfy your consumption you shouldn't think about it too much yeah.

ACuriousMind

I wish I could just delete it from my brain and experience it fresh again (it has surprisingly high replay value for such a linear game but the first time is really something else)

@JingleBells I don't think most euros are green :P

JingleBells

4:37 PM

@ACuriousMind You get the idea tho XD

Daniel Underwood

Thanks for not spoiling it! I'm probably only an hour in or so. Everything is pretty confusing, but it's also a nice unique experience since the main character is so confused! I've gotten far enough to see groups of people splitting a bit based on political views, which I'm a huge fan of in games
I was wondering about replay value since you have different stat options at the beginning, but don't know if I'm far enough to see the effect of those stats

ACuriousMind

I mean, you should have already gotten to hear from some of your stats ;)

how high your stat in something is determines how likely it is to interject, so playing with different builds leads to a lot of dialogue you don't get to hear with a different build

Daniel Underwood

Interesting...I started with the encyclopedia feat and have noticed it pop in a couple times, but have wondered if they might affect things in other ways beyond the die rolls. But I'll avoid asking any questions and keep it as a mystery :D

ACuriousMind

encyclopedia is a useless nerd and it's hilarious, I love it

Shiki Ryougi

6:53 PM

@JingleBells ;) 🌿🚬

Feynman_00

@ACuriousMind It reminds me of what I said after my first time watching Steins;Gate

Charlie

7:15 PM

Can anyone enlighten me as to why this would be true?

Shiki Ryougi

exactly

finally

Charlie

I've stared at the first equality for a good 10 minutes now and I think I am losing my sanity

Shiki Ryougi

Ive spent so many hours trying to figure it out

$\partial_1 e^{-ip_k x^k}=\partial_1 e^{-i(p_1x^1+p_2x^2+p_3x^3)}=-ip_1e^{-i(p_1x^1+p_2x^2+p_3x^3)}=-ip_1e^{-ip_k x^k}$

brake the exponential

and treat the rest as constant

Charlie

I have no problem with the second equality, that is relatively straight forward, I am just definitely missing something on the first

Feynman_00

What's wrong with it?

The minus sign?

Shiki Ryougi

7:22 PM

the minus sign sets you off?

Charlie

Yes :(

Oh no please don't tell me it's obvious

Shiki Ryougi

+- - - convention

Charlie

I might actually weep

Feynman_00

Yeah that's it

Charlie

That did cross my mind, that it was something to do with the MM metric convention used in the notes

But I can't see how to insert it

Feynman_00

7:23 PM

And I guess the sum is only on spatial index, the indexes being latin letters

So you have no problems with the time components (?)

Charlie

Oh right

$\vec {p}\cdot \vec{x}=p\cdot x\big{|}_{p_0=0}$?

Feynman_00

@Charlie If that makes you feel better, today I freaked out about Euler's angles

ACuriousMind

I'm with Charlie in that this is really bad notation - if your $\cdot$ is minus the spatial part of your actual scalar product, your convention is just bad :P

Shiki Ryougi

so $x_{\mu}y^{\mu}= x_0 y^0 - x_1 y^1 -x_2 y^2 - x_3y^3$ and $x_iy^i= - x_1 y^1 -x_2 y^2 - x_3y^3$

Charlie

AHA, got my equation working

Wait my equation is wrong, nevermind

all that work for nothing

Feynman_00

7:27 PM

@ACuriousMind What do you mean?

@Charlie that escalated quickly

Shiki Ryougi

the more i think about it the more it seems like awful notation

Charlie

I'm glad I'm not the only one that thinks there must be better ways of demonstrating the equality there

Feynman_00

Summing just over latin indexes like that is indeed quite misleading and I don't know if someone actually does that

Shiki Ryougi

you mean that? $x_iy^i= - x_1 y^1 -x_2 y^2 - x_3y^3$

Feynman_00

Yes, that's what I mean

Shiki Ryougi

7:32 PM

where I added the minus

@Charlie then how is it explained?

Charlie

Oh I think I get it

That derivative there is summed over by a $\gamma$ matrix next to it

Shiki Ryougi

(i pinged the message)

Charlie

What we're actually looking at is this, so $\gamma^j\partial_j f(\vec x)=\gamma^\mu\partial_\mu f(\vec x)$ because the $\partial_t$ term just annihilates on $f$ because it isn't a function of $t$

Feynman_00

Ok, I think this is really beyond my understanding

Charlie

Wait, ugh I actually don't think that makes sense

Shiki Ryougi

7:35 PM

no there is still a problem i think

Charlie

I can see how the introduction of $\eta^{\mu\nu}$ is going to lead to a negative sign, I just can't see how it's equivalent to what's there

Shiki Ryougi

because the exponent is a function of $^0$ isnt it?

ACuriousMind

@Feynman_00 I mean that while I understand what's going on, $\vec v \cdot \vec w = -v_kw^k$ is just really silly notation because usually the $\cdot$ is just the sum over without the minus. Yes, the minus comes from lowering one of the indices. This would be much less confusing either in the +--- convention or not using $\cdot$ in the first place

Charlie

The book is already in the +--- convention :(

This is Weigand's QFT notes

ACuriousMind

oh, I meant the -+++ convention :D

Charlie

7:37 PM

D:

ACuriousMind

all I'm saying is I understand why that confused you :P

Feynman_00

Oh I understand, you mean that also 4-vectors product is also denoted with the same dot

Charlie

I still legitimately do not understand how it can possibly be equivalent to just stick that minus sign in there

ACuriousMind

@Charlie you're not sticking a minus sign in there

Charlie

Although conceptually I can see how we're getting there

ACuriousMind

7:39 PM

you have $\vec p \cdot \vec x = \sum_i p^i x^i$ by definition of the Euclidean scalar product

Charlie

Like, if you were lowering the $k$ index with the Minkowski metric you'd get that, but $\eta^{\mu\nu}$ isn't defined on $3$-vectors

ACuriousMind

and due to +--- convention, we have $p^i = -p_i$, so $\vec p\cdot \vec x = -p_i x^i$ (now with "proper" summation convention but only over the spatial indices)

Feynman_00

@Charlie Yes, but $\eta_{ij}$ is. It's the submatrix

Charlie

Hmm

Feynman_00

That in the +--- convention is just the euclidean metric with a minus sign

May you forgive me for calling the metric tensor a matrix :P

ACuriousMind

7:41 PM

I have forgiven far graver sins

Charlie

The idea that 3-vectors are lowered with $-\delta^{ij}$ is strange to me

I really do see where everything is come from, maybe I've just never encountered it before

OHHHHHHHHHHHHHH

Feynman_00

@ACuriousMind Like what? :P

Shiki Ryougi

meanwhile Im high ☁️ and i got so confused. Gotta go eat something

Charlie

Sep 29, 2020 at 16:26, by ACuriousMind

"diffeomorphism invariance" ::eye twitches::

ACuriousMind

@Charlie lol

Charlie

7:43 PM

I think I've got it, is this why the $u(p)$ solution to the Dirac equation has the opposite sign in it's exponential?

ACuriousMind

that's a better answer than anything I would've come up with right now

Charlie

I have vivid memories of the discussion surrounding invariance and it's use and miss-use in physics here :P

Feynman_00

@ACuriousMind Are you educated as a mathematical physicist or a theoretical physicist?

Charlie

Weigand's notes have an opposite sign in the exponential to P&S, that must be why, because he's using a weird convention

Introducing that without explanation is absolutely criminal imo

ACuriousMind

@Feynman_00 something in between :P I didn't have a lot of courses that were mathematical physics, but I took a lot of pure math

Feynman_00

7:48 PM

I would like to do that too. There's not much freedom here, though

I don't understand why mathematics tends to slip out of someone's head more easily than physics

Shiki Ryougi

by next year I will try to apply for math masters

if i make it through this year :D

Feynman_00

And I will start my way through Theoretical Physics

Shiki Ryougi

are you starting a degree?

Feynman_00

Nope, I'm about to finish my undergrad

Shiki Ryougi

best of luck to you!

Feynman_00

8:02 PM

Thanks! Good luck to you too :P

I can't really wait to start studying QFT

Shiki Ryougi

yea its very exciting

Feynman_00

8:16 PM

@ShikiRyougi even fields are excited

Shiki Ryougi

HAHA

Matthew Christopher Bartsh

8:50 PM

@JohnRennie I'm not trying to correct all the errors in all the popular science books. I'm trying to make popular science books slightly but significantly better, along with TV documentaries, magazine articles, physics teachers, and laymen who talk to their sons and nephews and so on about relativity. You said it doesn't matter what people think about whether mass increases with speed because their opinions carry no weight (did you intend that pun?) but if those people

@JohnRennie want to believe true things and not untrue things, surely it matters to them. Shouldn't we try to help them. Also, a high school teacher's opinion carries weight with his students, and a layman's opinion carries weight with his children and grandchildren and so on.

@JohnRennie I don't understand your position at all, but I have some hope that you can justify it, because I respect PM 2Ring's opinion, and he seems to agree with you, although I don't see why.

antimony

11:08 PM

the theory goes something like this: parents around the world used to have more children because a percentage of them would die due to poverty, famine, poor access to healthcare etc. as a society becomes more 'advanced', life expectency goes up so you don't need to have as many children, because their chances of dying has gone down.

this is basically what seems to be happening all over the world. just different parts of the world are at different stages. but the trend is downwards, and is generally interpreted as a good thing because it means people are losing fewer children to sickness, disease etc.

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