3:24 AM
@ACuriousMind Sorry @DavidZ I didnt know moderators could grant access to someone with rep<20, also I thought, since this was done before.. We could do it now too..

4:02 AM
@Oswald I don't think we can. At least not to the general chat space. I tried it once.

@dmckee I see.. :)
277

I have noticed I have had great success using another co-worker as a metaphorical rubber duck (sometimes intentionally, sometimes unintentionally). It improves my productivity vastly. However, I know that it probably distracts others when I am using them in that way. That's why I want to buy a l...

4:23 AM
@DavidZ great, thanks! I'm a serious stackexchange fan at heart.

4:48 AM
@dmckee Not to chat in general, but we can do it on a room-by-room basis

@DHMO Hi! I have a definite integral for you

@anonymous isn't this gamma?

@DHMO I never used gamma function. I found this as an exercise. Can you evaluate it without gamma function ?

$\displaystyle \Gamma (z+1) = \int_0^\infty t^z e^{-t} \ \mathrm dx$
@anonymous not if $n$ isn't a natural number

@DHMO You can assume that n is a natural number

4:59 AM
@anonymous then it is equal to $n!$ I believe

@DHMO Yeah, but how did you get it ? (Don't use gamma function)

We can define $\displaystyle I_n = \int_0^\infty x^n e^{-x} \ \mathrm dx$

@anonymous integration by parts

And then prove that $I_n = n I_{n-1}$ and that $I_0 = 1$.

@DHMO oh sorry.. :D

5:00 AM
@Oswald welcome to the h bar

@DHMO Good. You know it then :). Lemme look for good problems for you ! I'm doing definite integrals today :D

@anonymous ok

Thanks @DHMO

@anonymous single variable?

@Oswald Thanks oswald! But I and DHMO are having a sort of quiz/competition where we challenge each other to solve integration problems-both definite and indefinite...you can join if you wish :)
@DHMO Yes :P I am weak at definite at the time being :D

5:03 AM
@anonymous I would love to.. but I'll probably be irregular here

Can't you do that one by taking n derivatives w/r to $\lambda$ of $f(\lambda)=\int e^{-\lambda x} dx$ and then set $\lambda=1$?

@anonymous $\displaystyle \int_0^{\frac\pi2} \frac {\mathrm dx} {1+\tan^e x}$
@ZeroTheHero that'd be another method
@anonymous be back in a moment

@DHMO I think that can be done by using $$\int_a^b f(x) dx= \int_a^b f(a+b-x) dx$$

yes

You could try the integral of $\sec^3(\theta)$

5:07 AM
The integral of secant cubed is a frequent and challenging indefinite integral of elementary calculus: ∫ sec 3 ⁡ x d x = 1 2 sec ⁡ x tan ⁡ x + 1 2 ln ⁡ | sec ⁡ x + tan ⁡ x ...
That's a famous one :D
I did it yesterday only :)

if you've done complex analysis - coutour integrals you've find plenty of definite integrals to solve

@anonymous $\displaystyle \int_0^\infty \frac {\ln x} {x^2 + 2x + 2} \ \mathrm dx$

what do you do if someone believes in pseudoscience and won't give up their beliefs even if you show them undeniable evidence against the beliefs?

@DHMO Trying that !
@DHMO Try this one ^ meanwhile :D
It seems like a good problem
@DHMO That's easy I think. Divide the integral from 0 to 1 and from 1 to infinity. Then in the second part substitute x=1/y. Then the second integral will probably reduce to -I where I is the first integral :)

@obe Beliefs IMO is a very tricky thing. As long as a person's belief doesnt hurt others it is perfectly fine :)

5:17 AM
basically how do you argue against the phrase "it's because science doesn't understand it yet" or "science can't explain everything, maybe in the future they will discover that ____ theory that you now call pseudoscience is actually true"

0

I asked a question ysterday. I explained there that I was unable to understand how can my speakers make sound when I receive a phone call. The question is put on hold with a reason This question appears to be about engineering. There was the link to get more details. But I think the question is...

@obe My parents/family is extremely religious and believe in several superstitions (most of which you will find ridiculous). I am completely opposite. As long as their beliefs don't harm me or anyone in general I just let it go. Live and let live :).
It is not your duty to make them believe in science.

though how can I let people who are important to me live in ignorance?
and allow others to take advantage of them using the belief systems they have in place.
I'm not talking about religion by the way, so please don't focus on that.

@obe If their beliefs are causing them any harm then maybe you should express your opinion and try to explain logically without accusing them of ignorance. But you can never win an argument against pseudo intellectuals unless they themselves open up their mind.

the funny thing is, they are telling me to open up my mind. in their eyes i'm the close minded one because I'm not willing to accept things outside the realm of science. (aka things that are untestable or not based on evidence)

5:23 AM
I agree with @anonymous you could may be try to change the mind of young people but its nearly impossible to convince the old

@anonymous $aI + bJ = \dfrac \pi 2$ and $aJ - bI = \ln...$

@Oswald every time I try to convince someone it leads to this:
8 mins ago, by obe
basically how do you argue against the phrase "it's because science doesn't understand it yet" or "science can't explain everything, maybe in the future they will discover that ____ theory that you now call pseudoscience is actually true"
and I can't think of a good response that will convince them they're wrong.
any ideas?

@DHMO good :)
is my solution to your problem correct ?
^
@obe There isn't any. Just say that "let us agree to disagree" and move on :)

@anonymous I havent tried so I dunno

@obe I used to say "Well... then prove that you are right", and the usual response I got was "Everything in the universe doesn't need proof, that is something science has cooked up". :D

5:29 AM
@DHMO Oh. I think my method is working. I tried it.

@Oswald I can definitely relate to that.
oh well

@obe hehe :D

I guess the only thing we can do is wait for science to fill in all the holes leaving no room for pseudoscience or superstition.

@Oswald flat-earther, anti-vaxxer, creationist,...

@DHMO wait... what are you talking about? Earth isn't flat? My whole life has been a lie :O
2

5:32 AM
lmao

@Oswald ya, I was quite shocked when I learnt the truth

:D

dude I swear if you take a flat-earther to space and orbit them around the planet they will be like "nope what i'm seeing is only an illusion" or some other bs like that
or if they're "smart" they will be like [insert ridiculously complicated pseudoscientific theory that describe why it might appear to be a sphere even though its flat]

and young universe...
c decay

@obe You will find thousands of people like that if you browse the youtube comments on science videos. They help me laugh and keep healthy :D

5:35 AM
haha

I remember the Area 51 conspiracy theories :P
My goodness !
Aliens,UFOs and what not :D

sigh
should we just abandon them and give up?

@obe the fight against anti-vaxxers must endure

@obe No no no. The present day comedy shows on tv are very boring. So I depend on the conspiracy theories for laughter :D They are a part of my life !
@DHMO True :)

@DHMO well I guess some forms of pseudoscience have immediately harmful effects. but how do you convince someone whose mind is zip locked?

5:41 AM
Like the comments on Global Warming and Climate Change by some famous president a few months back......? :P

comet ison is nibiru, open your eyes people, nasa is lying to you and science is wrong. (sarcasm)

can somebody enlighten me on the comet issue

it's from 2013 xD

is it real?

which part?

5:48 AM
The Nibiru cataclysm is a supposed disastrous encounter between the Earth and a large planetary object (either a collision or a near-miss) which certain groups believe will take place in the early 21st century. Believers in this doomsday event usually refer to this object as Planet X or Nibiru. The idea that a planet-sized object will collide with or closely pass by Earth in the near future is not supported by any scientific evidence and has been rejected by astronomers and planetary scientists as pseudoscience and an Internet hoax. The idea was first put forward in 1995 by Nancy Lieder, founder...

i heard a comet is coming to destroy us

rip

We have enough nuclear reserves to divert any approaching comet even if such a thing happens :)
And obviously I don't expect a planet like Jupiter to come flying at us :P

interesting

comet maybe but large asteroid, apparently not.
and idk 100% if we can do it for comets either but I'm guessing it's doable since they break up easily.

5:54 AM
@obe There has been a LOT of research on that topic. See en.wikipedia.org/wiki/Asteroid_impact_avoidance for example
Asteroid impact avoidance comprises a number of methods by which near-Earth objects (NEO) could be diverted, preventing destructive impact events. A sufficiently large impact by an asteroid or other NEOs would cause, depending on its impact location, massive tsunamis, multiple firestorms and an impact winter caused by the sunlight-blocking effect of placing large quantities of pulverized rock dust, and other debris, into the stratosphere. A collision between the Earth and an approximately 10-kilometre-wide object 66 million years ago is thought to have produced the Chicxulub Crater and the Cretaceous...

@anonymous I know.
TL:DR?

@obe We are prepared but not fully :)

@JohnathanRalls I can't give you any references I'm afraid as this isn't my area and I'm not familiar with the literature in it.

@anonymous $\displaystyle \int \frac {\sin x} {1 + \sin x \cos x} \ \mathrm dx$
the wrong approach can take you 10 pages

@DHMO Is that indefinite ?

6:04 AM
yes

Very easy
Divide it into s+c and s-c
at numerator
then write the denominator as the integrand of the individual numerator squared

$(\cos x + \sin x)^2 = 1 + 2 \sin x \cos x \ne 1 + \sin x \cos x$

@DHMO So what? ((s+c)^2-1)/2=sc
Just substitute y=s+c and dy=c-s

oh, I see
congratulations

6:08 AM
@BernardoMeurer It works! :-)
I'm glad you like the way it sounds. Exactly what sort of sound you like can be a very personal thing and I was a bit worried you simply wouldn't care for the Maranz style. Personally I love it.
Now you have a cable you might want to test all the inputs. I think some of them are a bit flaky because the contact are corroded. You may find the sound cuts in and out or crackles as you wiggle the RCA plugs around. Also check the balance control works properly across its range.

@DHMO hi

Hello @JohnRennie Is publishing research papers a good way to get into a physics career? should I start of with review papers?

@Oswald what is your current status e.g. are you at school, college, retired?

6:23 AM
@JohnRennie I am 24 yr old and working as a software developer in a private firm, I cannot afford to leave my job right now and pursue physics (financial reasons), so was thinking to work on a few papers and publish if possible. I do have a few good physicist friends, I do plan to do a Phd at maybe later points of my life.. till then I thought I could may be publish a paper if possible :)

@Oswald On what topic are you planning to publish a paper ? (If you don't mind ....)

@Oswald I think it's very difficult for an outsider to make a useful contribution. The trouble is you simply won't know what areas are fruitful to work in and what has already been done.

@anonymous I wish I knew :D.. I am going thru Arxiv everyday.. My mentor is a quantum physicist, so the paper would probably be in QM :D

Once you're part of the establishment you're surrounded by people who do know all this stuff and can guide you. I don't want to discourage you from trying, but I suspect you'll have a struggle to find anything useful to publish.

@JohnRennie yeah.. Its very hard to boil down to a topic to research about :( may be I'll have to find the right people...

6:41 AM
@JohnRennie Do you know of any physicist who has produced considerable amount of quality research papers without a formal phd degree? I mean is it possible? (Just curious)

I can't think of anyone.

@anonymous you would need a phd for a quality paper.. not so much for an ordinary paper, or a review paper I believe

Well, I can only think of Freeman Dyson at the moment...
@Oswald I see...I didn't know that

Well Lubos motl, who also happens to be a excellent contributor to PSE published a paper on String theory right after finishing UG, See quora.com/…

@Ramanujan shalom alaichem

6:56 AM
@ACuriousMind a friend brought me some pine liquor from Austria.
It is excellent.

Pine?
Sounds like Retsina

It's not retsina.
It's a red-ish color and doesn't taste like retsina.

@DanielSank
Like this ?
:P

Yes!

ZIRBENZ or some other brand ?

7:00 AM
@anonymous are you German/Austrian?
The label says "BERTLS \ Feinbrand \ ZIRBE"
\ means line break

@DanielSank No no. I'm from the Middle East (but of Indian Origin). That is actually a very famous liquor. It is available in many shops here. So I happen to know about it (my father is fond of it :P)

@anonymous Where you from? My mom's family is from Lebanon.

@DanielSank Oh, me? I'm from Kuwait
And you?
Which US city?

@anonymous My location is discernible from my profile page ;-)

Ah, Santa Barbara :)

7:10 AM
@DanielSank nice.. my brother-in-law and sister live in north carolina

@N1ng I don't get the bottom line.

OMG=WTF
In the picture :P
Lame XD

TIL Pluto is, by law, still a planet in New Mexico
It's in honor of Tombaugh, who was a longtime resident of New Mexico. New Mexico's House of Representatives also passed a law stating that March 13, 2007 was Pluto Planet Day.

@SirCumference I don't think it matters anymore...

7:21 AM
Still fun to know

Yep

7:42 AM
@DHMO
Another integral for you
I couldn't solve it :/
The limit is from 0 to pi/2
$$\int_{0}^{\pi/2} \frac{1+2\cos(x)}{(2+\cos(x))^2} dx$$
@Oswald Any ideas ? :)

8:02 AM
@anonymous have you tried cos(x/2)?

8:15 AM
try this.. add and subtract 4 in the numerator, this will get rid of the cos(x) in the numerator, then express cos(x) in terms of cos(x/2) and the express this in terms of sec(x/2) , this should work, though i havent tried

@Oswald Not working. It is becoming more complicated by that..
@DHMO Doesn't seem to work
@DHMO Did you solve it ?

8:33 AM
I cheated and used mathematica, and the integral is really simple. Though how you get to the integral is another matter.

@JohnRennie Does mathematica provide step by step solution? I know the answer using Wolfram Alpha though...
The integrand is surprisingly simple ;)

I don't think Mathematica has an option to tell you how it did the integration. Maybe it does and I just don't know it. You're right the result is really simple. It looked so simple I hand differentiated it to make sure it was correct and I hadn't set up the integration incorrectly.

Wolfram Alpha pro has step by step solutions. Anyone here has a pro account ?
I think the only way is Wiesrtrass substitution
And the other is guess work :P
I wish I was allowed to carry my mobile to the exam hall XD

There might be enough clues in the little it shows you
It seems remarkably hard for such a simple result. But then integrals are like that!

9:00 AM
@JohnRennie Uff, finally done :D Thanks. I never click on that button on the free version of Wolfram Alpha (as it mostly contains too less info)
It took me 3 pages :P
@DHMO It finally worked using Weierstrass :)

Maths courses get you to do page after page of integrals because it's important training. When you're struggling through some big complex problem it's important you don't get tripped up by every integral that comes along. Still, it's few people's idea of fun!

@anonymous I once figured out the entire process using only that button
it would show me the substitutions and I would follow

@DHMO I think that was in the older version. Now they only show the first one or two steps in the free version.

I know, I follow the substitution and make new queries

@DHMO Oh good idea :D
BTW Wolfram is very tempting and can make you lazy :P

9:13 AM
agreed

@DHMO A trick question: What is fastest method to manually calculate $$\int_0^{1}\sqrt{1-x^2}dx$$ ?
It should take you just 5 seconds ;)

isn't it divergent
but it is also arccos
oh wait i didn't read the latex
@anonymous x=sin theta?

@DHMO There is an easier way. You can find the answer mentally.

I can also do the substitution mentally

@DHMO Can you tell me the value of the integral mentally? I mean the final answer
(Within 5 seconds)

9:26 AM
pi/2?

oh shit
it is half a circle
a quarter*

Yesh!!!!!!!
You got it :D

nice

For any integral of the form $\sqrt{a^2-x^2}$ you can solve it like that

9:28 AM
thanks

This was another good sum
@DHMO You can try
Limits are 0 to pi/2 on left and 0 to pi/4 on the right integral

@anonymous split into two?

@DHMO Which two ?
Tell the split

0 to pi/4 and pi/4 to pi/2?

@DHMO I don't know. I solved in some other way...
Are you getting it using the split ?>

9:38 AM
let me try
@anonymous x=pi/4 - u?
we would have sin(pi/4 - u) and then sum of angle

@DHMO That might work
But at which step are you making that substitution ?
@DHMO
Ok yes, even the split method is working
I substituted $y=\pi/4-x$
Initially I had applied King's rule and then used substitution
But this method seems more intuitive
Thanks!

what is King's rule?
@anonymous

@DHMO Oh, it is just that $$\int f(a+b-x) dx=\int f(x) dx$$ rule
Where a and b are limits of integration

I see

Our teacher likes to name every rule :P That's why even I caught the disease XD
We have Queen's rule too :D

10:01 AM
what is that? @anonymous

King Queen and Jack :D
@DHMO

crazy

Hehe..it is crazy XD
Maybe because King and Queen are the most powerful rules in the topic
Can you do this ? ^
I found it slightly tricky
@DHMO

10:24 AM
@anonymous derivative of even is odd?

yes
you almost did it :D
good

this sounds like a good theorem to prove

@DHMO Which one ?

$\displaystyle f'(-x) = \lim_{h\to0} \frac {f(-x+h)-f(-x)}h = ..$
I can't prove it

Hey, guys :-)

10:27 AM
Use the fact that f(-x)=-f(x) for odd function
@DHMO

can't

12

Prove that the derivative of an even differentiable function is odd, and the derivative of an odd differentiable function is even. Here are my workings so far. Lets prove the derivative of an odd differentiable function is even first. Let the odd function be $f(x)$. We have $f(-x)=-f(x)$ and...

Hi @Kaumudi.H

Morning :-)

@anonymous thanks

$$\int_0^{\pi}\ln(1-\cos(x)) dx$$
@DHMO Next one !
Again a tricky one

10:41 AM
@anonymous king's rule yields conjugate

And then ?

Good..after that ln(sin(x)) integral is a bit lengthy
But you will be able to do it

ya

@DHMO Are you participating in the International Maths Olympiad ?

10:52 AM
no

Why not ? You seem to be pretty good in mathematics:)
I am not participating this year because I know almost nothing about number theory :P

not good enough

You know number theory ?

a little bit

I actually wanted to take part but due to my school work I didn't get enough time to prepare number theory and geometry. I am fairly good at combinatorics though
I bought this book last year ^ :P
I still didn't read more than a few pages XD

11:07 AM
interesting

$$$$\int_0^\infty\frac{\sin^2x}{x^2(1+x^2)}\,dx$$$$ This is one legendary question. Phew !
Don't search the solution on the net XD
Try to solve using rules of definite integration and indefinite integration only @DHMO

11:26 AM
@anonymous partial fraction?

@DHMO How?
The numerator is not algebraic
Maybe it can be done
I'm not sure

any hint?

@DHMO Go ahead and try partial fraction
You will encounter (sin(x))^2/x^2
Think how you can integrate it

I should get rid of infinity first
perhaps x=tan theta

@DHMO But x is also a part of sin(x)...
It will make it complex..

11:38 AM
we don't need the antiderivative

Ok try it

I have no idea lol

@DHMO Actually the solution is quite complicated using normal method
Even I couldn't do it
37

Here is my attempt: \begin{align} \int_0^\infty\frac{\sin^2x}{x^2(1+x^2)}dx&=\int_0^\infty\left[\frac{\sin^2x}{x^2}-\frac{\sin^2x}{1+x^2}\right]dx\\ &=\int_0^\infty\frac{\sin^2x}{x^2}dx-\frac{1}{2}\int_0^\infty\frac{1-\cos2x}{1+x^2}dx\\ &=\frac{\pi}{2}-\frac{1}{2}\int_0^\infty\frac{1}{1+x^2}dx+\f...

Here is one solution ^
Without using Feynman's method
Do you know Feynman's method of integration ? @DHMO

not really

I think we should learn it...
I found a good article

11:54 AM
It's just differentiation under the integral sign.

@anonymous I think (again) I know the method but not the name
@BalarkaSen namaste

we never really say that if we meet a people; the usual way to greet in bengali is a variation of that but it's rarely used
what's up

:D

yeah that's the variation

@BalarkaSen Can you solve the integral $$\int_0^{\infty} \frac{\cos(x)}{(1+x^2)} dx$$ without complex/contour integration or differentiation under integral sign ? I and DHMO couldn't do it

12:09 PM
I don't think I can.
But I also haven't tried much

No probs
I see

@anonymous what is the result?

@ACuriousMind I leave for five minutes and look what happens
bad edits get approved and posts pile up in the review queues smh
the chat is not monkey business anymore
people here chat about physics when I'm not around >_>
insufferable

1:10 PM
Someone here to help me with perfect numbers?
> Here “double proportion” means that each number is twice the preceding number, as in 1, 2, 4, 8, …. For example, 1 + 2 + 4 = 7 is prime; therefore, 7 × 4 = 28 (“the sum multiplied into the last”) is a perfect number.

Public Service Jimnouncement: I regret to inform you all that I will be reducing my activity on PSE for the next couple months. I'll still check in periodically; however, I've taken a side job as the consulting cosmologist for a documentary and, as a result, have less time to dedicate to PSE. But fear not! I will be back in full swing once production is complete and you will all be in my heart until I return.

Now 1+2+4+8=15 and 15×8=120 but it's not next number in perfect numbers :(

1:39 PM
Arre, @JohnR: U're still around?

@Ramanujan 15 is not a prime
@Kaumudi.H namaste

@DHMO _/\_

@DHMO hmm,thanks,so it should be 31×16=469 :-)

@Ramanujan 31 x 16 = 496

Oops,yes :P

2:00 PM
I don't know who named them, but 28 is not what I'd call perfect. For starters, any number that's not a perfect square is an imperfect square, and being imperfect in one of the characteristics of a number means it can't be a perfect number

@Jim numbers can be imperfect in one aspect and perfect in another
@anonymous considering that the answer is $\dfrac\pi{2e}$, I'd say no...

2:18 PM
@DHMO Great! Then they're perfect in that other aspect. To be a "perfect number", they have to be perfect in all aspects a number can have. Otherwise, it would be theoretically possible to find a more perfect number. The very concept of the word "perfect" implies that it shouldn't be possible to find something more perfect than perfect. No improvement can be possible. You can't do better than a perfect game in bowling; no storm worse than a perfect storm.
There shouldn't be any number better than a perfect number

@Jim Don't take "perfect" in the literal sense :P.

@anonymous but what will I complain about if I don't?

@Jim You lack things to complain about ? Talk politics! Uh oh, even that is banned here XD I empathize :D
@DHMO It seems so :(