« first day (2214 days earlier)      last day (2730 days later) » 

12:16 AM
@KyleKanos yes
 
12:29 AM
@DanielSank I have my last algebra exam in two weeks, today I didn't understand two shits about what happened in class, that book better be ready
 
hello everyone
 
@DanielSank Also, I need you to help me with what happened in class today lol
 
@heather hi
@BernardMeurer k...
 
@heather Howdy
 
0
Q: Accelerated ion beam current

heatherIf an electron gun creates a ten mA electron beam and each electron collides with a gas atom and creates an ion through impact ionization, can the ions then be accelerated with a separate negative voltage grid that is powered by a lower current capacity source but still maintain a ten mA current ...

^been around for a bit and doesn't have an answer
 
12:32 AM
hi heather
 
@DanielSank, did I properly fix the make-multiple-tex-files issue (logged as issue #4)?
 
How do electrons absorb photons in photoelectric effect?
 
@DHMO What do you mean, "how"?
 
@ACuriousMind the mechanism in terms of quantum mechanics
 
@heather will check in a minute
 
12:39 AM
@DanielSank, thank you
 
@DHMO It's called magic
I learned it in my Chemistry course
 
@BernardMeurer very funny
@BernardMeurer of course you don't learn quantum in chemistry course
@Kaumudi hi
 
@DHMO Yeah, right, you don't
 
user228700
@DHMO: Yello! How's it going?
 
@Kaumudi fine
 
12:40 AM
@Kaumudi, hello
 
@DHMO Except I do :)
 
@BernardMeurer I see
 
user228700
Hi Heather :-) And everyone else :-P
 
@DHMO I'm not sure what you mean by "mechanism". One writes down a Hamiltonian that has a term for the electromagnetic field in it, but I don't know if that's a "mechanism".
 
user228700
I'm just passing through to advertise my question on Chemistry SE for those who know Organic Chemistry:
 
user228700
12:42 AM
0
Q: Is the inductive effect always measured relative to Hydrogen?

KaumudiWikipedia has defined the Inductive effect thus: "In Chemistry and Physics, the inductive effect is an experimentally observable effect of the transmission of charge through a chain of atoms in a molecule, resulting in a permanent dipole in a bond." Recently, I learned from a teacher that t...

 
@ACuriousMind so the electron before absorption is different from the electron after absorption in the sense that the latter "carries" a term for the electromagnetic field?
 
@DHMO Not at all
All electrons are the same
The electron after absorption just has a little more energy
 
@ACuriousMind not really; some have higher energy
 
A Hamiltonian is not a property of a particle, it's a description of an interaction
 
@ACuriousMind can you explain the absortoption using QFT?
 
12:45 AM
Again, what do you mean by "explain"?
 
well... "explain" in the sense of "describe to a layman like me"
 
I can surely draw a Feynman diagram that shows a photon and an electron going in and only an electron going out (with some external nucleus to conserve momentum).
but, in the end, all this boils down is that I've written a term for electron-photon interaction into my Lagrangian/Hamiltonian because it's an experimental fact that electrons absorb photons and my physical theory should model that
 
@ACuriousMind How does an electron become excited in terms of atomic orbital theory?
 
@ACuriousMind you take the Socratic method so far that even I get annoyed :P
 
@DHMO As a just-so story, the electromagnetic wave passes by and the oscilliating fields in it make the electron oscillate between different energy levels. There's a certain probability that the electron will stay in the higher orbital after the wave has passed by, having absorbed the energy difference from the wave when doing do.
 
12:51 AM
@ACuriousMind how long does it take?
How can an electron oscillate between different levels?
 
@DHMO On the order of nanoseconds, I think
@DHMO Basic principle of quantum mechanics: All states can exist in superposition. If I have two states $\psi_1,\psi_2$ then a state like $\sin(\omega t)\psi_1 + \cos(\omega t)\psi_2$ "oscillates" between the two
 
@ACuriousMind I see
 
@DanielSank I'm just really bad at answering questions that just ask "how" or "why" because I never know what the expected level of the explanation is.
I'm also not always convinced it is meaningful to ask "why" :P
 
@ACuriousMind Why do some photons (ceteris paribus) not get absorbed?
 
@DHMO Because in which state the electron ends up is random, and if it ends up in its original state, no photon is absorbed.
 
12:59 AM
@ACuriousMind where exactly does the photon need to hit?
 
That's an ill-defined question because neither the photon nor the electron have a well-defined postion.
 
@ACuriousMind So, real talk: figuring out what the asker already knows and what they need to hear next is like 90% of teaching.
@ACuriousMind Right, so you could go on to explain what that's the case.
 
@DanielSank but I already know
@ACuriousMind why doesn't the photon in my right hand get absorbed by the electron on my left hand?
@ACuriousMind if it ends up in its original state, shouldn't it be the case that the photon is absorbed and then re-emitted?
 
@DHMO Where's the difference? Since you can't distinguish photons, you cannot tell the two situations apart
@DHMO I'm not sure I understand why you think it would.
 
You guys are really going out of your way to confuse each other.
 
1:05 AM
@ACuriousMind but the photon would have a different direction... whatever "direction" means
@ACuriousMind my question is why it would not
 
@ACuriousMind yeah this indistinguishable photon idea is bs unless we're talking about excitations of the same mode.
 
@DHMO Ah, well, that indeed happens for some photons! There's a cool experiment where you point a sodium lamp at a burner with sodium in it and the flame casts a shadow because some of the photons go in other direction than in that of the lamp after reemission
 
@ACuriousMind That's pretty cool.
I haven't seen that.
 
@ACuriousMind but most of the time the photon travels in its original direction?
 
@DHMO Photons travel in straight lines.
Always.
A photon can be absorbed and then re-emitted in a different direction.
But without being absorbed, they go in straight lines.
 
1:09 AM
@DanielSank but most of the time the photon travels in its original direction?
 
@DHMO After being absorbed? No, I don't think so.
I can't think of why that would be the case.
Hmmmm actually let me think...
 
@DanielSank so the photon is always absorbed?
 
After absorption, the atom has some linear momentum... but that's relative to the reference frame so it can't matter.
The photon would have had some polarization of course... I guess that affects the polarization of the re-emitted photon... but I don't think it would affect the emission direction.
@DHMO I have no idea what you mean. What is "the" photon? What situation are you thinking of?
 
@DanielSank well, you excite electrons using photons
 
@DHMO Sure.
If I shoot an electromagnetic wave at an atom, the atom's state changes in some way.
 
1:14 AM
@DanielSank but some photons don't get absorbed?
 
@DHMO Have you taken a quantum mechanics class?
 
heh, no
 
@DHMO Ah.
 
but I do know something about QM
 
What is your mental idea of "photon"?
 
1:16 AM
 
Oh. Ok.
Could you please read this:
51
Q: Which is more fundamental, Fields or Particles?

jpbrooks-user153707I hope that I am using appropriate terminology. My confusion about quantum theory (beyond my obvious unfamiliarity with its terminology) is basically twofold: I lack an adequate understanding of how the mathematics of quantum theory is supposed to correspond to phenomena in the physical world ...

 
@DanielSank which answer?
 
The one with all the upvotes.
 
@DanielSank ok done
@DanielSank which is another way of saying "my answer"
 
@DHMO In this case, yes.
Anyway, the point is that "photon" means "unit of excitation of a particular mode of the electromagnetic field".
which, incidentally, is why photons (in the same mode) are indistinguishable.
 
1:23 AM
@DanielSank and how does it answer my question?
 
Well, so far you question is ill-posed. I'm trying to help get us to a point where we can ask answerable questions :D
Now we know what a photons is, what is your question, exactly?
 
@DanielSank in what way?
 
@DHMO Well, suppose the electron in the atom has two states $|a\rangle$ and $|b\rangle$.
Suppose the energy difference is $E_b - E_a = h \nu$.
If I shoot an electromagnetic wave with frequency $\nu$ at the atom, the state of the electron will be $$|\Psi(t)\rangle = \cos(2 \pi f t) |a \rangle + e^{i \phi} \sin(2 \pi f t) |b\rangle$$ where the oscillation frequency $f$ depends on the strength of the electromagnetic wave and the dipole moment difference between states $|a\rangle$ and $|b\rangle$.
The phase $\phi$ depends on other stuff I don't want to get into.
 
Continue
 
That's all.
What else would you like to know?
 
1:29 AM
So it oscillates forever?
 
Oh I should point out that the formula there is for the case where the electromagnetic field is in a coherent state.
@DHMO Yes, if I keep applying an electromagnetic field the oscillation continues. This is called Rabi oscillation.
 
@DanielSank "why doesn't the electron on my left hand absorbs the photon on my right hand?"
 
Actually, the same thing happens if we put the atom inside a metal box with an electromagnetic mode at frequency $\nu$. That mode might have exactly one photon in it, in which case the atom behaves in exactly the way written above, but where now the frequency $f$ depends on:
1. The dipole moment of the electron transition
2. The field strength of the electromagnetic mode at the atom's position in the box
@DHMO What is "the photon on my right hand"? I don't know what you mean.
 
@DanielSank I'm holding a torch on my right hand
 
@DHMO ok
and?
 
1:32 AM
"why doesn't the electron on my left hand absorbs the photon on my right hand?"
(I'm implying "they are too far away from each other")
 
@DHMO Yes, I do believe I seen that sentence before...
I still don't know what you mean "the photon on my right hand".
Does anyone else understand this question?
 
@DanielSank the photons from the torch on my right hand
 
@DHMO Uh... many of them do get absorbed by atoms in your left hand.
 
@DanielSank i'm not shooting the photons at my left hand
 
This is rather obvious if you put your hands close enough together. You will feel left hand warm up when the torch is on...
@DHMO Well I can't read your mind. Would you kindly provide a diagram?
 
1:36 AM
 
Ok well since the torch is pointed at the floor, the photons from the torch are in an electromagnetic mode which has no overlap with your left hand.
 
@DanielSank why?
 
So, of course the photons are not absorbed by the left hand.
@DHMO Why what? And, are you trolling?
 
@DanielSank I am not trolling
 
1:38 AM
what does "overlap" mean
 
Oh, I just mean that the modes excited by the torch are in a different part of space than your left hand.
 
I thought electrons have a wavefunction all over the universe
 
Overlap indicates two things sharing a common space.
@DHMO Well... I suppose that's sort of true, but have you examined the wave function for an electron in a hydrogen atom?
The electron density is very, very small if you're that far away from the nucleus.
 
@DanielSank so you mean "the probability is too low"?
 
@DHMO It's insanely low, yes.
Insanely low.
 
1:40 AM
so it's all random?
 
@DHMO I don't really want to get into that, but yes, for most purposes the absorption is random.
 
Alright, another question
 
How does blackbody radiation occur?
 
@DHMO uhhhhh electrons move around and emit radiation.
No big deal there.
It's the same as emitting radiation from an antenna.
 
1:42 AM
@DanielSank ??
 
@DHMO ???
If you wiggle a charged particle it emits radiation.
 
@DanielSank so they lose energy all the time and eventually clash with the nucleus?
 
@DHMO Ah. No. Interestingly, we find that an electron in an atom can't lose all of its energy.
It's pretty interesting that that's the case.
 
when do they lose energy? after being excited?
 
The lowest energy an electron can have is an s-orbital with n=1. You can find pictures of those orbitals on Wikipedia.
 
1:44 AM
they can't lose energy in their ground state right
@DanielSank I know what orbitals are
 
@DHMO Yeah, exactly. Once they're in the ground state that's it.
But then, if you're not at zero temperature, eventually something bumps the electron up into a higher state. Then the electron falls down and emits radiation.
etc. etc
 
@DanielSank what happens when every electron reaches ground state?
 
@DHMO Well, that depends. Are we near something else with a nonzero temperature or not?
 
@DanielSank every electron in the system
 
@DHMO :|
 
1:47 AM
@DanielSank ?
 
Please describe the entire system you want to think about?
 
@DanielSank, thanks for your answer on the github repository
 
@heather Sure thing!
 
@DanielSank "every electron is in ground state" lol
 
@DHMO Then nothing happens.
 
1:48 AM
I guess I'm doing something wrong, because I'm not using the linux side of my computer, I was just using the options provided on the website
 
@DanielSank and we call it absolute zero?
(hey, the nuclei can still move!)
 
@heather Oh ha! You're doing everything through the github web interface?
 
@DanielSank, yeah =) so I didn't know how to make a folder there
 
@DHMO Ehh, well yeah if everything is in the ground state etc. then you're at absolute zero.
@heather Oh lol. I don't know either. Ask Google.
Hahaha that's kind of funny.
@heather the blind leading the blind.
 
=)
funny situation =P
 
1:49 AM
@DanielSank why does the (blackbody) radiation depend on the temperature?
 
Yeah sorry, I'm so used to using the command line that I didn't think of how to do stuff in the web interface.
@DHMO Higher temperature -> electrons wiggle more -> electrons emit more radiation.
 
@DanielSank why does the distribution depend on the temperature?
 
@DHMO Because math.
:-)
Think of it like this: there is some distribution.
The total power must depend on temperature.
I guess it's conceivable that increasing the temperature would increase the power but not change the distribution...
I never thought about this before. Let me think...
 
@DanielSank, the google told me: in the file title you add foldername/ and then type in filename
 
@heather Sounds legit.
Try it, see what happens.
 
1:55 AM
it worked
except not on images, because I uploaded them
 
@DanielSank, thanks!
 
@heather I Google real good.
 
@DanielSank, this is all made the more funny because you work for google =)
 
Indeed.
 
2:04 AM
@DHMO hi
 
@Ramanujan hi
 
Yesterday was terrible for others because you were not there
On math chat room
 
lol
 
@vzn I saw that also
 
user228700
3:22 AM
Will somebody please ping me for no reason just this once?
 
@Kaumudi, why?
 
user228700
Awesome! Ortho showed me a button to click and I've clicked it now and hurray, my phone notified me of the ping in five mins as opposed to 17!
 
user228700
Thanks :-P
 
vzn
3:45 AM
@DHMO you ask a lot of deep questions that have both conventional and unconventional answers. sometimes helps to have an "alternative view" :)
 
@vzn thanks
 
vzn
@DHMO yw. studying physics at school? what country?
 
@vzn I don't prefer to tell what country
I am studying phsyics in high school
 
vzn
@DHMO any plans for college?
 
@vzn math
 
vzn
3:48 AM
re blackbody radation, study of it led to discovery of early QM theory by plank.
 
@vzn the ultraviolet catastrophe
 
vzn
@DHMO exactly! not all physics books ref it by that name...
 
@vzn I'm studying these out of my syllabus
 
vzn
@DHMO studying what?
 
@vzn I mean those questions are out of my syllabus
 
vzn
3:51 AM
yeah. do you have a textbook? what are the classroom materials?
 
@vzn I do not have a textbook out of my syllabus
 
vzn
@DHMO urge you to get one, there are many cheap ones. there may be some fairly good (free) refs online, but havent seen a list myself... ofc the site (Physics) is good to browse via keywords... ofc many good youtube videos too etc... & wikipedia etc
 
@vzn thanks
 
vzn
quite a few of your Q's have Physics QA & wikipedia articles
 
thanks
 
4:12 AM
in Mathematics, 8 hours ago, by s.harp
In physics there is also a fun website http://snarxiv.org/vs-arxiv/ where it presents paper titles from the arxiv hep-theory section and randomly generated ones. You have to choose which one is real
 
 
2 hours later…
user228700
5:45 AM
@JohnRennie: Morning! :-) Dyou know any examples of liquids that mix w/ the intermolecular forces playing no role? You said that these cases are possible...
 
6:02 AM
You remember I suggested the enthalpy of mixing involved breaking A-A and B-B bonds and making A-B bonds in the mixture?
For bonds read interactions not actually chemical bonds.
Well you can measure this experimentally simply by measuring the temperature change when you mix the liquids. This is called the enthalpy of mixing or sometimes heat of mixing.
If the AA and BB bonds are stronger than the AB bonds then it takes energy to mix the liquids (the mixing is driven solely by entropy) and the liquids get colder on mixing. Likewise if the AB bonds are stronger than the AA and BB bonds then the liquids get hotter on mixing.
And if there is no difference the temperature remains constant on mixing.
Make sense so far?
 
user228700
Uhh.
 
user228700
Hang on, I've only just come back. Gimme a minute to read everything...
 
OK I'll go make a coffee ...
 
user228700
Yes, it makes sense.
 
user228700
@JohnRennie Dyou have a coffeemaker?
 
user228700
6:13 AM
OK, clearly not :-P
 
@Kaumudi No, I only drink instant coffee
 
user228700
Ohk...
 
I'm not a coffee connoisseur, I just like to have a mug to hand when I'm working.
 
user228700
Yeah, OK :-)
 
And it's cold in the UK this morning (just below freezing) and a warm mug of coffee is comforting :-)
 
user228700
6:17 AM
Just below freezing?!
 
Anyway, back to mixing ...
@Kaumudi yes, it's about -1C. That's not unusual for late November in the UK.
 
user228700
 
user228700
^ And I'm wearing socks.
 
:-) I'm in the wrong continent
 
user228700
I might actually die if I have to leave this place >.<
 
user228700
6:19 AM
OK, back to the wonderful mixing!
 
In a liquid you can never ignore interactions. The interactions are the reason we have a liquid not an ideal gas.
 
user228700
Right, of course...
 
But, if the interactions are the same in both pure liquids and the mixture then they average out i.e. there is no change on mixing.
 
user228700
Yes...
 
It's in that case that we get a purely entropy driven mixing.
 
user228700
6:21 AM
$\Delta H=0$
 
Yes
 
user228700
Right...
 
And you can measure $\Delta H$ just by measuring the temperature change on mixing.
 
user228700
Hmm, OK...
 
Why "hmm"? That seems straightforward ...
 
user228700
6:22 AM
(Convinced! Just "Hmm" ing :-P)
 
So you just need to find a pair of liquids that don't change temp on mixing. I'd have to Google enthalpies of mixing, but common experience should tell you that in general liquids don't change temperature much when they mix.
 
user228700
Yes, of course.
 
Apart from special cases, e.g. sulphuric acid and water, the magnitude of the enthalpy of mixing is small.
 
user228700
Hm, alright Sir! Thanks very much :-)
 
7:10 AM
@JohnRennie Sir, are you a physicist or a physical chemist?
 
Physical chemist
 
Oh great.
 
Though the distinction is a rather vague one.
 
Why so?
 
I spent my PhD X-raying thin films of silver and chalcogenide glasses, which is basically solid state physics.
 
7:12 AM
Ohk.
 
But I did it to investigate a chemical reaction, so that's chemistry.
 
Then why a physical chemist?
Oh
 
So I'm an unholy mixture of physics and chemistry :-)
 
Haha ;)
I wanted to ask you something, Sir.
What are your views on String theory?
Like, its correctness and all.
 
You hear lots of people making comments about string theory, but 99.999% of those people don't know what they are talking about. String theory is astonishingly hard and only a small number of people understand it.
3
 
7:18 AM
I believe you.
 
So most of the stuff you hear about string theory is being said by people who don't understand it and therefore aren't ina position to make comments.
 
I see.
 
I don't understand it at anything beyond a superficial level, so I'm not qualified to comment either.
 
I heard only 2000 understand ST till date.
Did you ever attempt to study it?
 
It's important to remember this. If I say string theory is rubbish or string theory is great then either statement would be meaningless because from me it would be just personal opinion not based on any facts.
 
7:20 AM
I see.
 
@SwapnilDas you need to know quantum field theory to even begin to understand string theory. I've been toying with QFT but not studying it seriously.
 
I wanted to know its accuracy in understanding the universe.
Oh!
 
So no, I've never attempted to study string theory.
 
That's cool. I want to communicate with string theorists, so much excited.
 
The simple fact is that we have no way of judging string theory because we don't know enough about the theory and there is no relevant experimental evidence.
 
7:22 AM
Yes.
I don't believe exps, actually 😛
 
At the moment string theory is an interesting mathematical model, but to what extent it is useful in describing the real universe is unknown.
 
Aah. Fascinates me. You seem to have a kinda PhD in GR?
 
No my PhD was solid state photochemistry. You can see the title (not the content) by clicking here.
 
But you know GR too well!
 
I've always been interested in GR, and when I quit full time work I decided to start learning it just for fun. And it is fun :-)
 
7:28 AM
Great. You are from Cambridge?!
 
No, I just went to university in Cambridge.
 
I meant a student of the university.
 
Ah, yes, I did both my degree and PhD at Cambridge.
 
You are a genius.
 
Sadly not :-)
 
7:29 AM
Have you met their Lucassian professors?
When I was in grade 5, I wanted to be one, so foolish.
 
I once saw Steven Hawking going past in his wheelchair, but that is as close as I've come to meeting a Lucassian professor. I've met lots of other professors.
 
So lucky!
Professor of Gravitational physics, as much I recall.
Does Cambridge university have the idiotic 'speed up' system? @JohnRennie
 
I've never heard of the speed up system so I guess not. Or at least it didn't when I was there, though that was 30 years ago.
 
Anonymous
8:22 AM
@JohnRennie That was really lucky _. I wish I was there and thank him for all the great books he has written. The books written by "the physicist in the wheelchair" was one of the main reasons that made me so much interested in Science, and influenced me to take up Science as my main stream in High School :-P. I got the whole collection of his books at home (except God Created The Integers which is too difficult to decipher myself, at present :-P) :).
 
Hawking was professor at the department of applied mathematics and theoretical physics (universally referred to as DAMTP - pronounced damped) but this is quite a small department.
Most undergraduates would be unaware the department even existed. I knew of it because it was quite close to my college and I passed it every day. But it would be wrong to think it was particularly famous even within the university.
Cambridge has Nobel prize winners coming out of its ears, so Hawking wasn't considered anything very special. When I was an undergraduate my tutor (Aaron Klug) was a Nobel prize winner - they are surprisingly normal people.
Incidentally I don't think God Created The Integers is a particularly good book. The really great books are ones that take a complicated subject and describe rigorously but ina way students can understand.
GCTI just exerpts from the works of the original authors. It's of historical interest, but it's not a great book to learn from.
 
Anonymous
8:42 AM
@JohnRennie Yes, that is expected as Cambridge has produced several Nobel Prize winners over the years :-P. However, there was a phase in 8 th grade when I started reading popular science books starting with the Illustrated Brief History Of Time and then went on to read 10 more similar books in a period of 3-4 months during summer vacations.
 
Anonymous
I agree that the books are nothing very special or in fact not even accurate, but that was a kick-start to my interest in Physics and Science as whole. (Otherwise I might have been studying commerce or arts now :-P). Moreover I found SH's life story extremely inspiring and motivating :). Now, I have moved on to more technical books though and I don't think I will be reading GCTI anytime soon :-P :)
 
user116211
8:54 AM
Massive power outage in London.
 
user116211
@JohnRennie, do you know the discontinuity of the derivative of vector potential across a boundary? I need halp.
 
@MAFIA36790 I'm afraid I can't help. Electrodynamics was one of the subjects I avoided as much as possible at university.
 
user116211
:(
 
user116211
okay.
 
user228700
11:14 AM
No oranges today. I had an enormous lunch with ice cream for dessert and everything! :-)
 
user228700
For most liquids, is the dew point temperature higher than that of its boiling point?
 
user228700
11:29 AM
OK, Yahoo Answers aren't at all reliable but I found this:
 
user228700
> "One would expect the bubble point would be higher. The dew point is the temperature at which water (dew) condenses from the air. The bubble point would be much higher."
 
user228700
What the hell is up with the phase diagram then?!
 
user228700
 
user228700
^ HOW?!
 
@Slereah Yo, I need ya
 
user228700
11:50 AM
Also, @JohnRennie: In addition to that, if u could perhaps enlighten me as to why the bubble curve is a curve rather than a straight line, that would be awesome!
 
12:25 PM
So Fidel Castro died.
 
The good, the bad, and the (in my case) indifferent. We all die. It's the ultimate proof we are all equal.
 
A (philosopher) friend of mine form undergrad used to say, "Despite all the medical advances we've made, doctors still can't cure death"
 
user223506
Hi all, how is everyone?
 
Somewhat sleep-deprived, but otherwise fine
(The coffee helps)
 
user223506
coffee is indeed good - why are you sleep deprived?
 
12:35 PM
Nov 13 at 18:54, by Kyle Kanos
Girl. Elizabeth. 9 lbs, 6 oz (4.25 kg)
 
user223506
@KyleKanos Hey! Congratulations!!
 
Thanks
 
user223506
Is he girl your first child?
 
Haha, no; she's the 5th
 
user223506
oh wow! A sister as well as a daughter!
 
user223506
12:43 PM
this is great news!
 
user223506
What do you do (asides from being a dad), @KyleKanos?
 
I work for a bank
 
user223506
ah excellent!
 
user223506
enjoy it?
 
Oh yes, lots of fun
 
user223506
12:51 PM
customer service?
 
No, I work in the securities sector as a quant
 
user223506
ah much better!
 
user223506
snoring hummingbirds!
 

« first day (2214 days earlier)      last day (2730 days later) »