This one.
I guess I might as well admit I didn’t get this one either.
Not sure about the first, but the second is a play on “an artist’s impression”.
One can conceive of an idea (or picture an idea) and a person.
I don’t think I’m explaining it well, but I laughed at the cartoon.
A picture of the conception of a person who painted pictures? Nah, too far, lost the funny.
Okay, I went to the xkcd forum and the jokes were explained.
nm
Linky? Please?
In case anyone else doesn’t want to visit the other forum:
The joke is that the circumference formula is really 2pir, but the r has a superscript “2” referencing a footnote. So it looks like 2pir^2 instead.
I think its just a joke about the overloading of superscripts in mathematical texts, they could indicate the squaring operation or footnotes. The mouse-over text makes a similar joke about apostrophes.
πr² is how you calculate the area of a circle. 2πr is how you calculate the circumference of a circle. Though it appears like he made a mistake and used the wrong formula by combining them both, which is possibly a common error people make a lot, he was really marking a footnote reference.
I thought that one was hysterical. I linked to it on Facebook and my mother-in-law didn’t get it at all. You’ve got to love puns or it’s probably not really all that funny.
Puns are fine, I just didn’t even notice the pun.
Ah… Thank you, I was scratching my head over that one this morning 
The second one reminds me of a quote from Follow That Camel (a.k.a. Carry On in the Legion):
(looking at the supply room of a Foreign Legion fort)
“Salt tablets, The Pill… The Pill? What do you suppose they use that for?”
“I cannot conceive!”
Not exactly. when an artist draws something that was described by someone else (an eye witness for example), they call it an Artist’s conception. That was the pun. Not one of his best but I smiled a little.
Today’s I did not get at all and was glad someone had asked about it.
When I went to the forums later, someone had linked to a dictionary saying that; While in the US ‘artist’s impression’ is (and has always been) the norm, in the UK it was a synonym for and superceded ‘artist’s conception’ as the common usage.
But again, for me it sucks the funny right out once we’re at this level of nitpicking.
ETA: Antigen; you, me and my kid (14).
ETA: Never mind, didn’t see your followup.
Didn’t visit the other forum, but this was my take when I saw the comic. Didn’t find this one as funny as the artist being conceived one, but it got a chuckle.
Of course we’ve all known these formulas since we were kids but it’s always bugged me that, while r is the radius, π is defined with respect to the diameter. A circle constant (τ) based upon the radius is more consistent and clearly shows how area is the result of an integration. Math should illuminate, not obfuscate.
c = 2πr = τr
a = πr² = ½τr²
Okay. another one. Time Machines.
I think I’ve got this one. There’s a really subtle change in the electric outlet. So the joke is that turning on the time machine changed the world but the guy doesn’t know it because now that time’s been changed it’s the world he’s used to and he thinks that’s the outlet that was always there.
Yes?
I think that’s a little too subtle. I read it as turning the machine on to travel backwards through time would immediately bring him back to a time before he turned the machine on. Thus making the machine worthless.
Then what’s the deal with the outlet? That implies he’s not back where he started.
I admit the point would be clearer if he had turned into a velociraptor or something like that.