Image text: 'Smilodon fatalis' narrowly edged out 'Tyrannosaurus rex' to win this year's Most Badass Latin Names competition, after edging out 'Dracorex hogwartsia' and 'Stygimoloch spinifer' (meaning 'horned dragon from the river of death') in the semifinals.

This comic is three parted (or four if you count the Latin name portion).

First, the names are sorted up by genuses (a genus (plural: genera) is a low-level taxonomic rank used in the biological classification of living and fossil organisms) from bottom to top of which animals would win in a fight.

Secondly, the names within the genus are then sorted by coolness of name from left to right.

Thirdly, in red you can see the direction that Apple has taken with naming their OS X Operating Systems.  They started at Cheetah and have moved through genuses from there in no order that this chart can make out.

And lastly, I'm pretty sure 'Dracorex hogwartsia' is a fake name because it has too much of the name "Hogwarts" in it, which is the magical school from the Harry Potter series of books and movies.

Image text: If you pledge more than $50 you'll get on the VIP list and have first dibs on a slot on ANY of the pledge levels in the actual campaign.

If you are not familiar with Kickstarter, it is (in their own words) a platform for funding creative projects in which anyone can give money at any level of funding starting usually as low as $10.  Funding at different levels gets you different perks.

In this comic, Black Hat is attempting (and as you can see, failing) to game the system by raising money to work on the perfect Kickstarter pitch.  That is surprising because usually Black Hat is successful with his gambits. The irony of the image text is that you do not need to be on any VIP list to have dibs on the pledge levels.  Anyone can give any amount of money.  That is the goal of Kickstarter and it has been wildly successful.

Image text: Normally pronounced 'THEH-buh-kon', I assume.

This comic plays off a typical American colloquialism in which "Bring home the bacon" means working hard and bringing money home to your family to put food on the table.

In this comic, Randall learns that "Bring home the bacon" is actually a double entendre for the above phrase and bringing home a drug that is known as "thebacon".  In case, you aren't familiar, Vicodin is a pain medication that can be used by some as a drug of abuse.

I don't know if this counts as a "White Hat" comic, but either way, I'm tagging it.

Image text: Saying 'what kind of an idiot doesn't know about the Yellowstone supervolcano' is so much more boring than telling someone about the Yellowstone supervolcano for the first time.

This is certainly a great approach to take with someone that doesn't know something, rather than taking the "idiot" approach.  However, this math assumes that 100% of people know certain things by the time they are 30.  I know that there are a lot of people over 30 that haven't yet seen Diet Coke and Mentos.  If you are one of those people, here you go. This also assumes that 10,000 people learn of something every day from the day they are born.  I don't know if there are people out there showing their newborns the Diet Coke and Mentos experiment.  But, I could be wrong.

If you are not familiar with the Yellowstone supervolcano and have missed the scare-tactics articles over the past 4 or so years, here's a great video explanation.

Image text: Someday I'll be the first to get a Ph. D in 'Undeclared'.

I believe 'Undeclared' is called "General Studies".

Here's a youtube video of "I Am the Very Model of A Modern Major's General" for those who need to get the tune.

Here's is Tom Lehrer's Elements.

And here is Supercalifragilisticexpialidocious from Mary Poppins.

I never did find that closed paren....

Image text: I hate when I read something like '... tension among the BASE jumpers nearly led to wingsuit combat ...', and I get excited because 'wingsuit combat' is underlined, only to find that it's just separate links to the 'wingsuit' and 'combat' articles.

This comic is a reference to how an internet browser will make the links of the pages that you have visited a different color than the links that you have not visited.  In the case of wikipedia, they are blue for non visited and purple for visited.  In this comic, Randall is ashamed of the pages he has visited, because with the color changes there is evidence of what he has done in the past.

So, I can't quite figure who who this fake article is supposed to be about, but the Macarena band is certainly from Dos Hermanas, Spain.  So, it is quite possibly a made up article from Randall.

Image text: The only things you HAVE to know are how to make enough of a living to stay alive and how to get your taxes done. All the fun parts of life are optional.

This comic is pretty well explained in the caption and the image text, but I'll extrapolate a little bit.  Here we have two ex-students taunting their old Algebra teacher because they have never used Algebra since they left (I'll assume) middle or high school.

Randall's argument here is that what part of your schooling that you use after you get out of school is all optional and up to you.  Lots of people use math after they graduate, lots of people use their music lessons, etc.  Lots of people don't use anything they learned in school in "real life".

I'm not sure why it is that people are hostile about their use of math after graduation, anyone have any theories?

Image text: I had a hard time with Ayn Rand because I found myself enthusiastically agreeing with the first 90% of every sentence, but getting lost at 'therefore, be a huge asshole to everyone.'

Again, I'm late.  Sorry.  Life getting in the way of my explaining.

This is a play off the typical "hidden door" in which  you pull down the right book and suddenly a wall of books turns into a hidden door.  In this case, the book is Atlas Shrugged and instead of a secret passage, the wall swings around and takes you to a message "You Have Terrible Taste".

Atlas Shrugged by Ayrn Rand is a novel described like this in wikipedia:

The book explores a dystopian United States where many of society's most productive citizens refuse to be exploited by increasing taxation and government regulations and disappear. They are led by John Galt. Galt describes the strike as "stopping the motor of the world" by withdrawing the minds that drive society's growth and productivity. In their efforts, these people "of the mind" hope to demonstrate that a world in which the individual is not free to create is doomed, that civilization cannot exist where every person is a slave to society and government, and that the destruction of the profit motive leads to the collapse of society. The protagonist, Dagny Taggart, sees society collapse around her as the government increasingly asserts control over all industry.
...
The story of Atlas Shrugged dramatically expresses Rand's philosophy of Objectivism: Rand's ethical egoism, her advocacy of "rational selfishness", is perhaps her most well-known position.

Image text: Fortunately, the internet has a virtually inexhaustible supply of code that doesn't work and people who are wrong, which bodes well for a return to normalcy. [Note: Click to read context for the cancer comics. She's doing well.]

Here's the link referenced in the image text, which is a blog post from 2011 regarding his fiancee's breast cancer.

As you can read at that link, that is what he's referring too.

The only other reference in this comic is Joss Whedon, who (per Wikipedia so I didn't miss anything) is best known as the creator and showrunner of the television series Buffy the Vampire Slayer (1997–2003), Angel (1999–2004), Firefly (2002) and Dollhouse (2009–2010).

The 2006-2007 timeline does not mesh with any of the airdates of the above shows.  It is possible Randall caught up with Firefly or Buffy at a later date, like most of us.

Image text: Two tips: 1) 8675309 is not just prime, it's a twin prime, and 2) if you ever find yourself raising log(anything)^e or taking the pi-th root of anything, set down the marker and back away from the whiteboard; something has gone horribly wrong.

Good lord.  I'm still on vacation and I'm not a math person, so this explanation will be as good as zero to all of you.  So, I'm opening it up to the comments.  I'll follow back up tonight and put the explanation you put in the comments with your name and a link to your comment with what you explained.  Thanks in advance.  You are my only hope!

UPDATES: (in no particular order)

Per Cindy: A twin prime is: "Per wikipedia: A twin prime is a prime number that differs from another prime number by two"

Per zibby: "“Rent Method” refers to the song “Seasons of Love” from the musical “Rent.” The song asks, “How do you measure a year?” One line says “525,600 minutes” while most of the rest of the song suggests the best way to measure a year is moments shared with a loved one.

Incidentally, 75^4 overstates the number of seconds in a year by 29 hours."

Per jstbell and Immo: Jenny’s Number = (867)-5309, “please don’t change your number on me” But since this is *explain*xkcd, let’s add that it’s from a song by Tommy Tutone: http://www.dailymotion.com/video/x20zsk_tommy-tutone-867-5309-jenny_music

Per Mathman: the complicated formula for the White House switchboard yields 0.2024561415. (202) 456-1415 was (at least during the Bush administration) the phone number for the White House switchboard.

And for the rest, I'll just drop in Immo's comment whole.  Thanks for all your help commentors!

Immo:

All these approximations actually work astonishingly well. There are re-occuring math jokes along the lines of, “3/5 + π/(7-π) – sqrt(2) = 0, but your calculator is probably not good enough to compute this correctly”, which are mainly used to troll geeks. Those interested in number theory may easily compute that sqrt(2) is not even algebraic in the quotient field of Z[π], which disproves the equality.

Furthermore, there are some useful approximations (which were even more useful in times before calculators) such as “π is approximately equal to 22/7”.

Randall makes fun of both of these, using rather strange approximations (honestly: you may handle 22/7, but who can calculate in a sensible way with 99^8, let alone 30^(π^e)?) to calculate some constants that are easy enough to handle in the decimal system, and stating such “slightly wrong” trick equations, one of which *is* actually correct (which may astonish only those who are not familiar with cosines).

Jenny’s number and the White House switchboard have already been explained. The other constants are either self-explanatory or simple physical constants that have decimal values you may google in about 1 sec. I am not going to explain what these constants mean. Three things to note: near the bottom, there is a constant which you may easily confuse for a 9. Instead, it’s a g, the standard gravity.

Now to the accuracy values: The fine structure constant is 0.007297something, which is approximately 1/137. Randall’s point here is that 1/137 is not a very useful approximation: Firstly, 0.007297 is input into a calculator as fast as 1/137, and it’s more accurate. Secondly, if you do not have a calculator, 1/137 earns you nothing, for 137 is a prime and therefore does not ease further computation. That’s why Randall stated he’s had enough of this crap.
The ruby laser wavelength varies because “ruby” is not clearly defined.
The mean earth radius varies because there is not one single way to make a sphere out of the earth. Theoretically, it should be possible to measure the distance from the center for any point on the Earth’s surface and compute the mean integral, but practically it’s not, so geodesy has defined some sets of radii to take the mean of, yielding different mean radii. If you are interested in details, ask Wikipedia. http://en.wikipedia.org/wiki/Earth_radius#Mean_radii Randall’s value lies somewhere in between, thus actually being a possible definition for Earth’s mean radius.

The image text gives more or less useful information. Twin primes have always been a subject of interest, because they are comparatively rare, and because it is not yet known whether there are infinitely many of them.
π is a natural constant that arises in describing circles or ellipses. As such, useful as it may be, it’s not supposed to occur anywhere in an exponent (unless you deal with complex numbers). Thus a sensible use of the π-th root would be as if you found an English-speaking extraterrestrian community – not really impossible, but of such low probability that nobody would believe you.
Same goes for the e-th power: e only appears in the basis of a power, not in the exponent.