Ten Thousand
by Jeff
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.
Forgot Algebra
by Jeff
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?
Approximations
by Jeff
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!
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.
Formal Logic
by Jeff
Image text: Note that this implies you should NOT honk solely because I stopped for a pedestrian and you're behind me.
The key part of this comic is "IFF", which in formal logic means "if and only if". "If and only if" represents a formal logic connector that the result is that the truth of either one of the connected statements requires the truth of the other, i.e., either both statements are true, or both are false. In the comic, if someone honks at this car, it means they like formal logic, there is not any other possible reason per this bumper sticker. (As we see in the image text.)
Have a great weekend everyone!
Backward in Time
by Jeff
Image text: People tell me I have too much time on my hands, but really the problem is that there's too much time, PERIOD.
Here's the spreadsheet which Randall used to calculate the times and dates for the comic. It also has a lot of other percentages and dates, so take a look if you are interested.
This comic has a lot of formulas that I'm not going to try to explain because I'm not a math person and it will probably make you dumber if I try. Any math people out there? Have at it in the comments. The reason I'm not going to try is that understanding the math is not a prerequisite for understanding the comic.
Cueball/Randall creates this formula which helps him wait for long stretches of time which goes increasingly faster into the past as more time goes by, which gives him the effect of looking like the time goes by quickly. Which assists in the waiting process.
And of course, there is a particularly obvious pun in the image text. He makes a play on the phrase "time period", which is used to describe large blocks of time throughout history. And of course, the other side is the punctuation mark: period.
(Also, the workout website, Fitocracy has been mentioned previously in xkcd.)
Percentage Points
by Jeff
Image text: Grayton also proposed making college scholarships available exclusively to sexually active teens, amnesty for illegal immigrants who create room for themselves by killing a citizen, and a graduated income tax based on penis size. He has been endorsed by Tracy Morgan, John Wilkes Booth's ghost, and the Time Cube guy.
Senator Grayton is a fictional name, made up for this comic, which is a bit surprising to me as the names used in xkcd are usually references to something.
I'll see if I can do a line on each of the issues that Grayton fictionally supports:
Tax Breaks to Drunk Drivers - Grayton proposed to give money back on their taxes for people who have been convicted of a DUI or DWI. Driving Under the Influence or Driving While Intoxicated
Predator Drones and the War on Christmas - The War on Christmas is a not a real war, it is simply Christians who believe that non-Christians are trying to get rid of Christmas trees, Christmas music and the endless barrage of Christmas-themed nonsense we get from Thanksgiving to Christmas. I don't know how his support would go down if he supported unmanned Predator Drones to destroy people who hate Christmas, knowing America. (Jokes!)
College Scholarships to Sexually Active Teens - Not sure how they would test for this on the scholarship application, but it is funny none the less.
Illegal Immigrants Who Murder - This is an argument for immigration, but only if they make "room" and possibly an open job for themselves by getting rid of another person. This one is pretty evil.
Income Tax Based on Penis Size - Wow, this one would never pass!
On To the Names:
Tracy Morgan is an actor in the TV Show 30 Rock, who plays Tracy Jordan, he is known for his outlandish statements on politics and everything else in the world. He has been reprimanded for controversial comments on homosexuals and Sarah Palin (in separate incidents).
Josh Wilkes Booth is the person who assassinated Abraham Lincoln. He was a sympathizer with the Confederate cause and was for slavery and all its trappings.
Time Cube Guy is Gene Ray, also known as Otis E. Ray. He has a website known as Time Cube (Thanks Wikipedia) where he sets out his personal model of reality, which he calls Time Cube. He suggests that all of modern physics is wrong, in addition to claiming religion to be evil, specifically Christianity, and the idea of family is poisoning children.
Ok, finally to the numbers:
If his polling is at 20% and drops by 19%, without specifying percentage points, that means that his support has only dropped 1% (EDIT: I'm bad at math. Thanks commentors, it is 3.8% percentage points), because 19% of 20% is only 1% 3.8%. That would mean after all his outrageous statements, his support dropped from 20% to 16.2%. However, if they had said his 20% polling dropped 19% (removed percentage sign for redundancy, thanks again commentors) percentage points, that would mean his support has dropped to 1%. Therefore, the distinction is important.
Set Theory
by Jeff
Image text: Proof of Zermelo's well-ordering theorem given the Axiom of Choice: 1: Take S to be any set. 2: When I reach step three, if S hasn't managed to find a well-ordering relation for itself, I'll feed it into this wood chipper. 3: Hey, look, S is well-ordered.
This comic is a pun on the phrase "Proof by Intimidation" which normally means (thanks Wikipedia) a jocular term used mainly in mathematics to refer to a style of presenting a purported mathematical proof by giving an argument loaded with jargon and appeal to obscure results, so that the audience is simply obliged to accept it, lest they have to admit their ignorance and lack of understanding.
However, in the comic, instead of using "Proof by Intimidation" in that way, the narrator's math teacher takes regular proofs and axioms and places threatening words into them so that the students will learn better because she threatens them with death or harm.
The axiom of choice (which has been referenced in previous xkcds) says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin.
In the image text, the well-ordering theorem states that every set can be well-ordered. A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering. This is also known as Zermelo's theorem and is equivalent to the Axiom of Choice.
Delta-P
by Jeff
Image text: If you fire a Portal gun through the door of the wardrobe, space and time knot together, which leads to a frustrated Aslan trying to impart Christian morality to the Space sphere.
This comic was posted late and now I'm late and I'm at work so I can't do as much explaining as I usually do, but I'll do my best. That's also why we have the best comment section on the Internet.
The basic idea of the formula and the comic are based on the books and movies of the Lion, the Witch and the Wardrobe in which a giant wardrobe contains a portal to a world known as Narnia. In the comic, someone connects an anchor to the wardrobe and throws it into the ocean which means that a steady stream of water at a velocity of 200 m/s will flow into Narnia.
The White Witch, the antagonist in the books and movies apparently won't know what hit her according to the caption.
The image text references the video game "Portal" in which you fire a portal gun into walls and etc to make "portals" that can open holes in other places so that you may portal through.
The image text also references the fact that CS Lewis wrote the Lion, Witch and Wardrobe books as a thinly veiled allegory of Christ's crucifixion with Aslan, the Lion in the title, playing Christ's part. (Spoiler alert! Sorry!)
This is a classic xkcd based on the intersection of literature, math and video games.
1 to 10
by Jeff
Image text: If you get an 11/100 on a CS test, but you claim it should be counted as a 'C', they'll probably decide you deserve the upgrade.
This one is a bit confusing, so let me see if I can sort it out. Please let me know if you interpret something else in the comic. Megan says "On a scale of 1 to 10", but if you are using binary numbers that is "On a scale of 1 to 2" because 10 in binary equals 2.
When Cueball answers '4', not using binary, Megan has no idea what a four is because in fact she was using binary in her question.
In the image text, 11/100 would be 3/4 or 75% which is why you could ask for a 'C' grade.
Working
by Jeff
Image text: And if you drive a typical car more than a mile out of your way for each penny you save on the per-gallon price, it doesn't matter how worthless your time is to you--the gas to get you there and back costs more than you save.
Ok, let me see if I can iron this math out. In this comic, gas is 10 cents cheaper per gallon 5 minutes away. That's 1 dollar saved on a 10 gallon fill-up. (The car in the comic is small, so I'm going to assume a 10 gallon fill-up. Sorry to all our international friends, this is all in American measurements.)
$1 saved/earned for 5 minutes comes out to $12/hour which is more than the US Federal minimum wage of $7.25/hr.
$1 saved/earned for 9 minutes comes out to $6.66/hour which obviously comes below that threshold.
And then the image text adds on the double whammy of having to pay extra money in gas if you go more than a mile out of your way to get the cheaper gas.