explain xkcd - User contributions [en]

216: Romantic Drama Equation

2015-06-21T21:32:18Z

108.162.254.145: /* Explanation */

{{comic
| number = 216
| date = January 29, 2007
| title = Romantic Drama Equation
| image = romantic drama equation.png
| titletext = Real-life prospective-pairing curves over things like age can get depressing.
}}

==Explanation==
The equations in the comic and the graph show how many different love pairs can be made if you know the number of females and males in a group. The text explains that it was inspired by TV Romantic Drama (in this case, the gay drama {{w|Queer as Folk (U.S. TV series)|Queer as Folk}}), but of course the formula is valid for any group of people. There are two graphs and equations - gay option is the case when we are looking for pairs with same gender, straight option is for heterosexual equations. The interesting/funny part about the results is that in most cases there are more possibilities when we consider the homosexual option. Also it is interesting to observe what is kind of obvious - in the heterosexual case the "best" case is if both genders are present equally and the possibilities drop very fast if there is substantial difference between genders.

The graph makes a note that it only holds true for large casts. Case in point, with a cast of only four people: a two-to-two female-to-male ratio will have four straight pairings to two gay pairings, while a three-to-one female-to-male ratio will have three straight pairings and three gay pairings.

The title-text mentions that Randall made a chart of his own prospective dating pool as he gets older, and was depressed by the results. A dating pools show how many possible partners you can choose from. As you get older less of these will be single. But as he later shows in [[314: Dating Pools]] the age is not the problem... He is!

===Formulas===
The formulas may be derived as follows:

Each straight couple needs to include one of the x males and one of the (n-x) females so there are x(n-x) possible ways of combining one of each. E.g., if there are n=5 people, of whom x=2 are male, then there will be 3 possible pairings involving the first male, and three possible pairings involving the second yielding 2(5-2)=6 possible pairings.

Each gay couple needs to include either two males or two females. To choose two males, we can start with any of the x males and choose any of the (x-1) remaining males. However, that counts each possible pairing twice. E.g., Adam&Steve got counted when we chose Adam first and Steve second, and again when we chose Steve first and Adam second. To avoid double counting the possible couples, we therefore need to divide that total by 2. So there are x(x-1)/2 possible male-male pairings. Similar reasoning involving the (n-x) females tells us that there are (n-x)(n-x-1)/2 possible female-female pairings. Multiplying these out and combining the male and lesbian couples together, we get the total number of possible gay couples is [x^2 - x + n^2 - nx - n - xn + x^2 + x]/2. That simplifies to [n^2 - n + 2 x^2 - 2 xn]/2. The left two terms can be combined together as n(n-1) and the right two terms can be combined together as -2x(n-x) or 2x(x-n) [which is negative, because x-n<0]. Since the sum of these terms was divided by 2, we get that the total number of possible same-sex pairs is n(n-1)/2 - x(n-x) or n(n-1)/2 + x(x-n), which is what the cartoon says.

===Equations and links to wolfram-alpha===

* Formula for Gay pairing: [https://www.wolframalpha.com/input/?i=n*%28n-1%29%2F2%2Bx*%28x-n%29 n*(n-1)/2+x*(x-n)]

* Formula for Straight pairing: [https://www.wolframalpha.com/input/?i=x*%28n-x%29 x*(n-x)]

As a worked example, For Firefly, of the 9 principal cast, 5 are men, and 4 are women. If all were gay there would be 16 possible hook-ups, if all were straight there would be 20.

===Assumptions===

The chart and the calculations assume that:

#No one is bisexual, asexual, polyamorous, celibate or of some other sexuality.
#The ENTIRE cast, male AND female, will ALL be of the same sexuality (all homosexual OR all heterosexual).
#All genders are constant. (If sex-change operations are allowed, then the number of possible pairings is n(n-1)/2, because any two individuals can undergo surgery to become a possible pair.)
#Gender is the only criteria for determining if a hook-up is possible.

==Transcript==
:TV Romantic Drama Equation (Derived during a series of 'Queer as Folk' episodes)
:[A table shows equations for possible romantic pairings in a TV show. The equation under "gay" is n(n-1) 2+x(x-n); the equation under "straight" is x(n-x).]
:x: Number of male (or female) cast members.
:n: total number of cast members.

:[A graph plots pairings (for large casts) against cast makeup. Each of the above equations forms a curve. "Gay cast" starts high for an all male cast, dips down at 50 50 cast makeup, and then rises again for all female. "Straight cast" starts at zero for an all male cast, peaks at 50/50 cast makeup, and then drops to zero again for an all female cast. The two curves intersect at two points close to the middle.]

{{comic discussion}}
[[Category:Charts]]
[[Category:Math]]
[[Category:Romance]]

Talk:1454: Done

2014-12-01T15:02:18Z

108.162.254.145: I dont think its a romance thing, sounds like a scam to me.

How do we know the girl is in the United States?? [[Special:Contributions/141.101.104.177|141.101.104.177]] 08:54, 1 December 2014 (UTC)

Is it a girl? I was thinking the hair is a bit like mick Jaggers... - Palitu {{unsigned ip|108.162.249.223}}

: I think it's a girl, and I think she's in the United States, as xkcd is a US-based comic, and pony-tail is a recurring figure also presumably in the United States. And I think it's all rather sad. Note that she's kneeling on her chair, not sitting - this is more common for girls than guys. My take is that she's the kind of person who can enter into a fantasy relationship with a person she doesn't really know, and then if/when they do ever meet in real life it will all break down because her fantasy is only that, and the real person will not match her expectations at all. --[[User:RenniePet|RenniePet]] ([[User talk:RenniePet|talk]]) 09:37, 1 December 2014 (UTC)

:: I look at that she was incredibly lucky - it's a classic internet relationship scam. Maybe I'm just a cynic. There's also the phrase [http://www.macmillandictionary.com/dictionary/british/do-over "Done Over"], although I think it's a British idiom, so I highly doubt it was meant as a double entendre. [[User:Oobayly|Oobayly]] ([[User talk:Oobayly|talk]])

Consider this as a possible reference to Kim Kardashian's photo.. An effect of her trying to "break the internet" -KLee {{unsigned ip|173.245.54.212}}

'''Identity of the writer?'''
:If the writer is based on a reoccurring character than it has to be either Megan or Danish. Is there a consensus as to who it is?[[Special:Contributions/173.245.56.163|173.245.56.163]]

:: Isn't she Caroline, or 'curly buns'. Similar curly haired girl has appeared in similar roles on several pages but it seems her age isn't entirely set and instead fluctuates according to the call of a particular strip.

I don't think that anyone literally said "shut it down", I believe it was a rhetoric, at least that's how I read it. [[User:Official.xian|Official.xian]] ([[User talk:Official.xian|talk]]) 11:47, 1 December 2014 (UTC)

Oh yes. Forget that the economy would go to hell without Internet. Forget how much science is done using Internet. The real reason for Internet to exist is so you can get in love with someone on different continent. -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 12:44, 1 December 2014 (UTC)
:I'm not so sure... it would seem it was primarily funny cat videos, the funniest possible of which was obviously posted, viewed, and judged as the final necessary use of the internet. It was thus agreed to shut it down, as there is really no need to continue with this charade variously coined as "commerce", "science", or other superfluous forms of so-called "communication" (that is the garbled blathering that is not funny cat pictures or videos), all depending of course on your preferred (but nonetheless obviously deluded) persuasion. This comic only serves to prove it. I am left wondering, though... how did Ponytail come to learn this? SMS? Phone Tree? -- [[User:Brettpeirce|Brettpeirce]] ([[User talk:Brettpeirce|talk]]) 13:55, 1 December 2014 (UTC)
::Is there perhaps a meme going around where instead of "lol" you write "internetover" to say "this is so good/funny, i can now die happy" and the comic author was annoyed with that and made this where the start situation is silly and the end is even sillier? --[[Special:Contributions/108.162.254.163|108.162.254.163]] 14:10, 1 December 2014 (UTC)

This could be far more than a romantic involvement. She says she thought she was asking too much. But then she found... a like-minded individual, someone who can... notice the 'glitches in the matrix', as it were. Much more might have been lost here than a believed love. [[Special:Contributions/173.245.54.169|173.245.54.169]] 14:13, 1 December 2014 (UTC)

It could mean the girl is in love or wants to adopt a child from a country like Iran, but before she can tell, the internet THERE is shut down by the government
(which happens all the time because of some youtube video or something). [[Special:Contributions/108.162.237.114|108.162.237.114]] 14:18, 1 December 2014 (UTC)

: Or the writer may be in a country like Russia, China, or Turkey, where the internet is widely used but under constant threat of political censorship.[[Special:Contributions/108.162.216.129|108.162.216.129]] 14:54, 1 December 2014 (UTC)

So I am the only one who thought the girl was either the author of spam, or had a feasible contact whom she could fool into travelling to her country with promises of money, only to put them in the trap of being stuck there reliant on her? You hear the story all the time, someone is given hope, but as they arrive the passport is taken and to receive food+lodging (or in some cases they are locked inside a room) they are forced to perform dubious services with questionable morality and legality. [[Special:Contributions/108.162.254.145|108.162.254.145]] 15:02, 1 December 2014 (UTC)Feha {{unsigned ip|127.0.0.1|12:34, 5 June 2012 (UTC)}}