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Posted: **Mon Jan 29, 2007 6:18 pm UTC**

by **warriorness**

The whole x(n-x) thing is all well and good, but that theoretically allows for polygamy. What formula would we need to express all possible arrangements (assuming each cast member is monogamous)?

It was only last year that we studied combinatorics, and yet I've forgotten everything about it, except for something about polynomial expansion and Pascal's Triangle :\

Posted: **Mon Jan 29, 2007 6:55 pm UTC**

by **TheTankengine**

thefiddler wrote:As for the comic:

I can't contribute anything! It made me smile? But I hate graphs.

Burn the witch!!!

Posted: **Mon Jan 29, 2007 6:58 pm UTC**

by **thefiddler**

TheTankengine wrote:thefiddler wrote:As for the comic:

I can't contribute anything! It made me smile? But I hate graphs.

Burn the witch!!!

I definitely weigh more than a duck, kthnx.

Shouldn't it be "burn the heretic!"??? Or maybe "burn the blasphemer!"???

Posted: **Mon Jan 29, 2007 7:46 pm UTC**

by **Peshmerga**

beard0 wrote:Peshmerga wrote:I much rathered life when being gay was unacceptable.

I'm amazed that comics of this intelligent a calibre would appeal to someone stupid enough to be a homophobe.

You took my quote out of context. That's a logical fallacy! And as I said, if you would have taken the time to interpret what I had written instead of reacting instinctively to the red alarms ringing in your head, you would have noticed I didn't say anything about any homophobic ideals; only referring to a time (post Byzantine Empire, pre 60s) when being a homosexual was generally an avoided topic of conversation.

Infact I myself am a little gay. Borderline, even. Actually, what are you doing later tonight?

### 3-member corollary

Posted: **Mon Jan 29, 2007 9:00 pm UTC**

by **Shishberg**

A corollary to this is that any cast of at least 3 has at least 1 gay pairing. However a unisex cast of any size has zero straight pairings.

Posted: **Mon Jan 29, 2007 9:24 pm UTC**

by **Belial**

As for Pesh being homophobic, I read it as "less to think about when a guy comes up and says hi" rather than "I hate faggots".

Indeed. How dare they complicate your life with their desire to have their sexuality openly accepted. Those extra neurons you had to exercise in your social subroutines were totally not worth social equality.

(this is not a criticism to pesh, as he's not evincing this philosophy, but rather another, inscrutable one.)

Apologies if I misread you Pesh Razz I think homosexuallity is morally wrong, so if you did mean you hate faggots that's cool too.

.....

Sigh. Filthy, worthless primates.

To repeat an earlier poster:

I'm amazed that comics of this intelligent a calibre would appeal to someone stupid enough to be a homophobe.

Posted: **Mon Jan 29, 2007 9:28 pm UTC**

by **athelas**

Ah, yes, those who disagree with me are stupid and/or evil. You'll win a lot of converts that way, my good sir.

Posted: **Mon Jan 29, 2007 9:28 pm UTC**

by **athelas**

warriorness wrote:The whole x(n-x) thing is all well and good, but that theoretically allows for polygamy. What formula would we need to express all possible arrangements (assuming each cast member is monogamous)?

Well, remember that this is a

TV show. Monogamy is much less conducive to dramatic fireworks.

Posted: **Mon Jan 29, 2007 9:54 pm UTC**

by **warriorness**

athelas wrote:warriorness wrote:The whole x(n-x) thing is all well and good, but that theoretically allows for polygamy. What formula would we need to express all possible arrangements (assuming each cast member is monogamous)?

Well, remember that this is a

TV show. Monogamy is much less conducive to dramatic fireworks.

By saying that the x(n-x) formula works for my situation as well, you imply that everybody must not only be polygamous, but also have a relationship with

every other cast member.

Posted: **Mon Jan 29, 2007 9:58 pm UTC**

by **Belial**

Ah, yes, those who disagree with me are stupid and/or evil. You'll win a lot of converts that way, my good sir.

Wasn't really trying for converts. There's no converting people who hold truly stupid opinions. Some epiphany on their own, otherwise, you just have to marginalize them as much as possible.

I was mostly expressing extreme frustration at their existence. That okay by you?

Posted: **Mon Jan 29, 2007 11:20 pm UTC**

by **Mike Graham**

MrBawn wrote:This comic leaves out bisexuals, which always ticks me off. But since we have number of males as a variable and total cast size as a constant, the graph wouldn't be very interesting (just a horizontal line).

Ah, good ol' biphobia.

The thing about that is, I can't think of a meaningfully bisexual character in a TV show.

Caveat: I am pretty out-of-touch with the mainstream American media.

Posted: **Tue Jan 30, 2007 12:15 am UTC**

by **william**

Mike Graham wrote:MrBawn wrote:This comic leaves out bisexuals, which always ticks me off. But since we have number of males as a variable and total cast size as a constant, the graph wouldn't be very interesting (just a horizontal line).

Ah, good ol' biphobia.

The thing about that is, I can't think of a meaningfully bisexual character in a TV show.

Caveat: I am pretty out-of-touch with the mainstream American media.

I can think of exactly one--Captain Jack Harkness.

"For you, saying hi

is flirting!"

Posted: **Tue Jan 30, 2007 12:15 am UTC**

by **Air Gear**

athelas wrote:Ah, yes, those who disagree with me are stupid and/or evil. You'll win a lot of converts that way, my good sir.

Funny how you're using this sort of argument to defend somebody whose argument is basically "ANYONE WHO IS NOT OF MY SEXUALITY IS IMMORAL" with the corollary of "BIOLOGICAL ORIGINS BE DAMNED".

Posted: **Tue Jan 30, 2007 12:39 am UTC**

by **aldimond**

Wait a sec... was there anyone that actually was being homophobic in this here thread?

The people that have been quoted are Pesh and VSM. I can't figure out what exactly Pesh was getting at... it sounds like he just said communicated badly, then called people out for a logical fallacty... which means we should just

cut his arm off and be done with it.

OTOH we all know VSM is ten steps from your door, ready to ring the bell and read you his favorite passages from Leviticus and try to bring you into the fold, but that's just who VSM is and we've come to live with his troglodytic ways.

Posted: **Tue Jan 30, 2007 1:22 am UTC**

by **Peshmerga**

Damn Munro and his foresight!

He saw this coming and drew a comic solely for it!

Posted: **Tue Jan 30, 2007 1:52 am UTC**

by **ohki**

warriorness wrote:The whole x(n-x) thing is all well and good, but that theoretically allows for polygamy. What formula would we need to express all possible arrangements (assuming each cast member is monogamous)?

It was only last year that we studied combinatorics, and yet I've forgotten everything about it, except for something about polynomial expansion and Pascal's Triangle :\

Um, the number of straight relationships (spontaneously monogamous) is limited by min(x,n-x). So, the number of pairings is whichever;s least, the number of men, or the number of women.

I think for gay pairings it would be something like x/2 + (n-x)/2, so number of women/2 + number of men/2. 'course with these you can get 1/2 people and they will be very sad and lonely.

These assume you just pair up people and they have no choice with who and then stick with them as t -> infinity.

Also, it seems a bunch of you are reading the comic totally wrong.. the formula give

Possible Romantic Pairings. So there's really no monogamy/polygamy involved. Its like saying 1 guy, 2 girls, allowing only straight relationships: there are 2 POSSIBLE pairings. I don't know where the implication that all the pairings were played out came from...

Posted: **Tue Jan 30, 2007 3:05 am UTC**

by **tylerni7**

Gah I'm always late to the comics because I never think about what days they are posted... anywho in response to

whoa whoa whoa, all you new people, whos names I'm not even reading, please introduce yourselves in the introduction thread. Else you might get deleted because we think you're a bot. We're pretty paranoid about that around here.

Don't you mean velociraptors?

Posted: **Tue Jan 30, 2007 4:02 am UTC**

by **iw**

beard0 wrote:Peshmerga wrote:I much rathered life when being gay was unacceptable.

I'm amazed that comics of this intelligent a calibre would appeal to someone stupid enough to be a homophobe.

Intelligence usually has very little to do with one's beliefs or prejudices.

Posted: **Tue Jan 30, 2007 6:11 am UTC**

by **warriorness**

ohki wrote:Also, it seems a bunch of you are reading the comic totally wrong.. the formula give Possible Romantic Pairings. So there's really no monogamy/polygamy involved. Its like saying 1 guy, 2 girls, allowing only straight relationships: there are 2 POSSIBLE pairings. I don't know where the implication that all the pairings were played out came from...

I read it right, I was just suggesting a new problem. (Perhaps this should go on the Logic Puzzles forum)

Posted: **Tue Jan 30, 2007 6:31 am UTC**

by **digitrev**

On topic: what is the optimal relationship between x and n to result in the maximal number of both straight and gay relationships? If we account for a third variable of bisexual males, how does that complicate things? Accounting for both bisexual males and bisexual females?

Off topic: as interesting as conversations on homosexuality are (they rarely are), can we please keep this to the proper forums. That is to say, not in the Individual Comic Thread forum. Just a personal request.

Posted: **Wed Jan 31, 2007 11:46 pm UTC**

by **Fleshpiston**

ohki wrote:I get the sneaking feeling that as n -> infinity, that percentage approaches 50% But I'm not sure

why I think this

Afterthought: Here's TonyD's code in a more forum friendly format:

good work (and fast!) by TonyD to answer my problem. Good work by ohki making it forum friendly. As for ohki's "sneaking feeling", you may be on the right track, but you are not quite right.

The answer is that as n approaches infinity, the probability of more straight than gay pairings approaches 0.6826, or more specifically:

1/(2*pi)^.5 * the integral from -1 to 1 of e to the (-x^2)/2 dx

I will let you consider why that is the right answer.

Posted: **Thu Feb 01, 2007 2:17 am UTC**

by **narfanator**

Is that (-x)^2 or -(x^2)? Likely the latter, but I want to make sure.

Posted: **Thu Feb 01, 2007 11:10 pm UTC**

by **Fleshpiston**

narfanator wrote:Is that (-x)^2 or -(x^2)? Likely the latter, but I want to make sure.

It is indeed the latter. I did not do a complicated limit to get this answer (68%), rather you should utilize some properties of the binomial distribution.

### The equation in the Romantic cartoon is incorrect

Posted: **Wed Feb 07, 2007 4:06 pm UTC**

by **david7**

Although parts of the equation are right, it is actually wrong because he leaves out certain variables which are significant.

The total number of possible unique pairing events constrained by sexual preference,

where the following assumptions are made:

g = number of gay males

m = number of straight males

f = number of straight females

l = number of lesbian females.

1) An individual A and an individual B pair at most one time,

2) Gay males do not pair with straight males or females

3) Lesbian females do not pair with straight females or males.

So the pairing function for g, m , f and l is:

P( g, m, f, l ) = C(g , 2) + m * f + C(l , 2)

Let g= 4 , m = 3, f = 3, l = 4,

P( g, m, f, l ) = C(g , 2) + m * f + C(l , 2)

= g(g -1) / 2 + m * f + l(l -1) / 2

= 4(3)/2 + 3 * 3 + 4(3)/2 =

= 6 + 9 + 6 = 21

So for g= 4 , m = 3, f = 3, l = 4 there are a total of 21 possible pairings.

In the xkcd Calculation:

If we take the chosen values above, the cartoonist's variables are the following:

n = g + m + f + l = 14 (all the cast members)

x = g + m = 7 (all the males)

so plugging into his formula:

n(n-1)/2 + x (x-n) = 14 (13) / 2 + 7 ( 7 - 14)

= 91 - 49 = 42

Which shows that his equation is totally over counting.

His equation should have given the value 21, which is clearly the

right answer even by inspection, when g= 4 , m = 3, f = 3, l = 4 .

Think about it, 4 people in a room will result in 6 hand shakes, so that gives you the result for the gay guys and the lesbians, and 3 straight males and 3 straight females will have at most 9 pairings.

that's 6 + 9 + 6 = 21. Which agrees with my equation but not his.

His equation fails because he left out a few variables that were essential to the problem.

Posted: **Wed Feb 07, 2007 9:00 pm UTC**

by **william**

Fleshpiston wrote:ohki wrote:I get the sneaking feeling that as n -> infinity, that percentage approaches 50% But I'm not sure

why I think this

Afterthought: Here's TonyD's code in a more forum friendly format:

good work (and fast!) by TonyD to answer my problem. Good work by ohki making it forum friendly. As for ohki's "sneaking feeling", you may be on the right track, but you are not quite right.

The answer is that as n approaches infinity, the probability of more straight than gay pairings approaches 0.6826, or more specifically:

1/(2*pi)^.5 * the integral from -1 to 1 of e to the (-x^2)/2 dx

I will let you consider why that is the right answer.

The binomial distribution approaches a normal distribution by the central limit theorem, and it's always approximately one standard deviation away.

Posted: **Sun Jun 10, 2007 4:31 am UTC**

by **Vortigen**

You know, although I do hate to bring up old topics...

Have we considered the variable of blood relations in the cast? Father/child, brother/sister, etc.

Posted: **Sun Jun 10, 2007 9:38 am UTC**

by **Belial**

I think you'd have to handle it by how you feel about that blood relation, because being blood related doesn't really dictate the type and quality of relationship you have with the person.

Posted: **Sun Jun 10, 2007 4:08 pm UTC**

by **Vortigen**

Maybe in real life, but I haven't seen too much incest in romantic TV dramas recently.

Posted: **Sun Jun 10, 2007 4:40 pm UTC**

by **Belial**

Maybe in real life, but I haven't seen too much incest in romantic TV dramas recently.

Not what I meant. I'm saying, just because they're your family doesn't mean you get along with them. So it's more useful to ask "Are they also your friend?" or "Do you totally hate this person?"

Posted: **Sun Jun 10, 2007 5:37 pm UTC**

by **Vortigen**

Belial wrote:Not what I meant. I'm saying, just because they're your family doesn't mean you get along with them. So it's more useful to ask "Are they also your friend?" or "Do you totally hate this person?"

Maybe you misunderstood, or maybe I'm misunderstanding you, but what I'm saying is this formula allows for incest.

Posted: **Sun Jun 10, 2007 5:40 pm UTC**

by **LE4dGOLEM**

Vortigen wrote:Belial wrote:Not what I meant. I'm saying, just because they're your family doesn't mean you get along with them. So it's more useful to ask "Are they also your friend?" or "Do you totally hate this person?"

Maybe you misunderstood, or maybe I'm misunderstanding you, but what I'm saying is this formula allows for incest.

Liking automatically equals sex?

Posted: **Sun Jun 10, 2007 5:49 pm UTC**

by **Vortigen**

Crap. I just checked the dictionary definition.

...well, I have some explaining to do to my friends.

My bad. I need to learn words.

Not

incest, but the formula allows for romantic relations by people who are related by blood.

We need a word for that.

### Re: "Romantic Drama Equation" discussion

Posted: **Thu Nov 29, 2007 12:58 am UTC**

by **immute**

Someone needs to redraw the comic adding a function for bisexuals. I have a feeling it would be a straight line connecting the two endpoints of the gay function

### Re: "Romantic Drama Equation" discussion

Posted: **Thu Nov 29, 2007 2:21 am UTC**

by **imatrendytotebag**

Meh, a line for "bisexuals" doesn't really make sense, since what he is graphing is possible number of gay couples and possible number of straight couples. And there is no such thing as a "bisexual" couple.. each couple is by definition either gay or straight.

In fact the whole scenario basically assumes everyone is bisexual, since every pairing is considered "possible", meaning any two people can feasibly get together regardless of gender.

### Re: "Romantic Drama Equation" discussion

Posted: **Thu Nov 29, 2007 3:43 am UTC**

by **GodShapedBullet**

imatrendytotebag wrote:Meh, a line for "bisexuals" doesn't really make sense, since what he is graphing is possible number of gay couples and possible number of straight couples. And there is no such thing as a "bisexual" couple.. each couple is by definition either gay or straight.

In fact the whole scenario basically assumes everyone is bisexual, since every pairing is considered "possible", meaning any two people can feasibly get together regardless of gender.

He's graphing number of pairings assuming an entirely gay or entirely straight cast. The lines only represent the number of straight or gay couples because that's the only kind of couple that can exist in either situation.

A line for bisexuals makes sense. It probably wasn't included because bisexuals are barely represented in romantic dramas on TV and certainly don't have a show all to themselves.

I don't know if the scenario assumes every pairing is possible. If it did, why would the curves for gay and straight casts change with gender distribution?

### Re: 0216: "Romantic Drama Equation"

Posted: **Sun Oct 28, 2012 7:07 am UTC**

by **edm3**

I think the equation for gay should be: pairings = choose(x, 2) + choose(n-x, 2).

### Re: 0216: "Romantic Drama Equation"

Posted: **Sun Oct 28, 2012 5:45 pm UTC**

by **J Thomas**

edm3 wrote:I think the equation for gay should be: pairings = choose(x, 2) + choose(n-x, 2).

To do that right, wouldn't you need for each gay a division of all the others into

(Cute:

troll:

troll I'd do anyway sometimes)

and then figure it on that basis?

### Re: 3-member corollary

Posted: **Sun Oct 28, 2012 7:40 pm UTC**

by **addams**

Umm. Funny graph.

The math? What are you looking for?

What number insures a positve real number inside the overlap?

In your head. (?) Or; On paper? On T.V.? That is a seperate and inclusive sexual type.

A theroy of the Ed Dept. Make it about sex or make it funny. This is both.

### Re: 0216: "Romantic Drama Equation"

Posted: **Tue Oct 30, 2012 9:28 am UTC**

by **snowyowl**

A theroy of the Ed Dept. Make it about sex or make it funny. This is both.

It's about romance, not sex. You can have one without the other, or indeed the other without the one. And xkcd is about "romance, sarcasm, math and language" - this comic hits "romance" and "math".

What number insures a positve real number inside the overlap?

For any n, there is an overlap. Specifically, when x = n/2 (or x=(n-1)/2 if n is odd), there are more straight pairings than gay pairings.

Quick calculation: When n = 2x, there are x men and x women, so there are x

^{2} straight pairings.

The number of gay man pairings is x choose 2, which is x(x-1)/2. The number of lesbian pairings is the same, so the total number of gay pairings is x(x-1), which is slightly less than x

^{2}.

When n = 2x+1, there are x men and x+1 women, which gives x(x+1) straight pairings and x(x-1)/2 + (x+1)x/2 gay pairings, which simplifies to x

^{2} gay pairings.

Therefore, there is always an overlap.

Corollary: You can't spell "theory". Proof: Left as exercise.

### Re: 0216: "Romantic Drama Equation"

Posted: **Sat Nov 03, 2012 4:34 am UTC**

by **addams**

I thought spell check was a gift to me. Now, I don't have spell check. I know I can't spell. I was required to have a dictionary on me at all times.

You smart thing, you; You understood a misspelled word.

Romance? Those Jersey Shore reality TV programs are about Romance?

Jeeze. I thought that stuff was porn for the masses.