0216: "Romantic Drama Equation"

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Postby warriorness » Mon Jan 29, 2007 6:18 pm UTC

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 :\

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Postby TheTankengine » Mon Jan 29, 2007 6:55 pm UTC

thefiddler wrote:As for the comic:
I can't contribute anything! It made me smile? But I hate graphs. :(


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Postby thefiddler » Mon Jan 29, 2007 6:58 pm UTC

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!"???

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Postby Peshmerga » Mon Jan 29, 2007 7:46 pm UTC

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?
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3-member corollary

Postby Shishberg » Mon Jan 29, 2007 9:00 pm UTC

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.

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Postby Belial » Mon Jan 29, 2007 9:24 pm UTC

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.
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Postby athelas » Mon Jan 29, 2007 9:28 pm UTC

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

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Postby athelas » Mon Jan 29, 2007 9:28 pm UTC

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.

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Postby warriorness » Mon Jan 29, 2007 9:54 pm UTC

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.

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Postby Belial » Mon Jan 29, 2007 9:58 pm UTC

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?
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Postby Mike Graham » Mon Jan 29, 2007 11:20 pm UTC

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.

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Postby william » Tue Jan 30, 2007 12:15 am UTC

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.

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Postby Air Gear » Tue Jan 30, 2007 12:15 am UTC

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".

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Postby aldimond » Tue Jan 30, 2007 12:39 am UTC

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.
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Postby Peshmerga » Tue Jan 30, 2007 1:22 am UTC

Damn Munro and his foresight!

He saw this coming and drew a comic solely for it!
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Postby ohki » Tue Jan 30, 2007 1:52 am UTC

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...
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Postby tylerni7 » Tue Jan 30, 2007 3:05 am UTC

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.


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Postby iw » Tue Jan 30, 2007 4:02 am UTC

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.

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Postby warriorness » Tue Jan 30, 2007 6:11 am UTC

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)

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Postby digitrev » Tue Jan 30, 2007 6:31 am UTC

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.
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Postby Fleshpiston » Wed Jan 31, 2007 11:46 pm UTC

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:
Image


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.

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Postby narfanator » Thu Feb 01, 2007 2:17 am UTC

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

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Postby Fleshpiston » Thu Feb 01, 2007 11:10 pm UTC

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.

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The equation in the Romantic cartoon is incorrect

Postby david7 » Wed Feb 07, 2007 4:06 pm UTC

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.

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Postby william » Wed Feb 07, 2007 9:00 pm UTC

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:
Image


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.
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Postby Vortigen » Sun Jun 10, 2007 4:31 am UTC

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.

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Postby Belial » Sun Jun 10, 2007 9:38 am UTC

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.
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Postby Vortigen » Sun Jun 10, 2007 4:08 pm UTC

Maybe in real life, but I haven't seen too much incest in romantic TV dramas recently.
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Postby Belial » Sun Jun 10, 2007 4:40 pm UTC

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?"
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Postby Vortigen » Sun Jun 10, 2007 5:37 pm UTC

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.
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Postby LE4dGOLEM » Sun Jun 10, 2007 5:40 pm UTC

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.


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Postby Vortigen » Sun Jun 10, 2007 5:49 pm UTC

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.
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Re: "Romantic Drama Equation" discussion

Postby immute » Thu Nov 29, 2007 12:58 am UTC

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

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Re: "Romantic Drama Equation" discussion

Postby imatrendytotebag » Thu Nov 29, 2007 2:21 am UTC

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.
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Re: "Romantic Drama Equation" discussion

Postby GodShapedBullet » Thu Nov 29, 2007 3:43 am UTC

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?

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Re: 0216: "Romantic Drama Equation"

Postby edm3 » Sun Oct 28, 2012 7:07 am UTC

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

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Re: 0216: "Romantic Drama Equation"

Postby J Thomas » Sun Oct 28, 2012 5:45 pm UTC

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

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and then figure it on that basis?
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Re: 3-member corollary

Postby addams » Sun Oct 28, 2012 7:40 pm UTC

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.
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Re: 0216: "Romantic Drama Equation"

Postby snowyowl » Tue Oct 30, 2012 9:28 am UTC

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 x2 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 x2.

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 x2 gay pairings.

Therefore, there is always an overlap.

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Re: 0216: "Romantic Drama Equation"

Postby addams » Sat Nov 03, 2012 4:34 am UTC

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.
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