0563: "Fermirotica"
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0563: "Fermirotica"
http://www.xkcd.com/563
AltText: I love how Google handles dimensional analysis. Stats are ballpark and vary wildly by time of day and whether your mom is in town.
I really enjoyed this one...math ftw.

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"Fermirotica" Discussion
Link: http://xkcd.com/563/
Alt:I love how Google handles dimensional analysis. Stats are ballpark and vary wildly by time of day and whether your mom is in town.
Re: "Fermirotica" Discussion
Hey now, my Mom IS in town!
I guess the only question is if your mom is holding up her end of the bargain...
I guess the only question is if your mom is holding up her end of the bargain...
Re: "Fermirotica" Discussion
wow i pulled up xkcd to kill time before bed while my neighbors are having sex
probability: 1 !!
edit: but what's the likelihood of reading an xkcd about probabilities of people having sex near you while you're listening to people having sex near you..
probability: 1 !!
edit: but what's the likelihood of reading an xkcd about probabilities of people having sex near you while you're listening to people having sex near you..
Last edited by tr0nk on Wed Apr 01, 2009 4:07 am UTC, edited 1 time in total.
Re: "Fermirotica" Discussion
Also, if your mom is in town, disregard gravity.
Re: "Fermirotica" Discussion
I don't quite get the title (hover) text; anyone care to explain?

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Re: "Fermirotica" Discussion
Close, but there needs to be a Dirac delta function, whose input is 0 if you are in a fraternity and 1 otherwise, in the expression.
 madhollywood
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Re: "Fermirotica" Discussion
Is X_{f} intended in the denominator instead of X_{r}? Also, I wouldn't necessarily thing that the duration of sex decreases the radius in which it was occuring. This would be distinctly untrue for something like rabbits. Still, I love the statistical eroticism.
Re: "Fermirotica" Discussion
that X_r term should be X_f?
also, forgetting the minutes/years conversion...interesting results
edit: madhollywood beat me to it, and with subscripts no less!
also, forgetting the minutes/years conversion...interesting results
edit: madhollywood beat me to it, and with subscripts no less!
Last edited by ck0 on Wed Apr 01, 2009 4:22 am UTC, edited 1 time in total.
 aion7
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Re: "Fermirotica" Discussion
aeris92 wrote:Also, if your mom is in town, disregard gravity.
Actually gravity still works, but since a supermassive object is in the near vicinity...
Spoiler:
Re: "Fermirotica" Discussion
The formula needs to be adjusted for units though, if you're going to give frequency in terms of 1/years and duration in minutes. A more accurate representation would be:
r = sqrt( 2*525948 / (pi * P_d * X_f * X_d) )
My result, using Randall's X_f and X_d is 440 m. Interesting...
r = sqrt( 2*525948 / (pi * P_d * X_f * X_d) )
My result, using Randall's X_f and X_d is 440 m. Interesting...
Re: "Fermirotica" Discussion
Make that 140 meters:
http://tinyurl.com/googleunits
(The title text refers to the fact that Google understands the units and does the adjustment for you. It also converts the miles to SI standard meters.)
http://tinyurl.com/googleunits
(The title text refers to the fact that Google understands the units and does the adjustment for you. It also converts the miles to SI standard meters.)
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Re: "Fermirotica" Discussion
Zenexer wrote:I don't quite get the title (hover) text; anyone care to explain?
In addition to the above post, more people are gettin' it on at night and everyone does your mom.
Also, great comic, and I hope that X_{f} vs X_{r} goof is fixed.
Re: "Fermirotica" Discussion
hthall wrote:(The title text refers to the fact that Google understands the units and does the adjustment for you. It also converts the miles to SI standard meters.)
Nice, I didn't realize google calc could do that.

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Re: "Fermirotica" Discussion
Anybody know where the 2 in the numerator comes from? I assume it has to do with sex involving two people? Other than that, seems like a pretty straightforward derivation... circle area and population density tell you how many people are within "r" of you, and the frequency tells you what the probability is that any given one of them is having sex.
Dimensional analysis FTW
Dimensional analysis FTW

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Re: "Fermirotica" Discussion
This formula looks to me like it only works on a 2D plane. I'm on the 19th story of an apartment building, which surely alters the data.
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 fenrir_darkwolf
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Re: "Fermirotica" Discussion
Dammit Randall, get out of my head! I was just admiring the dimensional analysis of google calculator a couple of days ago . why will it not add/subtract when dimensions don't match up! I'm too lazy to put all the units in!!
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Re: "Fermirotica" Discussion
coreyjkelly wrote:Anybody know where the 2 in the numerator comes from? I assume it has to do with sex involving two people? Other than that, seems like a pretty straightforward derivation... circle area and population density tell you how many people are within "r" of you, and the frequency tells you what the probability is that any given one of them is having sex.
Dimensional analysis FTW
yeah, with such a small number on top, and a large number on the bottom, wouldnt r always come out to be a very small number? itd be weird having people having sex within 6 inches of you...
Re: "Fermirotica" Discussion
If I recall correctly, Google handles unicorn horns and light years in a tablespoon, too.

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Re: "Fermirotica" Discussion
I was wondering where the two came from, but then I remembered what sex was.
What's the probability of a settled event?
No. The formula is exactly the same. The units are contained in the quantities: 18600 per square mile is .00718 per square meter. Eighty occurrences per year is 2.54 microhertz. It's this kind of thinking that makes people think the factor of two in kinetic energy is unitdependent.
tr0nk wrote:edit: but what's the likelihood of reading an xkcd about probabilities of people having sex near you while you're listening to people having sex near you..
What's the probability of a settled event?
ladron wrote:The formula needs to be adjusted for units though, if you're going to give frequency in terms of 1/years and duration in minutes. A more accurate representation would be:
r = sqrt( 2*525948 / (pi * P_d * X_f * X_d) )
No. The formula is exactly the same. The units are contained in the quantities: 18600 per square mile is .00718 per square meter. Eighty occurrences per year is 2.54 microhertz. It's this kind of thinking that makes people think the factor of two in kinetic energy is unitdependent.
Re: "Fermirotica" Discussion
I did the calculations for the world's densest city (Dhaka, Bangladesh) which has the population density of 43,752 Pplz KM^2 or 70003.2 Pplz Mi^2 and I got 71.8449256 meters WooHOOO!
Re: "Fermirotica" Discussion
Zenexer wrote:I don't quite get the title (hover) text; anyone care to explain?
The title is a reference to Enrico Fermi. He was quite well known for his ability to estimate just about anything. The most famous example is his estimation of the number of piano tuners in Chicago based only on approximations of population, piano ownership, average time between tunings, etc.

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Re: "Fermirotica" Discussion
Chuff wrote:This formula looks to me like it only works on a 2D plane. I'm on the 19th story of an apartment building, which surely alters the data.
The 3D equivalent would be simple to derive using the volume of a sphere and a cubed root instead.. but you'd have to somehow get a 3D population density.. haha.. I guess you could approximate the local population density by dividing the number of people in your building by its dimensions... interesting..
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Re: "Fermirotica" Discussion
madhollywood wrote:Also, I wouldn't necessarily thing that the duration of sex decreases the radius in which it was occuring.
Well, X_{f}X_{d} is the probability that a given person is having sex at a random point in time (using the values in the comic, 30 minutes and 80/year, you'd spend about half a percent of your life having sex... so by the frequentist definition of probability, if we picked a time at random, there'd be a 0.5% chance you'd be having sex then). So P_{d}X_{f}X_{d} is the expected local density of people having sex. Call this D, for brevity. Then you'd expect one couple (two people) per 2/D area... and since we're talking circles, our area is is pi*r^{2}. Solve for r, and you get the formula in the comic.
Last edited by phlip on Wed Apr 01, 2009 4:50 am UTC, edited 1 time in total.
Code: Select all
enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵╰(ಠ_ಠ ⚠) {exit((int)⚠);}
Re: "Fermirotica" Discussion
Chuff wrote:This formula looks to me like it only works on a 2D plane. I'm on the 19th story of an apartment building, which surely alters the data.
The extra distance you experience because of the vertical axis is more than made up for by the fact that you have a high local density (much higher no doubt then your city's average) as you could have neighbors around 10 feet above or below you as well as to the sides. No doubt you'd want to adjust the figure up instead. But this is only estimation. If you are really concerned about being entirely accurate you should install cameras in everywhere in a several mile radius and you would then be able to accurately answer the question without even using the formula. Don't forget to consider your mile high club members.
GoldFish
Re: "Fermirotica" Discussion
Chuff wrote:This formula looks to me like it only works on a 2D plane. I'm on the 19th story of an apartment building, which surely alters the data.
I think you could just include the people above and below you, and even the people in other buildings within the square mile. Like, you have the square mile as the boundary, but the z axis is still inside that boundary (well, only for a little bit. I dont think you can count the other side of the planet and aliens on the other side of the universe.)
Wouldnt two people be required to have sex?
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Re: "Fermirotica" Discussion
Delass wrote:Wouldnt two people be required to have sex?
That's the generally agreed minimum, yes.
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Re: "Fermirotica" Discussion
I'm curious where the numbers in the comic came from. And does the average frequency of 80/year include multiple rounds per night, or 80 unique days?

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Re: "Fermirotica" Discussion
The lack of April Foolsness is depressing.
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Re: "Fermirotica" Discussion
QuantumNightmare wrote:I'm curious where the numbers in the comic came from. And does the average frequency of 80/year include multiple rounds per night, or 80 unique days?
Multiple rounds per night could be included in either of the "80/year" or "30 minutes" values, but not both. IE either 80 unique days, for 30 minutes total per day; or 80 instances (including multiple instances per day), 30 minutes per instance. The maths works either way.
Last edited by phlip on Wed Apr 01, 2009 4:56 am UTC, edited 1 time in total.
Code: Select all
enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵╰(ಠ_ಠ ⚠) {exit((int)⚠);}
Re: "Fermirotica" Discussion
reminds me of the onion's Report: Someone Totally Doing It Somewhere Right Now
Re: "Fermirotica" Discussion
The phrase "on average" bugs me.
It seems like we should be setting up some kind of confidence interval (use 95% for the heck of it) and then maybe use a Poisson distribution. This way, you could say with 95% certainty that somebody is having sex within r meters of you.
It seems like we should be setting up some kind of confidence interval (use 95% for the heck of it) and then maybe use a Poisson distribution. This way, you could say with 95% certainty that somebody is having sex within r meters of you.
 josiahstevenson
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Re: "Fermirotica" Discussion
flashstorm wrote:The lack of April Foolsness is depressing.
You've not seen the bit about changing the xkcd domain name, then?
Re: "Fermirotica" Discussion
For a split second I thought he was going to go a different direction and calculate "The average number of people having sex with you at this moment."
I think it is worth noting that there is very little value in estimating that.
GoldFish
I think it is worth noting that there is very little value in estimating that.
GoldFish
Re: "Fermirotica" Discussion
EDIT: Nevermind....... I found it.
Last edited by afarnen on Wed Apr 01, 2009 5:09 am UTC, edited 1 time in total.

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Re: "Fermirotica" Discussion
Denyvem wrote:I did the calculations for the world's densest city (Dhaka, Bangladesh) which has the population density of 43,752 Pplz KM^2 or 70003.2 Pplz Mi^2 and I got 71.8449256 meters WooHOOO!
hum... I did the same calculation before coming here,
square root( 2 / ( pi * 43,752 * 80 * 30 ) ) = 7.7863780385990247411070697617746e5 kilometers
thats approximately .000077863 km... or 3 inches.
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Re: "Fermirotica" Discussion
Quantumplation wrote:Denyvem wrote:I did the calculations for the world's densest city (Dhaka, Bangladesh) which has the population density of 43,752 Pplz KM^2 or 70003.2 Pplz Mi^2 and I got 71.8449256 meters WooHOOO!
hum... I did the same calculation before coming here,
square root( 2 / ( pi * 43,752 * 80 * 30 ) ) = 7.7863780385990247411070697617746e5 kilometers
thats approximately .000077863 km... or 3 inches.
You have 80 bouts per year and thirty years per bout (yikes!) or 80 rounds a minute, at thirty minutes apiece.
 phlip
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Re: "Fermirotica" Discussion
Quantumplation wrote:square root( 2 / ( pi * 43,752 * 80 * 30 ) ) = 7.7863780385990247411070697617746e5 kilometers
7.78x10^{5} km (years/minutes)^{1/2}
Get your units right.
[edit] Also:
Denyvem wrote:43,752 Pplz KM^2 or 70003.2 Pplz Mi^2
43752/km^{2} is 113317/mi^{2}. It's area, not distance  you have to multiply by 1.609^{2}.
Both of these could be avoided if you followed the advice in the title text, and just used Google calculator and its automatic unit conversion features.
Last edited by phlip on Fri Aug 02, 2013 2:30 am UTC, edited 2 times in total.
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enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵╰(ಠ_ಠ ⚠) {exit((int)⚠);}
 BrainMagMo
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Re: "Fermirotica" Discussion
Of course, a proper calculation would need to take into account the variance in the distribution of people, considering P_d depends on r.
Re: "Fermirotica" Discussion
I wonder if 18600 people / square mile is already adjusted for little children and senior citizens, who are doubtful to have sex 80 times a year, for 30 minutes.
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