0563: "Fermirotica"

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0563: "Fermirotica"

Postby rho421 » Wed Apr 01, 2009 4:00 am UTC

Image

http://www.xkcd.com/563

Alt-Text: 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

Postby HenryGifford » Wed Apr 01, 2009 4:00 am UTC

Image
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.

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TheHand
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Re: "Fermirotica" Discussion

Postby TheHand » Wed Apr 01, 2009 4:03 am UTC

Hey now, my Mom IS in town!

I guess the only question is if your mom is holding up her end of the bargain...

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Re: "Fermirotica" Discussion

Postby tr0nk » Wed Apr 01, 2009 4:05 am UTC

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..
Last edited by tr0nk on Wed Apr 01, 2009 4:07 am UTC, edited 1 time in total.

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aeris92
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Re: "Fermirotica" Discussion

Postby aeris92 » Wed Apr 01, 2009 4:07 am UTC

Also, if your mom is in town, disregard gravity.

Zenexer
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Re: "Fermirotica" Discussion

Postby Zenexer » Wed Apr 01, 2009 4:10 am UTC

I don't quite get the title (hover) text; anyone care to explain? ;)

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Re: "Fermirotica" Discussion

Postby MiserereNobisAlex » Wed Apr 01, 2009 4:11 am UTC

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.

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madhollywood
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Re: "Fermirotica" Discussion

Postby madhollywood » Wed Apr 01, 2009 4:12 am UTC

Is Xf intended in the denominator instead of Xr? 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.

ck0
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Re: "Fermirotica" Discussion

Postby ck0 » Wed Apr 01, 2009 4:14 am UTC

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!
Last edited by ck0 on Wed Apr 01, 2009 4:22 am UTC, edited 1 time in total.

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Re: "Fermirotica" Discussion

Postby aion7 » Wed Apr 01, 2009 4:14 am UTC

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...
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Re: "Fermirotica" Discussion

Postby ladron » Wed Apr 01, 2009 4:15 am UTC

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...

hthall
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Re: "Fermirotica" Discussion

Postby hthall » Wed Apr 01, 2009 4:16 am UTC

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.)
Look at me, still talking when there's Science to do.

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Re: "Fermirotica" Discussion

Postby Wii Owner 3.14 » Wed Apr 01, 2009 4:18 am UTC

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 Xf vs Xr goof is fixed.

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Re: "Fermirotica" Discussion

Postby ladron » Wed Apr 01, 2009 4:19 am UTC

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

Postby coreyjkelly » Wed Apr 01, 2009 4:23 am UTC

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

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Re: "Fermirotica" Discussion

Postby Chuff » Wed Apr 01, 2009 4:24 am UTC

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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Re: "Fermirotica" Discussion

Postby fenrir_darkwolf » Wed Apr 01, 2009 4:25 am UTC

Dammit Randall, get out of my head! I was just admiring the dimensional analysis of google calculator a couple of days ago :P. 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

Postby LapsesofSanity » Wed Apr 01, 2009 4:28 am UTC

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...

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Re: "Fermirotica" Discussion

Postby pgn674 » Wed Apr 01, 2009 4:31 am UTC

If I recall correctly, Google handles unicorn horns and light years in a tablespoon, too.

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Re: "Fermirotica" Discussion

Postby SocialSceneRepairman » Wed Apr 01, 2009 4:33 am UTC

I was wondering where the two came from, but then I remembered what sex was.

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 unit-dependent.

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Re: "Fermirotica" Discussion

Postby Denyvem » Wed Apr 01, 2009 4:35 am UTC

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!

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Re: "Fermirotica" Discussion

Postby KyleOwens » Wed Apr 01, 2009 4:39 am UTC

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

Postby coreyjkelly » Wed Apr 01, 2009 4:40 am UTC

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

Postby phlip » Wed Apr 01, 2009 4:42 am UTC

madhollywood wrote:Also, I wouldn't necessarily thing that the duration of sex decreases the radius in which it was occuring.

Well, XfXd 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 PdXfXd 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*r2. Solve for r, and you get the formula in the comic.
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enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
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Re: "Fermirotica" Discussion

Postby GoldFish » Wed Apr 01, 2009 4:42 am UTC

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.

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Re: "Fermirotica" Discussion

Postby Delass » Wed Apr 01, 2009 4:43 am UTC

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

Postby poxic » Wed Apr 01, 2009 4:44 am UTC

Delass wrote:Wouldnt two people be required to have sex?

That's the generally agreed minimum, yes.
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Re: "Fermirotica" Discussion

Postby QuantumNightmare » Wed Apr 01, 2009 4:47 am UTC

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

Postby flashstorm » Wed Apr 01, 2009 4:49 am UTC

The lack of April Fools-ness is depressing.

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Re: "Fermirotica" Discussion

Postby phlip » Wed Apr 01, 2009 4:54 am UTC

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.
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Re: "Fermirotica" Discussion

Postby adavies42 » Wed Apr 01, 2009 4:55 am UTC


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Re: "Fermirotica" Discussion

Postby NerdKing » Wed Apr 01, 2009 4:57 am UTC

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.

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Re: "Fermirotica" Discussion

Postby josiahstevenson » Wed Apr 01, 2009 4:58 am UTC

flashstorm wrote:The lack of April Fools-ness is depressing.

You've not seen the bit about changing the xkcd domain name, then?

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Re: "Fermirotica" Discussion

Postby GoldFish » Wed Apr 01, 2009 4:58 am UTC

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.

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Re: "Fermirotica" Discussion

Postby afarnen » Wed Apr 01, 2009 5:01 am UTC

Am I the only one who doesn't know where this formula came from? What does the "Fermi" in "Fermirotica" refer to?

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

Postby Quantumplation » Wed Apr 01, 2009 5:03 am UTC

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 ) ) = 7.7863780385990247411070697617746e-5 kilometers

thats approximately .000077863 km... or 3 inches.

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Re: "Fermirotica" Discussion

Postby josiahstevenson » Wed Apr 01, 2009 5:09 am UTC

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 ) ) = 7.7863780385990247411070697617746e-5 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.

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Re: "Fermirotica" Discussion

Postby phlip » Wed Apr 01, 2009 5:11 am UTC

Quantumplation wrote:square root( 2 / ( pi * 43,752 * 80 * 30 ) ) = 7.7863780385990247411070697617746e-5 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/km2 is 113317/mi2. It's area, not distance - you have to multiply by 1.6092.

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.
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enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
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Re: "Fermirotica" Discussion

Postby BrainMagMo » Wed Apr 01, 2009 5:15 am UTC

Of course, a proper calculation would need to take into account the variance in the distribution of people, considering P_d depends on r.

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Re: "Fermirotica" Discussion

Postby HiPhil » Wed Apr 01, 2009 5:17 am UTC

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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