718: The Flake Equation

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The Flake Equation
Statistics suggest that there should be tons of alien encounter stories, and in practice there are tons of alien encounter stories. This is known as Fermi's Lack-of-a-Paradox.
Title text: Statistics suggest that there should be tons of alien encounter stories, and in practice there are tons of alien encounter stories. This is known as Fermi's Lack-of-a-Paradox.

[edit] Explanation

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The Flake equation is a parody of the Drake equation, which estimates the number of detectable extraterrestrial civilizations in our galaxy. It does so in similar manner: by multiplying number of stars by consecutive probabilities of the star having certain characteristics making detectable life possible. Just like the Drake equation, exact numbers are unknown, but can be estimated, and the equation shows the guesses about the values.

[edit] Explanations of values

Symbol Assumed value Explanation
WP 7,000,000,000 World population at the time of the creation of the comic, taken as a starting value.
(CR + Mi) 1/10,000 + 1/10,000 Fraction of people who would believe they had been visited by aliens. This is assumed to be people who are crazy, want to feel special, or misinterpret physical phenomena as alien sightings. It is assumed that one in 10,000 people belongs to each of these groups. Multiplied by the world population we get the number of people who believe to have been visited by aliens
TK 1/10 The fraction of those people, who believe to have experienced an alien sighting, that tell others about their experience. Multiplying with the previous values we get the number of people who believe to have experienced an alien sighting, and tell others about it.
F0 10 Average number of people they tell about their "sightings". Multiplying with the previous values we get the amount of people this is the amount of people who hear about the alien sighting from the "primary source".
F1 10 Average number of people that they decide to tell about the "firsthand" account. Multiplying with the previous values we get the amount of people who hear a second-hand account.
DT 9/10 The probability that the details will be slightly adjusted during the retelling process, making the account believable. The total is now the amount of believable alien sighting stories.
AU 1/100 The proportion of people who have the willingness and ability to share this story with the with a broad audience. The total is now the amount of believable alien sightings that are published to a wider audience.

The final results tells us that there should be about 100 000 stories about aliens that have reliable explanation. The data is obviously highly uncertain, and as with the Drake Equation, you can plug in your own numbers, but if you keep your guesses realistic, you will most likely get a very large number. This convinces the reader that the fact that there are many stories about aliens does not necessarily means that many people actually met aliens.

The title text refers to Fermi's Lack-of-a-Paradox as a parody of the Fermi paradox: The contradiction between the high estimated probable existence of extraterrestrial civilizations and the lack of establishing contact to such civilizations by humans.

Another comic parodying this equation is 384: The Drake Equation. The credibility of paranormal reports in general is revisited in 1235: Settled, which posits that if such phenomena were real they should have been unambiguously captured on camera by now.

[edit] Transcript

The Flake Equation:
P = WP × (CR + MI) × TK × F0 × F1 × DT × AU ≈ 100,000
Where:
WP = World Population (7,000,000,000)
CR = Fraction of people who imagine an alien encounter because they're crazy or want to feel special (1/10,000)
MI = Fraction of people who misinterpret a physical or physiological experience as an alien sighting (1/10,000)
TK = Probability that they'll tell someone (1/10)
F0 = Average number of people they tell (10)
F1 = Average number of people each friend tells this "firsthand" account (10)
DT = Probability that any details not fitting the narrative will be revised or forgotten in retelling (9/10)
AU = Fraction of people with the means and motivation to share the story with a wider audience (blogs, forums, reporters) (1/100)
Even with conservative guesses for the values of the variables, this suggests there must be a huge number of credible-sounding alien sightings out there, available to anyone who wants to believe!


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Discussion

Anybody notice that the real product of the numbers he gives is 6.3 (10), not 100,000? 02:32, 16 April 2017 (UTC)

No, it's not - you've multiplied Cr and Mx when you should have added them. The real product is 126,000 = 100,000. 162.158.69.51

There was a later comic about our capabilities' precluding of UFO sightings and such. I may find it at some point. --Quicksilver (talk) 02:51, 20 August 2013 (UTC)


Settled

googlesearch=site:explainxkcd.com ufo

http://www.explainxkcd.com/wiki/index.php/1235:_Settled

Kevin McCready (talk) 13:25, 10 May 2014 (UTC)

Is there any significance to the word "flake"? Urban Dictionary says it stands for "unreliable person", but certainly not in context of alien sightings. --162.158.90.217 13:34, 26 August 2015 (UTC)

 It's a portmanteau of "Drake" and "Fake". --172.68.10.94 10:58, 4 February 2017 (UTC)
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