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.


This strip parodies the Drake equation, which is an method for estimating of the number of detectable extraterrestrial civilizations in our galaxy. The Drake equation starts with the best estimate for the number of stars in our galaxy, then multiplies it by successive probabilities (such as the number of stars with planets, the number of planets which can support life, etc), to ultimately calculate how many civilizations exist. While such a calculation necessarily uses speculative numbers, it gives a good sense of how many civilizations could potentially exist.

The Flake equation presented in this strip provides an estimate about how many false or fake stories about aliens are likely to exist. It does so in similar manner as the Drake equation, by starting with the entire population, estimating how many people are likely to believe that they've had an alien encounter, and then calculating how likely those stories are to become public. Just like in the Drake equation, exact numbers are unknown, but can be estimated, and the equation in the comic shows Randall's guesses about these values. See an explanations of values below.

"Flake" is American slang for a person who is casually dishonest or unreliable, implying that such a person would be likely to imagine an alien encounter. Note that, while the Flake equation includes people who imagine encounters "because they're crazy or want to feel special", it doesn't attempt to include outright lies or deliberate hoaxes.

The final results tells us that there should be about 100,000 stories about aliens that have reliable explanations. (The numbers given in the equation gives 126,000 stories). The data is obviously highly speculative, 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 mean that many people actually met aliens.

The title text refers to Fermi's Lack-of-a-Paradox. The Fermi paradox refers to the contradiction between high numbers of calculated civilizations and the total lack of verified alien contact with earth. This is related to the Drake Equation, many estimates calculate that there should be large numbers of civilization in the galaxy, and they should have existed for long periods of time, suggesting that humanity should have been contacted by them, or at least seen some clear evidence of their existence. There are multiple explanations for this paradox, but it remains a question of scientific debate. The Lack-of-a-Paradox in this strip, however, is that the math suggests that there should be huge numbers of claimed alien sightings, and that's exactly what we observe.

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.

Explanations of values

Symbol Assumed value Explanation
WP 7,000,000,000 Approximate 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 falsely believe they had been visited by aliens. This is attributed to either a person imagining an encounter, and believing that it was real (due to mental illness or a desire to feel special), or to people misinterpreting something as an alien encounter (this can include possibilities as broad as unusual lights in the sky to actual hallucinations). It is estimated that one person in ten thousand falls into each of these categories, suggesting that one person in five thousand either has or will, at some point, believe they've encountered aliens.
TK 1/10 The fraction of people who believe they have experienced an alien sighting that tell others about their experience. Randall estimates (rather conservatively) that 90% of people who believe they've encountered aliens will keep quiet about it (likely out of fear of not being believed), and only one in ten will talk about their 'experience'. Multiplying with the previous values we get the of first-hand accounts of alien encounters.
F0 10 Average number of people they tell about their "sightings". Multiplying with the previous values we get the number of people who hear about an 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 of a false story.
DT 9/10 The probability that the details will be slightly adjusted during the retelling process, making the account believable. Randall estimates that 90% of accounts that are actually shared have detailed changed when they're retold. This is exceptionally common when stories are passed from person to person, it's rare for all the details to survive unchanged. In this sort of case, "not fitting the narrative" implies that some details will be unbelievable, or falsifiable, or will be insufficiently dramatic, and those tend to morph over time (often innocently, as people don't remember the original version perfectly). Multiplying this probability by the previous numbers gives number of believable-yet-false alien sighting stories in circulation.
AU 1/100 The proportion of people who have the willingness and ability to share this story with a broad audience. Randall assumes that the overwhelming majority of people who hear such stories either have no platform to share stories to more than a handful of people at a time, or aren't willing to share these stories. But enough people in modern times have broad audiences (this number includes people with internet audiences), that it's estimated that 1% of the population both can and wants to share second-hand accounts of alien encounters. The total is now the amount of believable-yet-false alien sightings that are published to a wider audience.


The Flake Equation:
P = WP × (CR + MI) × TK × F0 × F1 × DT × AU ≈ 100,000
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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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.

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)


googlesearch=site:explainxkcd.com ufo


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. -- 13:34, 26 August 2015 (UTC)

 It's a portmanteau of "Drake" and "Fake". -- 10:58, 4 February 2017 (UTC)
It's not actually a portmanteau, more like a play on words :) -- The Cat Lady (talk) 13:57, 19 August 2021 (UTC)

The transcript looks pretty complete to me? Why is it tagged incomplete? Mushrooms (talk) 07:50, 22 March 2022 (UTC)

What if one of the aliens were to come forth and reveal themself? --Your favorite aura doggo (talk) 04:06, 26 June 2024 (UTC)