XKCD, a science-savvy webcomic, has a recent installment called The Flake Equation (a play on the Drake Equation which provides the formula for calculating the likely number of technological civilizations in the universe). I am now going to take his brief and elegant point and beat that horse to death.

While XKCD applies his equation to UFO sightings, it applies equally well to any paranormal or pseudoscientific phenomenon – bigfoot, ghosts, alternative medicine healings, etc. Often we are told by believers that “where there is smoke there is fire.” In other words – with so many people reporting sightings or healings, there must be something going on.

Skeptics, of course, recognize this as a fallacy. There is a major unstated premise or assumption in this position. We must ask ourselves – in a hypothetical world in which we are not and have never been visited by aliens, what would we expect in terms of sightings and experiences? Is such a world compatible with the current number and quality of sightings? I think the answer to this is a pretty clear “yes” – and that is exactly the point that XKCD is making.

There are a host of psychological, cultural, and situational factors that would lead people to believe they have had a paranormal or extraterrestrial encounter. Most of us have had weird experiences we may or may not have been able to explain.

We add to this the fact that human memory is both flawed and biased toward interesting and meaningful narratives. We tend to morph memories over time simply because they fade with time, and are susceptible to merging with other memories and even contamination. Have you ever “remembered” an event that you never experienced but someone else told you about. You imagined the story, and then years later confused your imaginings with your own first-hand memory.

Further, we tend to smooth over the rough edges of our memories – distorting details to fit the theme. So if we think that our encounter with a strange light was an encounter with an alien spacecraft, over time the details of the story will fit a UFO encounter better and better. We will drop or alter disconfirming details, and enhance or even confabulate supporting details. Details from other witnesses will also contaminate our memories (and may give the false impression of independent confirmation).

In the end we have a story that sounds very compelling, and the person telling the story likely really believes it and the supporting details. Often believers are compelled by the sincerity of those with such tales to tell. First, sincerity can be faked. But even if we assume it is genuine, it is meaningless because people can be sincerely mistaken.

XKCD makes the further point that given the number of people in the world we would expect a large number of even unlikely events (mundane but unusual or highly coincidental), and some of this will be further distorted in the telling, and some of these will become widely spread.

The take home message for skeptics is that even in a world without ghosts, aliens, and bigfeet we would expect there to be large numbers of anecdotes that sound very impressive, told by people who seem sincere. In a world with these things, we should also expect some objective and verifiable evidence – and that is what is lacking.

The notion of “where there is smoke there is fire” simply does not apply, because human brains and the cultures in which they are embedded are smoke machines.