Apophenia and Extreme Confirmation Bias

by John Allen Paulos

Rorschach Inkblot Test

I recall a party game I once wrote about. The game, described by philosopher Daniel C. Dennett in his book “Consciousness Explained,” is a variant of the familiar childhood game requiring that one try to determine by means of Yes or No questions a secretly chosen number between one and one million. (Twenty questions are sufficient.)

In Dennett’s more interesting and suggestive game, one person is selected from a group of people at a party and asked to leave the room. He (or she) is told that in his absence one of the other partygoers will relate a recent dream to the other attendees. The person selected returns to the party and is then told that, through a sequence of Yes or No questions about the dream, he should try to do two things: reconstruct the dream and identify whose dream it was.

The punch line is that no one has related any dream. When asked, the individual partygoers are instructed to respond either Yes or No to the subject’s questions according to some completely arbitrary rule. Any rule will do, but should be supplemented by a non-contradiction clause so that no answer directly contradicts an earlier answer or contradicts obvious facts. The Yes or No requirement can also be loosened to allow for an occasional Maybe.

Now let me change the scene. Instead of the unlucky partygoer, consider an ardent QAnon member. Instead of the other partygoers let’s substitute people who pretend to be from the news media (to rouse the member’s antagonism) but who agree to be governed by similar arbitrary rules. Finally, rather than having the subject try to reconstruct the dream and identifying the dreamer, let’s examine whatever disgusting scandal the QAnon member believes to be the case and to whom he attributes it.

Clearly this is more a thought experiment than an empirical result, but I would guess that the likely outcome in both cases is that the subject, impelled by his (or her) own obsessions, will often concoct an outlandish dream or gruesome story in response to the random answers he elicits from the partygoers or the “media” people. The situation is a kind of Rorschach test without the inkblots.

The subject himself is the dream weaver in one case and the conspiracy monger in the other. His preoccupations dictate his questions which, even if answered negatively at first, frequently receive a positive response in later formulations of the questions. In both situations, people’s hypothesis-generating ability is alive and active, but their ability to test or falsify these hypotheses is impaired for a variety of reasons, including personal bugaboos or perhaps being in thrall to a lying, charismatic demagogue.

Add large numbers to the picture, and these speculations and metaphors are all the more potent. Having so much unfiltered information (websites, Facebook postings, tweets, TicTok videos, youtube interviews, celebrity excesses, financial statements, etcetera) with which to work and having no specific focus or objective warrant, any wild hunch or obsession regarding Covid, abortion, race, or other hot button issues can be pursued doggedly without fear of disconfirmation. There are so many factoids and odd news stories that it’s easier than ever to dream up a nonsensical conspiracy. The resulting combinatorial explosion of connections and interconnections among these bits of information will always provide ample raw material for the development of any group’s preferred bete noire. Given 10 random news stories, for example, any one of the approximately 1,000 subsets of them might go viral if artfully woven together. Omit these facts, include those facts, and see how compelling what you get is.

The cognitive foible known as the conjunction fallacy further contributes to the ease with which these stories can be developed. Asked to say which is more probable – option A: a sociologist with a Ph.D. in the subject and many books to her credit spends her weekends with drug dealers, or option B: this same sociologist spends her weekends with drug dealers and she’s writing a book about the prevalence of overdoses. The perhaps counterintuitive answer is that option A is more probable because the probability of two (or more) events being true is always lower than the probability of just one of them being true. Note, however, that option B, although less probable, is more plausible. In fact, there is often a tradeoff between plausibility and probability, and the internet, it should be reiterated, makes it very much easier to come up with somewhat plausible, but quite improbable salmagundis. Search for more and more tasty ingredients from an ever expanding larder and cook them up.

A useful exercise is writing up your own preposterous but semi-plausible story about some issue or person. Doing so helps one realize how easy it is and how much fun it can be. Just don’t publish it anywhere, except maybe in a supermarket tabloid that specializes in the sightings of Bigfoot.

Apophenia or the noting of connections where they don’t exist is always a risk. As has often been said, we’re pattern-seeking animals. Another exercise further illustrates this. Take a large piece of white paper and partition it into small squares so that it looks like a checkerboard. Flip a coin and color the upper left corner red if it lands heads and blue if it lands tails. Proceed to the next square and flip and color again. Continue in the next row and so on. When you’ve colored the whole paper, look it over and it’s likely that you’ll note patterns and connected clumps of similarly colored squares. The clumps are not disease clusters, evidence of child trafficking, obscene dreams, or demonic coins. They’re just the record of a bunch of coin flips.


John Allen Paulos is a Professor of Mathematics at Temple University and the author of Innumeracy, A Mathematician Reads the Newspaper, and a new book, Who’s Counting –Uniting Numbers and Narratives with Stories from Pop Culture, Puzzles, Politics, and More, which was just released.