Apophenia: Definition and Analysis

By Sandra L Hubscher
Article ID: 117

Introduction to Apophenia

August Strindberg, the early 20th century Swedish playwright, chronicles in Inferno/From an Occult Diary his descent into what would likely be diagnosed as schizophrenia in modern times:

“There on the ground I found two dry twigs, broken off by the wind. They were shaped like the Greek letter for “P” and “y”… [I]t struck me that [they] must be an abbreviation of the name Popoffsky. Now I was sure it was he who was persecuting me, and that the Powers wanted to open my eyes to my danger.”

This is an eerie and extreme glimpse at the propensity of the human mind to commit what the statisticians Neyman and Pearson (1933) termed Type I error. As a statistical error, it is the acceptance of a false positive, that is, believing to see a difference or meaning when the given result is attributable to chance. Strindberg, in this example, was driven to interpret the random arrangement of sticks as non-random written letters. Although he was laboring under mental illness, the tricks of his mind were not hallucinations, but over-interpretations of his actual sensory perceptions as being more meaningful than reality warranted.

Brugger (2001) puts this weakness of human cognition as a “pervasive tendency of human beings to see order in random configurations,” which Klaus Conrad in 1958 had refined and termed as apophenia, or the “unmotivated seeing of connections [accompanied by] a specific feeling of abnormal meaningfulness.” Modern examples of apophenia (and its subset corollary pareidolia1) are so numerous and sufficiently well-known to hardly need enumerating, but are amusing enough to merit repeating: Drosnin’s The Bible Code, in which arrangements of letters pulled from scripture predicted events such as 9/11 (and, heads-up, an earthquake – “the big one” – will hit in 2010), the infamous grilled cheese sandwich virgin Mary, Led Zeppelin’s Stairway to Heaven crooning “My sweet Satan,” when played backward, the face on Mars, and, apparently, psychoanalysis2.

Assessing Randomness

But how do we interpret the randomness of events occurring around us? By what criteria do we decide whether our experiences are just coincidences, or represent a true pattern at work? Cohen (1960) summed up our deficiencies by saying that, based on his experimental results, “nothing is so alien to the human mind as the idea of randomness.” The problem appears to be two-fold: one is that “the very nature of randomness assures us that combing random data will yield some patterns,” and that “if the data set is large enough, coincidences are sure to appear,” (Martin, 1998). More generally, this can be summed up by the Ramsey theory (Graham and Spencer, 1990) in which Frank P. Ramsey proved mathematically that “Complete disorder is an impossibility… [e]very large set of numbers, points or objects necessarily contains a highly regular pattern.” If humans are pattern seekers, and randomness necessarily contains patterns, then we’ve arrived at our first stumbling block.

The second prong in our failure to detect randomness is the method by which the human mind assesses randomness. In 1937, the Zenith Corporation unwittingly provided a simplistic glimpse into this human perception (Goodfellow, 1938). During a series of radio broadcasts, psychics appeared on one of their programs and “transmitted” telepathically a five-digit randomly-generated sequence of binary digits4. Listeners were asked to record the sequence and send it in to the company to determine if “people are sensitive to psychic transmissions,” (Griffiths and Tennenbaum, 2001). Although there was no true correlation between the listeners’ sequences and those “transmitted,” the listeners were found to have a predilection to create certain “random” sequences in preference to others. For example, the top three sequences sent in were 00101, 00110, 01101, which were submitted about ten times as often as sequences such as 00000 or 00001. Importantly, the responses indicated that listeners believed alternations of numbers (e.g. 0101) were much more representative of randomness than long strings of the same digit. More simply, the listeners perceived randomness to be a change (alternation) from the previous digit.

Falk and Konold (1997), in a similar vein, conducted an experiment in which subjects were asked to assess the randomness of long strings of randomly generated binary digits. An ideally random sequence has a probability of alternation of 0.5, that is, the digits within the sequence alternate about half the time5. They found, however, that “sequences with overalternations are perceived [by the subjects] as more random than their [mathematically-assessed] randomness warrant6.” They go on to suggest that this human predilection for perceiving randomness in alternations is attributable to the core method humans use to assess randomness: difficulty of encoding (memorizing). This is related to the idea of compressibility of data – that an “ideally” random sequence is incompressible to a simpler form because the information encoded has no “patterns”. Therefore, a sequence with easy to memorize patterns (long strings of non-alternating digits) is perceived as being non-random, although, as given earlier, clumping of data or “runs” are a natural feature of randomness. Tellingly, Falk and Konold also noted that the time required for subjects to memorize a given sequence correlated directly to the randomness assigned to it by other subjects. That is, the sequences rated most random were also the most difficult to memorize.

This fallacy of the human mind has not gone unnoticed. In fact, it’s been named after the most notorious pattern seekers of all: Gamblers. The Gambler’s Fallacy holds that in a sequence of random events, past outcomes influence future outcomes. The oft-cited example is a game of roulette where black has spun seven times in row. The players around the table begin to feel that their luck is running out and that red is “due” soon (or, in corollary, that they are having a “streak” and black will continue to appear), when in actuality the probability of the next spin being red (or black) is the same as ever – 0.5. We instinctively believe that the past has an influence on the future because, well, it usually does. Our financial advisers, understanding our fallibilities all too well, always remind us in the small print that “past performance is no indication of future success.” Thus, the Zenith listeners, sitting at home and scribbling out digits, took care to note what digits they had already recorded and then added numbers that gave the appearance, in their minds, of randomness7. Similarly, Falk and Konold’s subjects were assuming a “connection” between individual digits, that is, they believed a given digit was less likely to be followed by the same digit in a “random” sequence, although again, the probability of the following digit was in no way influenced by what preceded it.

This brings us to a number of deficiencies in the natural human assessment of randomness. One is that randomness, by virtue of its nature, does contain some patterns. Being pattern seekers, we focus on and over-interpret these patterns. Secondly, we don’t quite know how to recognize randomness when we see it; our expectation is that if some sense can be made of it, (in the binary digits examples, this took the form of ease of memorization), then the data are not random. Finally, we have an instinctual belief that the past influences the future, even in the occurrence of random events. Knowing our fallibilities, the next question obviously becomes, why? Why is it we see order in disorder, faces in clouds and lucky streaks at the roulette table?

Apophenia’s Evolutionary Origins

Philosopher Daniel Dennett says in his 2006 book, Breaking the Spell, “Humans are creatures that crave to find order and meaning in their environment. Not only do we want to find meaning in our surroundings, but we needto do this.” A common illustrative example is this scenario: imagine you are warily traveling through a wooded area, aware that there have recently been incidents of other travelers being robbed in the vicinity. You see a dark outline behind some bushes. What should you do? If you believe the outline to be a robber and it turns out to be a shadow, well, rather safe than sorry. But if you assume the outline to be only a shadow and it turns out to be a robber, well, you lose. In an evolutionary sense, then, there is great advantage to assuming to see forms in randomness, robbers in shadows. Dennett puts this category of thinking as a “Good Trick… that is so useful to so many different ways of life that it evolves over and over again in many different species.”

Traveling through life without seeing or making assumptions about patterns would be not only dangerous, but nearly impossible. Tomatoes, introduced to Europe in the 16thcentury, were almost universally considered poisonous throughout the continent and Britain – and rightly so. They are a member of the nightshade family, have a strong resemblance to those fruits and contain glycoalkaloids, a neurotoxin, in their leaves and stems. If you’ve already learned (patterned) that fruits of one plant are poisonous, why would you eat some from a very similar plant8? We may know now that, regardless of their association, tomatoes are nutritious and safe to eat, but it would be foolhardy for us to eat anything we find, using the assumption “safe until proven otherwise.”

Pre-historic peoples learned to pattern the changing of the seasons and track game and harvests by it. But this strong inducement has become a cup that overfloweth. Now we hear of baseball players, when having a good season won’t change their socks, or thousands claiming to have “felt something so deep in my heart” because of an “image” of the Virgin Mary formed by road salt on a highway underpass in Chicago (BBC, 2005).

Science and Stick Signs

An author, Lisa Shiel, received a write-up in our local paper when she released, through her own publishing company, the book Backyard Bigfoot: The True Story of Stick Signs, UFOs and the Sasquatch. In a spirit of community affection and curiosity I bought a copy. Echoing Strindberg and his sticks, she devotes 52 pages and no less than 56 black and white photographs to the phenomena of “stick signs,” which she describes as “sticks arranged in meaningful and distinctly unnatural displays [which] serve as the medium for their [bigfoots9] nonverbal communication.” The “stick signs” she catalogs are arrangements of simple shapes: squares, triangles and crosses, although she asserts that “parallel sticks and crossed sticks seem to dominate.”

It’s really a lovely example of apophenia in action. If we remember Conrad’s two tier definition: an unmotivated seeing of connections and a specific feeling of abnormal meaningfulness, we can see both of these here. The author has seen shapes (connections) in the arrangements of the sticks and has ascribed a great deal of meaningfulness to them by associating them with a supernatural creature. When we think back to Ramsey (and common sense), we know that it would be difficult not to see some sort of patterned arrangement among sticks lying on the ground.

In numerous studies, neurobiologist Brugger has searched for the underlying physiological principles of apophenia and paranormal beliefs. He has found that “people with high levels of dopamine are more likely to find significance in coincidences, and pick out meaning and patterns where there are none,” (Philips, 2002). In one trial in which “skeptics and [paranormal] believers were both given the drug L-dopa, which increases dopamine levels in the brain, the skeptics began to perform much more like the believers.”

Most fascinating of all is the link between creativity and apophenia. Brugger describes a “‘relativity of creativity,’ i.e., [a] continuum from creative detection of real patterns at one end, to the ‘hypercreative’interpretation of patterns in ‘noise’ [randomness] at the other end.” Brugger further links “the ability to associate, and especially the tendency to prefer ‘remote’ over ‘close’ associations, [to] the heart of creative, paranormal and delusional thinking.” Heilman (2003) similarly describes creative innovation as “the ability to understand and express novel orderly relationships.” Leonardo Da Vinci, utilizing this tendency in order to harness the creativity of his students, advised them to

Look at walls covered with many stains . . . with the idea of imagining some scene, you will see in it a similarity to landscapes adorned with mountains, rivers, rocks, trees, plains, broad valleys, and hills of all kinds… [also] battles and figures with lively gestures and strange faces and costumes and an infinity of things which you can reduce to separate and complex forms.

I find that non-fiction authors who are the most effective at their craft are those who can freely relate obscure and neglected ideas and anecdotes to their main points. Richard Dawkins, a favorite writer of mine, in a passage comparing the transcendency of science to religion, is reminded of an Anglican priest who taught at his primary school:

Our sport during lessons was to sidetrack him away from scripture and towards stirring tales of Fighter Command and the Few…[it was then with] something of the affection that I still retain for the Church of England…that I later read John Betjeman’s poem:

Our padre is an old sky pilot,

Severely now they’ve clipped his wings,

But still the flagstaff in the Rect’ry garden

Points to Higher Things…

In a single short passage he deftly links the abstract notion of transcendency to a favorite childhood memory and a warmly remembered poem. These connections draw out what would otherwise be a dry piece of academia into a richly well-illustrated and meaningful insight.

Strindberg was obviously well-endowed with the ability to “see order in random configurations,” and to give it a “specific feeling of abnormal meaningfulness.” He writes of a thunderstorm:

Usually the fury…abates in a short time…, but this one remained over my village for two solid hours, and I am sure that it was an attack on me personally, that each flash was aimed at me…


In spite of the fact that all this was perfectly natural…I could not help asking myself what demon it was who had put these two insignia of witches [on these rocks].

Although at times he was reduced to near madness, he nonetheless produced creative works prodigiously throughout his life, generating 58 plays, a nine volume autobiography and numerous novels and short stories.

Our ability to discern forms in randomness and patterns in chaos is not necessarily a negative trait. From survival strategies of primitive times to the more enriching and impalpable pursuit of beauty and art, we have derived a tremendous benefit by attaching creativity to free association. The entire enterprise of science, after all, is the organized and rational search for order in the seeming randomness surrounding us. Nobel Prize winner Max Born [wrote] “Science is not formal logic-it needs the free play of the mind in as great a degree as any other creative art.”

Alfred Wegener in 1912, partly on the strength of noticing the puzzle-piece like fit of the continents, proposed the modern theory of continental drift. Lacking a plausible mechanism for the movement, however, his theory languished for about 30 years until further evidence vindicated the “coincidences” he had noted. Although this account could be taken to be representative of the short-sightedness or intractability of established science, this is not so. As in the case of Strindberg or Shiel’s “stick-signs,” merely noting patterns or coincidences in not proof in and of itself but, applied properly, can be the creative leap needed to devise new and testable hypotheses.

As with most human traits, there is a spectrum of appropriateness. Bereft of apophenia, we find ourselves in an unquestioning, patternless existence where everything occurs seemingly without reason. There is no learning from experience: “Once bitten, twice shy,” becomes “Once bitten, never shy,” and the rhythms of the natural world are unappreciated. At the other extreme we find those such as Strindberg, in whose existence objects and events are drowning in meaning and asphyxiated in over-interpretation. Apophenia, in its more benign state provides us a powerful tool to make sense and safety of the world and people around us. In its more extreme forms, however, it is a well-spring of pseudo-science and nonsense, an irrational leap bypassing reason and rationality.


1. The Skepdic defines pareidolia as ”a type of illusion or misperception involving a vague or obscure stimulus being perceived as something clear and distinct.” This is similar to apophenia but describes only visual misperceptions – a more narrow focus of mis-interpretation.

2. Brugger relates that in 1929 psychoanalyst Paul Federn hypothesized that the common avoidance of stepping on cracks in the sidewalk is attributable to the sexual fear of treading upon a crack (vagina) with the foot (penis). Similarly, another psychoanalyst interpreted the large number of women failing to return their pencils following one of his exams as proof of the validity of penis envy. Psychoanalysis is rife with apophenia to its very core. Freud (1938), in The Dream-Work writes:

When one has familiarized oneself with the extensive employment of symbolism for the representation of sexual material in dreams… one even thinks of attempting to compile a new dream-book on the lines of the cipher method.

He then proceeds to give an inventory of common dream symbols, from which I’ve pulled some of the best: Going up and down ladders and stairs = sexual intercourse, playing with or beating a little child = masturbation, the lizard (on account of its ability to re-grow a lost tail) = insurance against castration, the number three = male genitals, necktie = penis (this seems obvious but Freud confusingly adds that this is “not only because [it] hang[s] down in front of the body… but also because one can select them at pleasure, a freedom [prohibited in] in original.”2Jung, in a similar vein of apophenia, developed the principle of synchronicity – which posits that a number of events may occur which are causally unrelated but are nonetheless meaningfully related to one another. More simply, he believed that events, thoughts and the environment around us are all interconnected. Examples would include having a friend call you on the phone while you were thinking about him or stumbling across a lost key just when you needed to open that particular lock.

3. This reminds me of the song “Detachable Penis” which my college roommate, who was a DJ on our campus radio station, was often requested to play. In the song, the male singer bemoans loosing his penis at a party or having it misplaced by his mother. No doubt Freud could have gladly written an entire volume about the lyrics.

4. The psychic transmitters actually used symbols such as heads and tails, and black and white. For simplicity these have been “translated” to zeros and ones.

5. Falk and Konold use the probability of alteration, P(A), to characterize sequences. The basic idea here is that a sequence with no alterations, (e.g. 1111111) would have a P(A) of 0 while a sequence with nothing but alterations, (e.g. 1010101) would have a P(A) of 1. Random sequences of sufficient length should have a P(A) of about 0.5 and are characterized by “runs” of digits, (e.g. 110100001 has a P(A) of 0.5).

6. For those who are mathematically minded, Armstrong (2004) presents the many different formulae used to assess randomness. It is no easy task to mathematically assess the randomness of sequences; consider these two sequences of coin tosses: THHTTTTHTH and THHHHHHHHT. The first one I generated by flipping a quarter while sitting at my computer and the second I fabricated non-randomly; however, both of them have the same probability of occurring randomly (one in 1,024) although the second sequence looks a bit fishy to human sensibilities. If they both have the same probability of occurring, what, then, is the method by which we mathematically classify the second sequence as non-random? The equations developed by mathematicians generally use two arithmetic criteria for assessing randomness: Runs testing, which examines the number of times a repeated symbol appears and frequency testing, which assesses the proportionality of all occurrences of a given symbol. Thus, in the second example sequence I gave, the equations pick up both the preponderance of Head outcomes and the unusually long run of Heads. It is quite possible, however, to do an end-run around the mathematical method of assessing randomness entirely and define the randomness of a series by the process from which it was generated instead of by its content. Thus, the sequence itself, no matter what digits it may contain, can be branded as random if it can be shown that it was derived in a random manner. Falk and Konold give a delightful anecdote relating to this notion:

This reminds us of an episode told by Gell-Mann. On one of his early visits to the RAND Corporation in Santa Monica, California, he was handed a stack including the “RAND Table of Random Numbers.” A small piece of paper fluttered out of it and fell to the floor. When he picked it up, he found it was an errata sheet to the tables.

7. Falk and Konold relate that Alberoni (1962) conducted an experiment in which subjects were asked to assess the randomness of a sequence. A later analysis of this experiment by researchers, however, revealed that the “random” sequence used was almost certainly generated purposefully and non-randomly by Alberoni himself. The P(A)(see footnote 4) of the sequence Alberoni used was 0.81, as is commonly produced by people asked to generate a random sequence, rather than 0.5, what would be expected by chance. It seems likely that Alberoni, in his desire to create a perfectly random sequence for his experiment, didn’t want to leave it to chance.

8. A story of dubious historicity has an otherwise forgotten man, Robert Gibbon Johnson, eating an entire basket of tomatoes on the courthouse steps of Salem, New Jersey in 1820 in order to prove their edibility. He supposedly said to the astonished crowd before biting into the first one that “the time will come when this luscious golden tomato, rich in nutrition, a delight to the eye, a joy to the palate whether fried, baked, broiled or even eaten raw will form the foundation of a great garden industry.”

9. I didn’t research the correct usage, but I’m guessing that the plural of Bigfoot is not Bigfeet.

Starred references (*) are recommended for further reading on apophenia.


Alberoni F. 1962. Contribution to the Study of Subjective Probability: I. Journal of General Psychology. 66: 241-264.

*Armstrong, SA. 2004. A Meta-Analysis of Randomness in Human Behavioral Research. Master’s Thesis, Louisiana State University.

*Brugger, Peter. 2001. From Haunted Brain to Haunted Science: A Cognitive Neuroscience View of Paranormal and Pseudoscientific Thought. In Hauntings and Poltergeists, ed. James Houran and Rense Lange, 195-213. North Carolina: McFarland & Company, Inc.

Cohen, J. 1960. Chance, skill, and luck: The psychology of guessing and gambling. Baltimore, MD: Penguin Books.

Conrad K. 1958. Die beginnende Schizophrenie. Versuch einer Gestaltanalyse des Wahns. Stuttgart: Thieme.

Dawkins, Richard. 2006. The God Delusion. New York: Houghton Mifflin Company.

Dennett, Daniel. 2006. Breaking the Spell: Religion as a Natural Phenomenon. New York: Penguin Group.

*Falk R and Konold C. 1997. Making Sense of Randomness: Implicit Encoding as a Bias for Judgment.Psychological Review. 104: 301 – 318.

Freud, Sigmund. 1938. The Basic Writings of Sigmund Freud. Translated and edited by Dr. AA Brill. New York: The Modern Library.

Goodfellow LD. 1938. A Psychological Interpretation of the Results of the Zenith Radio Experiments in Telepathy. Journal of Experimental Psychology. 23: 601-632.

Heilman K, Nadeau S, and Beversdorf DO. 2003. Creative Innovation: Possible Brain Mechanisms.Neurocase. 9: 369-379.

Graham RL and Spencer JH. 1990. Ramsey Theory. Scientific American. July 1990: 112-117.

*Griffiths TL and Tenenbaum JB. 2001. Randomness and coincidences: Reconciling intuition and probability theory. Proceedings of the 23rd Annual Conference of the Cognitive Science Society, 370-375.

Martin B. 1998. Coincidences: Remarkable or Random? Skeptical Inquirer. 22(5): 23-28.

Neyman J and Pearson E. 1933. On the Problem of the Most Efficient Tests of Statistical Hypotheses.Philos Trans Roy Soc A. 231:289-317.

Philips H. 2002. Paranormal Beliefs Linked to Brain Chemistry. New Scientist.

Salem County Historical Society. 2005. The Story of Robert Gibbon Johnson and the Tomato. Newsletter: The History Highway.

Shiel, Lisa. 2006. Backyard Bigfoot: The True Story of Stick Signs, UFOs & the Sasquatch. Lake Linden, Michigan: Slipdown Mountain Press, LLC.

Strindberg, August. 1979. Inferno/From An Occult Diary. New York: Penguin Classics.

British Broadcasting Company. (April 2005) ‘Virgin Mary’ on US Motorway Wall.

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