So this post has been stimulated partly by a podcast chat about apophenia, and partly by the updated blog post, Dots Don't Make The Man. (It's also based on some writing that didn't make it into my final PhD thesis, which is why it has references and footnotes 😱.) Apophenia is the process by which people find meaning within randomness. An example is seeing images in cloud formations. When they are conducting good research (i.e. the procedure isn't too sloppy), parapsychologists are on the front line of studying randomness (whether they know it or not) and often conclude erroneously that they have discovered something meaningful. If you examine the first graphic, you can see a number of paranormal or fringe topics that (I am claiming) are the direct result of misinterpreting randomness (or more explicitly, some order in randomness) as meaningful.

What is randomness? Good question. Well this isn't the place for an exhaustive discussion. In Mandelbrot (1997), he actually defines seven types of randomness, and equates the different types as analogous to the different forms of matter: some types of randomness are more ordered (think solid) where some are much more unpredictable (like a gas). Randomness can be a very difficult thing to determine (i.e. is that sequence random?). Consider Champernowne’s constant, C = 0.12345678910111213... It is obvious that this number has a pattern and one that is directly predictable (the next digits are 1516171819 etc.), however Mandelbrot reports that this number passes all known tests of randomness! Contemplation on this number illustrates exactly one of the difficulties in understanding and validating randomness. If we imagine the digits progressing up the number-line, we can see that any one digit change from C results in a number that is (a) different and (b) completely uninteresting to us. As the shallowest of discussions, I would conclude that randomness is one of those topics that appears both simple ("Throwing a die ain't rocket science!" comes a shout from the back) and complex at the same time.

So let's consider electronic voice phenomena (EVP). Traditionally this has involved people listening to some kind of static noise and reporting hearing messages from the dead in the noise. It seems obvious to me that any meaningful message is being imposed on the underlying randomness, rather than being objectively part of the randomness (there are no voices, only sounds which are interpreted as voices). Ellis, 1978 (coincidentally the year I was born) concluded that the voices studied by EVP researchers were more than likely the result of pirate radio broadcasts (and thus there *were* voices on the tapes) or a consequence of interpreting the random hiss of static as a message. Or take coincidences (something that we discuss with some frequency on the podcast). Either the coincidental events are not connected or they are meaningful (and thus connected presumably by some cosmic or supernatural process). The apophenic map is not intended as an exhaustive list, merely it illustrates the ways in which human encounters with randomness may lead to misinterpretations of meaningful experiences. (Of course even if the underlying phenomenon is random, the experience can be personally meaningful, though that is not the point of this post.)

Take an extreme example, not from parapsychology. It is generally understood that \(\pi\) is a ‘random’ sequence, with no inherent pattern [1], but great utility [2]. Consider Puente (2000, 2003) who makes the serious argument that the digits of \(\pi\) contain a pattern which when graphically iterated (much like a Mandelbrot fractal) creates patterns that have analogues in the real world. Specifically Puente (2003) argues that he has discovered the pattern of B-DNA within the digits of \(\pi\) and presents considerable graphical evidence to support his claim. The second graphic of this post reproduces one of Puente's examples [3]. So let's be clear. Either Puente has found genuine order within \(\pi\) (a hidden message) or the claim of structure is really just random variation which has been misidentified as a pattern with meaning (garbage in, garbage out). Are there other ‘meaningful’ patterns in \(\pi\)? Convert my name into digits (A-I, J-R are numbered 1–9, with S-Z numbered 1–8 respectively). Although my full name does not appear in the first 200 million digits of \(\pi\) as a straight sequence (3639511441), the first name and surname do appear separately, as well as my initial and surname (e.g. 311441 occurs at position 22,366 from the decimal point), along with my date of birth (18111978 occurs at position 37,766,026 from the decimal point) [4]. Either these results are a chance coincidence or they have some meaning. It is my contention that the former is the case, not the latter [5].

Consider Monod’s excellent book, Chance and Necessity. Monod (1971) asks his readers to imagine that an alien scientist has landed his robotic explorer on Earth and it has just come across two objects: a rock and a crystal. It identifies the rock as a natural object, given its roughness and irregularity, and the crystal as an artefact, because of its regularity. Nobody makes every grain of sand or every snowflake, yet each has a structure independent of and different from, all others of the kind. Parapsychologists (and those making claims like Puente) have made the same mistake. Identifying naturally occurring patterns within randomness as an indicator of intelligence. Obviously, not every significant result in parapsychology is the result of apophenia. That would be a far too generous assessment. Most significant results are the consequence of fraud or sloppy methodology. The usual sceptical criticisms. But no doubt some of what we have discussed here, the EVP, the patterns in \(\pi\), they are very likely the result of apophenic misattribution. Of seeing meaning where there is in fact none.

Lastly, David Luke has suggested the term randomania for those who attribute to chance, that which is truly meaningful. The opposite of apophenia then. Well David is signed up for an upcoming podcast appearance, so maybe we can chat about apophenia and randomania in the near future. But of course there is meaning in the world. No-one is claiming that the books in the library were written by chance (well in a way they were 😉). No, the question is, is the noise in the dark meaningful (the whispering of a burglar say) or just the wind? Did god write a message in \(\pi\)? Does randomness sometimes appear more ordered than our intuitions would suggest? We shouldn't write off all meaning as randomness, but I think it is clear that we do have a cognitive bias towards concluding in a positive way that there is meaning when there is not, and if we are working in domains which encounter such phenomena we must be aware of this.

[1] | Carl Sagan was criticised by some for using a pattern within \(\pi\) as a plot device in his fictional novel Contact. Some \(\pi\) related coincidences: Posamentier and Lehmann (2004) report that a sequence of twelve nines (999999999999) can be found in the digits of \(\pi\), from the 897,831,316556^{th} decimal place. They also note that the number 360 is the 360^{th} digit of \(\pi\) (3 is 359, 6 is 360 and 0 is 361). Gardner (1991, p.273) notes, “the fact that the sixteenth and seventeenth digits of \(\pi\) and e are identical (23) is... meaningless.” |

[2] | Maor (2009) notes that in the infinity of numbers, the most important to humans (0, 1, \(\sqrt{2}\), e and \(\pi\)) are all between 0–4 on the number-line. |

[3] | It has been argued in a serious scientific context that the chances of finding this pattern using the digits of \(\pi\) is so astronomical as to be proof of design (god). The same author also references the anti-Darwinian book, Darwin’s Black Box (Behe, 1996). The similarity and commonality between these related lines of argument are that the patterns they have found are too unlikely to have occurred by chance, thus they must have meaning. Again, it is my contention that these are random, chance findings, without intelligence and are a consequence of apophenic misattribution. |

[4] | These searches were conducted using The Pi Searcher website: http://www.angio.net/pi/bigpi.cgi |

[5] | Matthew Smith has pointed out in conversation that this appears similar to finding Stephen Hawking's intitials in the cosmic background radiation. The authors of that paper argue that any pattern is a posteriori, that is, apophenic. |

## References

Behe, M. J. (1996). Darwin’s black box. New York, NY: Free Press.

Ellis, D. J. (1978). The mediumship of the tape recorder. London: D. J. Ellis.

Gardner, M. (1991). Fractal music, hypercards, and more. New York, NY: W. H. Freeman.

Mandelbrot, B. B. (1983). The fractal geometry of nature. New York, NY: W. H. Freeman.

Mandelbrot, B. B. (1997). Fractals and scaling in finance. New York, NY: Springer.

Maor, E. (2009). e: The story of a number. Princeton, NJ: Princeton University Press.

Monod, J. (1971). Chance and necessity. New York, NY: Knopff.

Posamentier, A. S. & Lehmann, I. (2004). Pi: A biography of the world’s most mysterious number. Buffalo, NY: Prometheus Books.

Puente, C. E. (2000). DNA, \(\pi\), and the bell. Complexity, 6(2), 16–22.

Puente, C. E. (2003). Treasures inside the bell: Hidden order in chance. London: World Scientific.