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Anomalistics: Apophenia & Periphenia

Jake Shannon – October 03, 2016

It is obvious that knowledge changes over time. For example, Ptolemaic cosmology gave way to the Copernican view of the universe, Lamarck’s worldview overtook the Creationists view of biology, which, in turn, was replaced by Darwin’s, and both Einstein’s Relativity and Quantum Physics have superseded Newton’s classical mechanics. Each time, a revolutionary new model came along to replace the old one, only to be eventually replaced by an even better model.

But how do we know when to switch from the old model to the new one? At the very heart of these revolutions is Anomalistics. Few talk more concisely about the subject than Marcelo Truzzi:

Anomalistics has two central features. First, its concerns are purely scientific. It deals only with empirical claims of the extraordinary and is not concerned with alleged metaphysical, theological or supernatural phenomena. As such, it insists on the testability of claims (including both verifiability and falsifiability), seeks parsimonious explanations, places the burden of proof on the claimant, and expects evidence of a claim to be commensurate with its degree of extraordinariness (anomalousness). Though it recognizes that unexplained phenomena exist, it does not presume these are unexplainable but seeks to discover old or to develop new appropriate scientific explanations.

As a scientific enterprise, anomalistics is normatively skeptical and demands inquiry prior to judgement, but skepticism means doubt rather than denial (which is itself a claim, a negative one, for which science also demands proof). Though claims without adequate evidence are usually unproved, this is not confused with evidence of disproof. As methodologists have noted, an absence of evidence does not constitute evidence of absence. Since science must remain an open system capable of modification with new evidence, anomalistics seeks to keep the door ajar even for the most radical claimants willing to engage in scientific discourse. This approach recognizes the need to avoid both the Type I error – thinking something special is happening when it really is not – and the Type II error – thinking nothing special is happening when something special, perhaps rare, actually occurs (Truzzi, 1979a and 1981). While recognizing that a legitimate anomaly may constitute a crisis for conventional theories in science, anomalistics also sees them as an opportunity for progressive change in science. Thus, anomalies are viewed not as nuisances but as welcome discoveries that may lead to the expansion of our scientific understanding (Truzzi, 1979b).

As children, many of us look at the moon and see a face. Our minds find a pattern where none exists. Type I errors are better known as false positives and Type II errors as false negatives. Fortunately, terms like “Pareidolia” and “Apophenia” (as coined by Nazi psychiatrist Klaus Conrad) already exist to describe Type I errors. In our reasoning we strive to avoid both Type I and II errors but, until recently, there hasn’t been a term for the equally, if not more dangerous, tendency toward Type II errors. I coined the term “Periphenia” in 2009 to describe these Type II errors. Detecting periphenia is key to anomalistics.

Michael Shermer (the founding publisher of Skeptic Magazine) coined his own term as well, “patternicity”, and it seems to describe the relationship between Apophenia and Periphenia quite well:

Harvard University biologist Kevin R. Foster and University of Helsinki biologist Hanna Kokko …demonstrate that whenever the cost of believing a false pattern is real is less than the cost of not believing a real pattern, natural selection will favor patternicity. (Shermer 2008)

Shermer then gives a simple, put powerful example of the importance of guarding against periphenia:

For example, believing that the rustle in the grass is a dangerous predator when it is only the wind doesn’t cost much, but believing that a dangerous predator is the wind may cost an animal its life.” (ibid)

Such concerns aren’t just theoretical, however. Premier mathematician (and father of fractal geometry) Benoit Mandelbrot reminds us of the practical importance:

So on August 4, the Dow Jones Industrial Average fell 3.5 percent. Three weeks later, as news from Moscow worsened, stocks fell again, by 4.4 percent. And then again, on August 31, by 6.8 percent…

The standard theories, as taught in business schools around the world, would estimate the odds of that final, August 31, collapse at one in 20 million — an event that, if you traded daily for nearly 100,000 years, you would not expect to see even once. The odds of getting three such declines in the same month were even more minute: about one in 500 billion. Surely August had been supremely bad luck, a freak accident, an ‘act of God’ no one could have predicted. In the language of statistics, it was an ‘outlier’ far, far, far from the normal expectation of stock trading.

Or was it? The seemingly improbable happens all the time in financial markets. A year earlier, the Dow had fallen 7.7 percent in one day. (Probability: one in 50 million) In July 2002, the index recorded three steep falls within seven trading days. (Probability: one in four trillion) And on October 19, 1987, the worst day of trading in at least a century, the index fell 29.2 percent. The probability of that happening, based on the standard reckoning of financial theorists, was less than 105—odds so small they have no meaning. It is a number outside the scale of nature. You could span the powers of ten from the smallest subatomic particle to the breadth of the measurable universe–and still never meet such a number.” (Mandelbrot and Hudson 2004)

The anomaly that Mandelbrot notes is a huge and glaring one; price changes modeled using a Gaussian ‘normal’ distribution will routinely overlook ‘outliers.’ Outliers live in the tails of distributions(tails that in financial markets should be much fatter[1]).

Perhaps the most well-known contemporary popularizer of the dangers of periphenia is Nassim Taleb, although he calls them “Black Swans” (a nod to the brilliant Scottish cartographer of inductive reasoning, David Hume) but there have been others. In 1919, his book The Book of the Damned, Charles Fort promoted the idea that social values (what philosopher of science Thomas Kuhn would later call ‘paradigms’) influence what scientists consider “true” or not. Charles Fort promoted his magazineThe Fortean Times upon the strength of the demand for the novel and unusual. It was this spirit that also fostered the success of Robert Ripley in the early twentieth century. His ‘Ripley’s Believe It or Not’ cartoon strip started its very own cottage industry of books, television shows, and museums here in America.

Later, in the 1960s, American physicist and writer William R. Corliss began his own documentation of scientific anomalies along much more conservative lines than Fort. Corliss claims to be at least partially inspired by Fort and went so far as to check some of Fort’s sources. Corliss concluded that Fort left more work to be done with regard to the cataloging of scientific anomalies (Corliss, A Search for Anomalies 2002).

My second unanticipated discovery made me realize that anomalies were common in all branches of science. This happened in 1953 in the library at the University of Colorado when I was trying to find out what was known about the solar spectrum in the far ultraviolet. (The Physics Department had spectro-grams of the sun taken at high altitudes during flights of captured V-2 German rockets.) Right next to a book I desired was Charles Fort’s The Book of the Damned. Naturally, I had to take out that book, too. It turned out to be chock full of anomalies of all sorts, all of which Fort had extracted from major science journals prior to 1930. Fort designated these anomalies as ‘damned’ because they were generally ignored by mainstream science. (Corliss 2002)

In Unexplained! author Jerome Clark explains the difference between Corliss and Fort by saying that Corliss is “more interested in unusual weather, ball lighting, geophysical oddities, extraordinary mirages, and the like — in short, anomalies that, while important in their own right, are far less likely to outrage mainstream scientists than those that delighted Fort, such as UFOs, monstrous creatures, or other sorts of extraordinary events and entities” (Clark 2003, 466-467). The study of the unusual or paranormal in psychology is called parapsychology, and it has begun to attract serious attention in academic and intelligence circles, although most people aren’t aware of the research. ESP (extra-sensory perception) has received the most attention.

One form of ESP that has received vast amounts of study and funding (both from public and private sources) has been ‘remote viewing.’ Remote viewing is the act of attaining information about some person, place, or thing in particular without engaging one of the five senses. Following the declassification of documents related to the 20 million dollar ‘Stargate Project’[2], [3]sponsored by the U.S. Federal Government in the 1990s, ESP surfaced as a subject that was no longer taboo to study. Not all the programs in parapsychology are governmental, however; some are actually thriving in academia. The ubiquitous Rockefeller money funded the Princeton Engineering Anomalies Research (aka PEAR) for many years before they closed their doors. Goldsmiths, University of London, has the Anomalistic Psychology Research Unit[4] and Garret Moddel at University of Colorado, Boulder, offers an ‘Edges of Science Course,’[5] among others.

One of the largest private institutions to seriously research parapsychology is SRI International,[6] based in Menlo Park, California. In 1970, the entity was spun off from Stanford University to become an independent non-profit research organization. The U.S. Government funded the psychic research at SRI until 1989. In 1974, two of its research scientists Hal Putoff[7] and Russell Targ published the first full-length peer-reviewed paper on telepathy in Nature titled ‘Information transfer under conditions of sensory shielding’ (Putoff and Targ 1974).

In 1990, government funding for this type of research transitioned to Science Applications International Corporation (SAIC) under the direction of Dr. Edwin May, who had been employed in the SRI program since the mid-1970s and had been Project Director from 1986 until the close of the program.

In 1988, Edwin May and his colleagues analyzed all psi experiments conducted at SRI since 1973. The analysis was based on 154 experiments, consisting of more than 26,000 separate trials, conducted over those sixteen years. Of those, just over a thousand trials were laboratory remote-viewing tests. The statistical results of this analysis indicated odds against chance of 1020 to one (that is, more than a billion billion to one) (Radin 1997, 107). To repeat Mandlebroit’s words quoted earlier:

The probability of that happening, … was less than 105—odds so small they have no meaning. It is a number outside the scale of nature. You could span the powers of ten from the smallest subatomic particle to the breadth of the measurable universe—and still never meet such a number. (Mandelbrot 2004, 3-4)

In 1995, the US Congress asked two independent scientists to assess whether the $20 million that the government had spent on psychic research had produced anything of value. One of the reviewers was Jessica Utts, a statistics professor at the University of California, Irvine, and an author of textbooks on statistics, who maintained that there had been a statistically significant correlation:

It is clear to this author that anomalous cognition is possible and has been demonstrated. This conclusion is not based on belief, but rather on commonly accepted scientific criteria. The phenomenon has been replicated in a number of forms across laboratories and cultures (Utts 1995).

The other scientist, Ray Hyman, while skeptical said “I agree with Jessica Utts that the effect sizes reported in the SAIC experiments and in the recent ganzfeld studies probably cannot be dismissed as due to chance” (Hyman 1996 ). Despite this, the program was shut down in 1995 for failing to find convincing evidence that it had any value to the military or intelligence community.

Are the statistics used to study Psi phenomena creating a Type I error due to bad experiment design (the use of Gaussian distributions to approximate randomness as a benchmark)? Are the social sciences like ‘parapsychology’ plagued by the same problems as financial modeling? Maybe, our expectations of human abilities aren’t wrong; maybe, it is our understanding of randomness and chance that needs reformulating.

The unlikely financial event of Black Monday happened, despite overwhelming odds and so have the positive events in the test for remote viewing. Does this tell us something anomalous about the nature of reality (for example, that ESP exists) or does it tell us that our benchmark of measuring chance (randomness via a Gaussian distribution) is wrong? As outrageous as it may seem, I’d venture to say the latter would generate more opposition than the former since it would require a revision of an enormous amount of our current scientific ‘knowledge.’ That is to say, I bet that scientists would prefer to include parapsychology under the penumbra of science than to revise all the inductive knowledge that has modeled chance by using Gaussian distributions.

So if our analogy for chance is misleading, how else are these Psi phenomena being explained away? Famed neuroscientist Michael Persinger has noted correlations between repeated paranormal experiences and geomagnetic phenomena as early as 1985. He researched 25 published cases of profound paranormal activity and their correlations to global geomagnetic activity at the time of their occurrence. Every reported experience happened on days that exhibited geomagnetic activity that was less than the norm for those particular months of the year. The results were “commensurate with the hypothesis that extremely low fields, generated within the earth-ionospheric cavity but disrupted by geomagnetic disturbances, may influence some human behavior” (Persinger 1985).

Persinger went on to create what has come to be called the ‘God Helmet,’ a helmet equipped with electromagnetic field-emitting solenoids on the sides aimed at the temporal lobes of the wearer.

Persinger has tickled the temporal lobes of more than 900 people before me and has concluded, among other things, that different subjects label this ghostly perception with the names that their cultures have trained them to use – Elijah, Jesus, the Virgin Mary, Mohammed, the Sky Spirit. Some subjects have emerged with Freudian interpretations – describing the presence as one’s grandfather, for instance – while others, agnostics with more than a passing faith in UFOs, tell something that sounds more like a standard alien-abduction story. (Hit 1999)

So it seems that there may be some sort of connection between the paranormal and EMF or geomagnetic field (GMF) activity. However, the questions persist: do electromagnetic fields create hallucinations or augment our perceptions, yielding way to a deeper level of awareness? Are psychic phenomena happening more often than what chance would predict or is our idea of chance wrong? Again, a position other than agnosticism at this point seems overreaching, even arrogant. Even noted author and proponent of scientific skepticism Sam Harris writes:

While there have been many frauds in the history of parapsychology, I believe that this field of study has been unfairly stigmatized. If some experimental psychologists want to spend their days studying telepathy, or the effects of prayer, I will be interested to know what they find out. And if it is true that toddlers occasionally start speaking in ancient languages (as Ian Stevenson alleges), I would like to know about it. However, I have not spent any time attempting to authenticate the data put forward in books like Dean Radin’s The Conscious Universe or Ian Stevenson’s 20 Cases Suggestive of Reincarnation. The fact that I have not spent any time on this should suggest how worthy of my time I think such a project would be. Still, I found these books interesting, and I cannot categorically dismiss their contents in the way that I can dismiss the claims of religious dogmatists. (Harris 2009)

Radin is one of a cadre of statistically trained parapsychologists shaping a paradigm that is attempting to integrate psychic phenomena into mainstream science. Many of these parapsychologists leverage the ideas of quantum mechanics to validate their new paradigm, in particular the concept of a Zero-Point Field. In her book The Field, bestselling author Lynne McTaggart talks about Zero-Point energy. In it she makes the argument that since everything in the universe is connected and we too are part of this vast dynamic web of energy exchange, supernatural phenomena make sense ‘scientifically.’ Radin is the standard bearer here.

Scientist Dean Radin says it very succinctly: ‘The fact that quantum objects can become entangled means that the common sense assumption that ordinary objects are entirely and absolutely separate is incorrect.’

Quantum theory implies that the universe is a single integrated system containing innumerable subsystems. Everything in it is ‘entangled’ with everything else. But what’s so ‘spooky’ about that? It is, after all, what the word ‘universe’ means. It’s only ‘spooky’ if the idea of being a part of a larger entity is disturbing to you.

We are trained from birth to see things as disconnected. Our language does it. Learning is as much learning NOT to see as it is learning to see. What a child sees initially is an undifferentiated whole. By careful training it learns to carve pieces out of that reality and look at them as separate material objects. But why should that be considered more ‘real’? It’s just one way of seeing. People with greater ability to communicate telepathically aren’t ‘gifted’–they simply haven’t been as thoroughly indoctrinated. Instead of asking why some people (perhaps everyone at birth) can communicate telepathically, we should be studying the mechanism that enables us to shut out that information most of the time. (Slater 2009)

Parapsychologists like Radin have been accused of abusing the anomalies, enigmas, and confusing nature of quantum mechanics into some sort of explanation of psi phenomena (for example, see James Alcock’s Parapsychology’s Past Eight Years: A Lack-of-Progress Report 1984). Again, extraordinary claims require extraordinary proof.

More generally, we have learned that our colleagues’ tolerance for any kind of theorizing about psi is strongly determined by the degree to which they have been convinced by the data that psi has demonstrated. We have further learned that their diverse reactions to the data themselves are strongly determined by their a priori beliefs about and attitudes toward a number of quite general issues, some scientific, some not. In fact, several statisticians believe that the traditional hypothesis testing methods used in the behavioral sciences should be abandoned in favor of Bayesian analyses, which take into account a person’s a priori beliefs about the phenomenon under investigation (e.g., Bayarri & Berger, 1991; Dawson, 1991). (Bem and Honorton, 1994)

The anomalist is skeptical of skepticism and as such seeks evidence that challenges the status quo. It isn’t nihilistic; it is creative destruction like the demolition of an old building in favor of a newer, more functional and accommodating one. This isn’t relativism since the anomalist doesn’t hold that all belief systems are equal. Ultimately, the anomalist stands opposed to the problems presented by the centralization of meaning and isn’t afraid to present evidence that may subvert the dominant paradigm, whether it be a scientific, political, or cultural one. To paraphrase David Hume, the anomalist “proportions his belief to the evidence.”

In the final analysis, however, we suspect that both one’s Bayesian a prioris and one’s reactions to the data are ultimately determined by whether one was more severely punished in childhood for Type I or Type II errors. (ibid.)

Anomalies, however, can be a real blessing to those that are inclined to pay sincere attention to them.

Scientific development depends in part on a process of non-incremental or revolutionary change. Some revolutions are large, like those associated with the names of Copernicus, Newton, or Darwin, but most are much smaller, like the discovery of oxygen or the planet Uranus. The usual prelude to changes of this sort is, I believed, the awareness of anomaly, of an occurrence or set of occurrences that does not fit existing ways of ordering phenomena. (Emphasis added) (Kuhn 1977, xvii)

In closing, I would like to quote the Principia Discordia:

The Aneristic Principle is that of APPARENT ORDER; the Eristic Principle is that of APPARENT DISORDER. Both order and disorder are man made concepts and are artificial divisions of PURE CHAOS, which is a level deeper that is the level of distinction making. With our concept making apparatus called “mind” we look at reality through the ideas-about-reality which our cultures give us.

Type I errors would correspond to apophenia, false positives, creating meaning out of meaningless noise or the Aneristic Principle while Type II errors are related to periphenia, false negatives, dismissing meaningful data as meaningless or the Eristic Principle. Hail Eris!

[1] In stark contrast to the Gaussian distributions used by Sharpe and Markowitz, Mandelbrot suggests a much better distribution, one with much fatter tails — a Cauchy distribution. It is sometimes known also as a Lorentzian distribution. For those who speak the language of statistics, a Cauchy-Lorentz distribution has no moment generating function (“moments” in statistics simply represent the mean, i.e., first moment, the variance, the second moment, the skewness, the third moment, and kurtosis, the fourth moment.

For a Cauchy, the first moment is non-existent and the second moment is infinite, which seem like much better assumptions for modeling the unknown. While a Cauchy distribution might over estimate volatility, it is better to be overcautious when wagering with other people’s money (or the entire global financial system for that matter). This is why it is crucial to increase the statistical power of our inductive reasoning, and by ‘statistical power,’ I mean specifically the probability of rejecting false negatives, aka “Periphenia” (this might favor more of a Bayesian approach than a frequentist or Neyman-Pearson approach to statistical power, in my opinion).

[2] Other such covert research programs sponsored by the CIA went by names like ‘Sun Streak’ and ‘Grill Flame’.

[3] Under the Freedom of Information Act, you can request for STARGATE (remote viewing program) RECORDS that have been released up to the current date. The entire collection totals 89,900 pages in nearly 12,000 documents.

[7] It is rather interesting that three of the most influential figures within the remote viewing program, Puthoff and remote viewers Ingo Swann and Pat Price, have all achieved the high ranks within L. Ron Hubbard’s Scientology system, with Puthoff and Swann achieving the highest rank at the time, Operating Thetan VII.


Clark, Jerome. Unexplained! Detroit: Visible Ink Press, 2003.

Corliss, William R. “A Search for Anomalies.” Journal of Scientific Exploration 16, no. 3 (2002): 439-453.

Bem, Daryl J., and Honorton, Charles. “Does Psi Exist? Replicable evidence for an anomalous process of information transfer.”Psychological Bulletin 115 (1994): 4-18.

Harris, Sam. “Response to Controversy.” Sam Harris. August 11, 2009. http://www.samharris.org/site/full_text/response-to-controversy2/ (accessed October 10, 2009).

Hit, Jack. “This is Your Brain on God.” Wired (Online), November 1999.

Hyman. “Evaluation of a program on anomalous mental phenomena.” Journal of Scientific Exploration, 1996 : 39-40.

Kuhn, Thomas S. The Essential Tension: Selected Studies in Scientific Tradition and Change. University of Chicago Press, 1977.

Mandelbrot, Benoit. The (Mis)behavior of Markets. New York: Basic Books, 2004.

Persinger, Michael A. “Geophysical Variables and Behavior:XXX. Intense Paranormal Experiences Occur during Days of Quiet, Global, Geomagnetic Activity.” Perceptual and Motor Skills 61, no. 320 (1985).

Putoff, Hal, and Russell Targ. “Information transfer under conditions of sesory shielding.” Nature 252, no. 5476 (October 1974): 602-607.

Radin, Dean. The Conscious Universe. New York: HarperCollins, 1997.

Shermer, Michael. “Patternicity.” Scientific American, December 2008.

Slater, Philip. “Why What Frightens ‘Skeptics’ Frightened Einstein.” The Huffington Post. April 8, 2009.http://www.huffingtonpost.com/philip-slater/why-what-frightens-skepti_b_184778.html (accessed Ocober 10, 2009).

Truzzi, Marcello. “Anomalistics: The Perspectives of Anomalistics.” Skeptical Investigations. 1998.http://skepticalinvestigations.org/anomalistics/perspective.htm (accessed October 10, 2009).

—. “On Pseudo-Skepticism.” Zetetic Scholar, 1987: 12-13.

Utts, Jessica. “An Assessment of the Evidence for Psychic Functioning.” UCDavis: University of California–Department of Statistics. 1995. http://anson.ucdavis.edu/~utts/air2.html#copyright (accessed October 10, 2009).

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