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Elliot BenjaminElliot Benjamin is a philosopher, mathematician, musician, counselor, writer, with Ph.Ds in mathematics and psychology and the author of over 150 published articles in the fields of humanistic and transpersonal psychology, pure mathematics, mathematics education, spirituality & the awareness of cult dangers, art & mental disturbance, and progressive politics. He has also written a number of self-published books, such as: The Creative Artist, Mental Disturbance, and Mental Health. See also:


Agnosticism, Probability
and Apophenia

Elliot Benjamin

Last week I was in the Caribbean, fully expecting a complete break from anything resembling finding meaningful patterns in license plates. And I am almost embarrassed to have to report that as my significant other and I were walking into the nearby town from our resort, I could not help but notice the license plate on the first car parked in front of me—and yes I saw another “496.” But this time the numbers were not in succession, as it was “4696” and I laughed to myself that this was coincidence—not synchronicity. But soon I could not help wondering why a few minutes later when we went into a novelty shop in the town there were license plates on display in the store and the very top license plate had the number “496” and this time it was in clear succession.

David Lane [1] portrays this as “apophenia,” which he describes in his recent Integral World article [2] to be a term defined as follows: “unmotivated seeing of connections [accompanied by] a specific feeling of abnormal meaningfulness.” And David went to much trouble in his article "Apophenia and the Intentional Fallacy" [2] to fully demonstrate why the examples I described in my Integral World License Plate Synchronicity article [3] were nothing more than illustrations of apophenia, which he explains can be thought of more commonly as “the Intentional Fallacy.”

Let me say at the outset that I have much respect and admiration for David Lane, as I became familiar with his name in the 1980s from his astute portrayal of the falsification of the historical basis of the modern version religion of Eckankar as described by it's 1960s founder Paul Twitchell [4]. I actually share much of David's perspective in regard to not jumping to mystical conclusions and keeping an open-minded scientific perspective to explain unusual phenomena, and I referenced David's book about Eckankar in my own Modern Religions book [5]. However, where David Lane and I part company appears to be in the context of what it means to truly have an open-minded scientific perspective, which for me is akin to having a truly “agnostic” perspective in the context of religious and spiritual matters.

David portrays a highly traditional quantitative laboratory science model to ascertain the laws of the universe, and as a mathematician I fully appreciate and am immersed in the kind of logic and scientific scrutiny that David promotes. But as William James described just about a hundred years ago in his philosophy of “radical empiricism” [6], in order to make sense of the deepest and most mysterious phenomena that a human being experiences, it is incumbent upon us to utilize a wide variety of methods that run the gamut from quantitative scientific objectivity to qualitative phenomenological understanding of the deepest experiences of others, to self-immersion into the researcher's own experiences. Perhaps a brief quote describing James' ideas of radical empiricism will help illustrate what he meant (with italics as quoted):

“Any and all sources of evidence, ways of knowing, and ways of working with and expressing knowledge, findings, and conclusions can be brought to bear on the issues being researched. Both emic and ethic; both subjective/experiential and objective/observational modes of knowing, are recognized and honored. There is an epistemological stance of what William James (1912/1976) called radical empiricism—a stance that excludes anything that is not directly experienced but includes everything that is directly experienced, by anyone involved in the research effort. Thus, the researcher participants' subjective experiences and self-perceptions are treated as valid data, as are the experiences and perceptions of the investigator. There is an important place for intuitive, tacit, and direct knowing, for various arational ways of processing information; and for a variety of forms of creative expression in conducting and communicating research.” [7].

I realize that David Lane will likely say yes, but this is not science. In other words, he will likely say that it is fine to use our subjective experiences but that we should not consider it “science.” Well he is correct that traditional science calls for objectivity in as strict a sense as possible. But I believe that when we are studying the deepest realms of human experience, subjectivity becomes essential to truly gain understanding of what these experiences are all about. This was one of Ken Wilber's key points in his description of experiential knowledge in his book Eye to Eye [8], and it is also a foundation of what is referred to as “extended science” [9].

But the point is not to accept any and all subjective portrayals as legitimate scientific knowledge—I am every bit as skeptical as David Lane in regard to many of these kind of “new age” subjective portrayals of esoteric phenomena. It is indeed strange for me to realize that I have been lumped into this mystical believer category by David Lane, and it is a good exercise for me to try to not react defensively but to honestly question myself in the light of these accusations. And what I come up with is once again the mathematics involved.

In my recent Integral World Synchronicity and Mathematics article [10], I said that I would welcome mathematical responses regarding any of my probability calculations in which it appeared to me that the mathematical probability of some of the license plates that I witnessed was so incredibly small that I could not logically believe that chance factors could entirely explain them. I believe I made it clear that I was talking about a series of three or four numbers or letters within a full license plate depiction of 6 or 7 possible slots, as I gave a number of concrete illustrations of this. I also believe I made it clear that I made the theoretical assumption that I was looking at a multitude of license plates at the rate of 1 per second for a few hours, thereby taking into account numerous “misses.”

But the crux of my mathematical argument involved the succession of different events taking place, in which the probabilities of independent events become multiplied. This is the basis in which I argued against the Lanes' description of the Littlewood Law of Miracles and their Desultory Decussation [11] to explain what I referred to as my license plate synchronicities. And I am still left with these same questions, as David Lane has chosen to not respond to my mathematical portrayals, claiming that the “easier, even more rudimentary explanation for the phenomenon” is the fallacious meaning that I have imparted to these “random” events.

While I am still eager to receive a mathematical response to how I portrayed what I understand to be an astronomically low probability of particular events taking place, at this point I can only respond to the argument that David Lane utilized to show the “unscientific” nature of what I described in my articles.

Of course my portrayals were motivated by my personal circumstances, whether they were involved with my upset of losing my mental health job, my love of numbers and amazement at seeing “496” right after I gave my “496” perfect number lesson to my son and his friends, the exact four digits of the ages of my “significant other” and son a few days after their birthdays just as I was thinking about this, or the exact first seven letters of my deceased mother's name.

But ironically, all of this is not necessarily beyond scientific explanation if one enters the realm of quantum physics, where if my limited understanding of quantum physics is correct, thoughts can indeed affect physical realities and “spooky action at a distance” is the norm. I believe that the Lanes have frequently referred to these kinds of incredible occurrences in the world of quantum physics [12], and I wonder if perhaps they have a partial misunderstanding of my views in this realm.

My views are what I would refer to as “agnostic,” meaning that I am open to various interpretations of the events, and these various interpretations include chance factors as well. But from what I understand of the mathematical probabilities involved, these chance factors appear to me to be extremely unlikely to fully explain certain events that I have experienced, and yes I am still thinking in particular of my “496” license plate experiences, and this is where I am open to other explanations. As the Lanes have argued [12], at least as far as I understood them, the distinction between what we think of as spirituality and science may be much less than we realize. This is actually the crux of one of my own recent Integral World articles as well [13], and when I use the term “spiritual” this is what I have in mind.

I wonder if perhaps “some” of the clash between the Lanes and myself is involved with semantics, but at any rate I sincerely invite the Lanes and anyone else to engage in respectful dialogue with me—without sarcasm and condescending remarks. I know we are all trying with the best of our abilities to truly understand the nature of who we are and what the world is, regardless of what we call it by name—science, spirituality, quantum physics, or God.

As I stated above, it has been an exercise on my part to try my best to not react defensively to David Lane's article, and seeing the subtitle of his article: “Why License Plates are Not Messages from the Beyond” with the Texas 1968 Trailer “496” license plate number, I must admit that it was challenging for me to keep my calm. I realize that my use of the terms “scientistic” and my reference to '''fundamentalist' allegiance to rigid dogmatic narrow-minded beliefs that are dressed up in a scientific language but in actuality are completely the opposite of the true nature of open-minded scientific investigation” [10] was not received well by the Lanes, and I can somewhat understand the sarcastic and condescending tone of David Lanes's response article.

Perhaps this is why David chose to utilize a number of phrases that I of course found quite insulting, but more importantly I feel that he misrepresented the agnostic open-ended extended science perspective that I engage in. I am referring to David's use of phrases such as “Kids do it all the time at school, but they don't then proceed to scientifically argue that something 'magical' is transpiring”; “(given his predisposition in finding meaning in these things) used the same as illustrative of a mysterious synchronicity”; “I think it is the height of hubris to think that the universe is contouring to my internal whims”; “At this stage, one might think that Elliot is suffering from apophenia which 'is the experience of seeing meaningful patterns or connections in random or meaningless data'” [2].

I could continue to give more examples but my main point is that the tone of David Lane's article appears to me to be quite out of character for him in anything else I have read in the Lanes' Integral World articles. I find this disturbing, as I do not think it is conducive to the kind of respectful philosophical dialogue that Integral World has been designed for. I think that David Lane and I can disagree with one another in mutually respectful ways, and I will accept my share of the blame in some of the language I have used as well.

But getting back to the thrust of my open-ended agnostic perspective, for me it all goes back to what William James described as radical empiricism in an extended science context.

I would like to conclude this continued public dialogue with David Lane by ending with a mathematical illustration that relates to how I began this article. So I am back in the Caribbean and I am walking past a few cars and the first license plate I notice says “4696.” I do some quick mathematical calculations and come up with something like a probability of perhaps 1 in 2000, utilizing the same kind of probability assumptions as I did in my Synchronicity and Mathematics article [10] and taking into account that the “496” is not in succession. But then in a few minutes I see the “496” in succession at the top of the pile of license plates in a novelty store, and I'll assign the probability of something like 1 in 10,000, taking into account there are 6 slots of possibilities. Finally, since these two events are mathematically independent to the best of my knowledge, I multiply the probabilities together to arrive at (1/2000) X 1/10,000) = (1/20,000,000) = 1/20 million. As I described in my previous Synchronicity and Mathematics article [10], this is the kind of problem I have with explaining highly unusual events completely by chance and coincidence, and why I continue to be open to alternative explanations, in whatever terms one is comfortable in using—science, spiritual, etc.

And I am even open to chance and coincidence as the full explanation, but thus far the probability of nothing other than chance and coincidence and “apophenia” as explanations still appears to me to be logically highly unlikely, to say the least. My mathematical probability estimations are meant to be merely illustrative of possibilities, and I welcome mathematical responses in regard to more accurately describing these probabilities in regard to how the Motor Vehicles Bureau assigns license plate numbers and letters, as well as to the actual mathematical calculations. But at this point I must respectfully disagree with David Lane that the most logical way of explaining what I have referred to as my license plate synchronicities are by chance, coincidence, and “apophenia.”


1) I am responding specifically to David Lane in the Lanes' recent Integral World article Apophenia nd the Intentionality Fallacy, as David has included a number of personal examples in his article and the article is written in the first person.

2) See David and Andrea Lane (2010), Apophenia and the Intentional Fallacy. Integral World website;

3) See Elliot Benjamin (2010), License Plate Synchronicity. Integral World website;

4) See David Lane (1983), The Making of a Spiritual Movement: The Untold Story of Paul Twitchell and Eckankar. Del Mar, CA: Del Mar Press.

5) See Elliot Benjamin (2005), Modern Religions: An Experiential Analysis and Expose'. Swanville, Maine: Natural Dimension Publications.

6) See William James (1976). Essays in Racial Empiricism. Cambridge, MA: Harvard University Press. (Original work published 1912)

7) See William Braude and Rosemary Anderson (1998), Transpersonal Research Methods for the Social Sciences: Honoring Human Experiences. London: Sage (quote on page 241).

8) See Ken Wilber (2001), Eye to Eye: The Quest for the New Paradigm. Boston: Shambhala.(Original work published 1983).

9) See Brian Josephson & Beverly Rubik (1992), The Challenge of Consciousness Research. Frontier Perspectives, 3(1), 15-19; and reference [7] above.

10) See Elliot Benjamin (2010), Synchronicity and Mathematics. Integral World website;

11) See David and Andrea Lane (2010), Desultory Decussation: Where Littlewood's Law of Miracles Meets Jung's Synchronicity. Integral World website;

12) See David and Andrea Lane (2010, Mysterium Tremendum. Integral World website;

13) See Elliot Benjamin (2010), Perhaps Science and Spirituality Can Go Together. Integral World website;

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