Apparent Complexity and Underlying Simplicity

© Richard Bolstad

Our Admiration of Complexity

Life appears vastly complex. That is part of its beauty. Whether we study the tiniest subatomic particles or the vastest galaxies in their splendour, the world is intricate and it is simply not possible for us to comprehend its complexity with the number of neural connections we have. The part cannot understand the whole. At the same time, this complexity is self-organised at every level from the most elegant and simple algorithms. Physics emerges from a few simple laws, and biological evolution from a few simple principles and a molecule with very basic repeated parts. The science of Complexity Theory (Chaos theory) helps us understand this paradox and even to use it in change work.

In the 1970s, Professor Alex Bavelas of Massachusetts Institute of Technology completed an intriguing series of experiments. Two subjects are in separate rooms studying photos of human cells. They have been told that some of these cells are healthy and some are sick. Each time a photo is shown they either press the “healthy” button or the “sick” button, and two signal lights tell them whether their guess was “right” or “wrong”. The first subject gets correct feedback, and within half an hour he is able to guess correctly 80% of the time. The second subject, unknown to him, is getting almost random feedback, because he is getting the feedback from the first person’s guesses. There is, therefore, no way the second person can find out what identifies healthy cells. However, this does not stop the second person from developing a theory and believing that they are learning to distinguish sick from healthy cells. Their theory is necessarily convoluted: eg “a cell is sick if it has this shape, unless it has this colour or two of these patterns” and so on. This second theory is of course a complete delusion. It has no basis in reality whatsoever.  

After half an hour, the two subjects have a tea break, and invariably, they chat about the experiment and share ideas. The first person has worked out the simple distinctions that enable one to see which cells are sick and which are healthy most of the time. The second person also has a theory about how to tell healthy from sick, and it is a very complex one. Every time the experiment is run, the first person now becomes convinced that they have been naive. The second person’s theory seems absolutely brilliant to them. It has so many subtle nuances that they never noticed. They immediately accept it as true. When the two subjects go back to their experiment, the first person now performs as badly as the second person. They have been convinced by the delusions. Bavelas points out that once someone has a theory about what is going on, contradictory evidence does not actually cause them to abandon their theory; it causes them to elaborate that theory with more and more complex provisos. Furthermore, people are actually attracted to more complex, elaborate theories; they think they are somehow intrinsically more intelligent.

Paul Watzlawick quotes Gregory Bateson’s comment about such experiments. Bateson was interested in schizophrenia. He said that the schizophrenic would be the person who claimed “These buttons don’t mean anything. Someone in the other room switches the light whenever he feels like it (Watzlawick, 1976, p 48-54) Watzlawick sites an important example of this research in real life. Freudian psychotherapists believed that their elaborate method of dealing with phobias, involving perhaps ten years of psychotherapy, was the correct approach, and explained that phobias had a very complex inner structure involving repressed childhood “Oedipal” fears of castration. In the 1960s, behaviour therapists showed that they could cure phobias in a few weeks using conditioning processes. Freudian psychoanalyst Leon Salzman explained that it was obvious that the behaviour therapist “defines the condition in a way that is acceptable only to conditioning theorists and does not fulfil the criteria of the psychiatric definition of this disorder. Therefore, his statements should not apply to phobias, but to some other condition.” Since a phobia is defined as an oedipal fear, Salzman says, defining it as a simple anchored response means that some other condition is being treated. On the other hand, since a phobia represents repressed childhood fear by definition, then only psychoanalysis of that childhood fear can relieve it.

Why does our brain love fancy explanations? Is there an evolutionary advantage in making simple things more complex? Maybe there doesn’t need to be any reason. That’s where “spandrels” become relevant….

Spandrels: Not Everything in Nature is Intentional or Useful

Stephen Jay Gould (Gould and Lewantin, 1979, p. 581) studied an architectural phenomenon called the “spandrel”. In a building that has domed ceilings, such as St Mark’s Cathedral in Venice, there are inevitably tapering triangular spaces between the tops of arches. In medieval times these spaces, called spandrels, were used as the focus of intricate religious art: so intricate and so well designed to fit the space that an unknowing observer would suspect that the space was deliberately created to frame the art. Gould, a biologist, argued that this is an excellent metaphor for many of the phenomena that we observe in biology, such as nipples in men. Men’s nipples may look like some kind of artistic design feature, but they are an evolutionary accident – they occur because the genetic instructions are so valuable to women who breastfeed, and nature had no reason to install some fancy system to remove them in half the species.

An area of the brain called the Fusiform Gyrus is dedicated to recognising human faces, and even newborns will spend more time looking at a human face than at any other object. This has clear survival value for human infants, who need to be able to find a source of food, love and protection fast. It has an obvious spandrel though. Face pareidolia is the tendency to see human faces in other objects. Perhaps the most famous examples are foodstuffs that seem to have a burned area in the shape of a face (often interpreted as the face of a spiritual teacher such as Jesus) and the “face on Mars”. When this rock formation in the Cydonia region on the planet Mars was first photographed by Viking 1 in July 1976, the shadows seemed suggestive of a human face. Clearer photos 20 years later (see below) showed that the irregular hill is not actually a remnant of an ancient civilization but an accidental result of Martian geology (Carl Sagan, 1995, p. 41).

How does this imposition of a familiar pattern on random shadows occur? Impulses from the retina of the eye go first to the lateral geniculate body in the thalamus, where they interact with data from a number of other brain systems. The results are then sent on to the visual cortex, where “seeing” is organised. Only 20% of the flow of information into the lateral geniculate body comes from the eyes. Most of the data that will be organised as seeing comes from areas such as the hypothalamus, a mid-brain centre which has a key role in the creation of emotion (Maturana and Varela, 1992, p 162). What we “see” is as much a result of the emotional state we are in as of what is in front of our eyes. In NLP terminology, this understanding is encapsulated in Alfred Korzybski’s  statement “The map is not the territory”. The map your brain makes of the world is never the same as the real world.

The identification of patterns in perceptual data is increased in psychiatric clients at the time they are first diagnosed schizophrenic, and decreased later in the progress of their “disorder”. “Enhancement of gestalt perception is found in prodromal and incipient schizophrenia, which was characterized by Conrad (1958) as the trema stage. Reduction of gestalt perception is found in chronic schizophrenia, especially in patients with poor premorbid adaptation” (Tschacherand and Junghan, 2008, p. 326). These people seem to be hypersensitive to potential patterns (like conspiracy theorists) and to potential cause-effect relationships between events. It may be that they intentionally dial down this sensitivity later, once they realise that it is not achieving useful results.

Noam Chomsky, whose work was central to the early development of NLP, noted that human language allows for features such as infinite recursion (you can go on meta-commenting on meta-commenting on things as long as you like). This is a feature that is hardly likely to have had adaptive value in the Paleolithic, but which has become extremely important to human philosophers. “We consider the possibility that certain specific aspects of the faculty of language are “spandrels”—by-products of pre-existing constraints rather than end products of a history of natural selection” (Hauser, Chomsky and Fitch, 2002, p. 1574). Chomsky argued that even our immense skill at categorising things may be an ancient spandrel. At first, it was thought that since all human speech contains nouns (even nominalisations) and other aids to categorising, that humans evolved this ability ourselves. “A famous example is categorical perception, which when discovered seemed so finely tuned to the details of human speech as to constitute a unique human adaptation. It was some time before the same underlying perceptual discontinuities were discovered in chinchillas and macaques, and even birds, leading to the opposite conclusion that the perceptual basis for categorical perception is a primitive vertebrate characteristic that evolved for general auditory processing, as opposed to specific speech processing.” Chomsky’s proposal is that the use of categorisation to create language (the ability behind what NLP calls nominalisation) is a spandrel. Categorisation evolved to help us find food etc. and we have only incidentally used it to label things like “depression” and the “oedipal complex”.

Chaos Theory: The Simple Origins of Complexity

In 1980, a New York scientist, Benoit Mandelbrot, working on an IBM computer, created a graph of a mathematical equation, now named after him. Not sure what a “graph of a mathematical equation” is? To start at the beginning: a simple equation can be shown on a graph as a kind of picture. The equation x² + y² = r² creates the picture of a circle (see below). This means that, for any point that appears on the red circle in the diagram below, the x distance and the y distance have a special relationship to each other. That relationship is that “X multiplied by X” plus “Y multiplied by Y”, will always equal “R multiplied by R”. Let’s take an example: if “X” is 3, and “Y” is 4, then we can be sure that “R” will be 5, because 3×3 plus 4×4 = 5×5 (9 + 16 = 25). This is something that a Greek mathematician named Pythagoras wrote in about 500 BCE, though the Babylonians had been using the idea to build buildings at least 1500 years earlier. It makes sense that such a “simple” equation makes a nice simple picture (a circle) on a graph. In a mathematical sense, that pretty circle is just the result of an infinite series of points with the same equation. The circle, mathematically speaking, is a spandrel.

The Mandelbrot picture (Francis, 2025) is made from an equation almost as simple as the one for the circle, an equation written as z = z²+c, where c is any constant number and where z is a “complex number”. A complex number is a kind of imaginary number. Basically, mathematicians have imaginary numbers, just like we have imaginary “things” that don’t exist as solid objects in the real world (honesty, depression, wisdom … what NLP calls nominalisations). To make the Mandelbrot picture we need to “iterate” the equation – we use it on itself again and again.

To get an idea what iteration means in the real world, let’s imagine that we want to know how many rabbits we will have in one year, if we release one breeding pair into the wild today. We discover that one rabbit pair can produce an average of 6 babies every 3 months. But after the second 3 months, the first 6 babies are also sexually mature and can have babies, so there are now 4 pairs of rabbits, each having 6 babies. After the third period of 3 months, there are … a lot of rabbits! Pretty soon it gets hard to add up the numbers, and that is why mathematicians use iterative equations (applying the same equation to itself again and again).

When we do this with the Mandelbrot equation, from a simple equation we get a picture which is at once immensely complex and immensely beautiful. If you zoom in on this picture (below: there is actually a zoomable version online at Francis, 2025) it has more and more detail, and eventually even has little examples of itself inside the picture, which have more little examples inside them and so on. What amazed scientists about the pictures created by the Mandelbrot equation is how such a complex image could emerge from such a simple set of instructions.

Then scientists realized that a lot of the phenomena in nature that we think of as “chaotic” or immensely complex actually emerge from such simple equations. Our bodies emerge from DNA instructions which interact with their environment in just such an iterative way. The intricate workings of a human being cannot be predicted in a linear way from a study of the DNA sequences. But their continuous iterative interactions with the physical, psychological and cultural world, in which they emerge, create this higher order “self-organizing” system.

David Pincus (Pincus, 2008, p. 357) points out that John Gottman’s research on couples relationships shows how iterative processes cascade personal relationships either to continuity or divorce, having an effect that would be hard to predict from the simplicity of the actual interactions. Person A saying something critical rather than something complementary, for example, may lead to Person B saying something critical about Person A’s “critical style” of conversation, which in turn may lead to Person A saying something critical about Person B’s “critical personality” which evades recommendations and focuses on critical styles. By iterating the same process, they are now accusing each other of being broken human beings (a stance that Gottman categorised as “contempt”). Iterating complementary language produces the opposite effect: an atmosphere of mutual adoration. Gottman showed that actual personality tests can find no differences between the “personalities” of couples who have great marriages and the couples who divorce. A couples therapist who buys into their client’s theories about how the other person is a “dependent personality with a damaged attachment style” or has “Oedippal envy” is just buying into a fake over-complex explanation similar to that described in the experiment on identifying healthy vs sick cells, at the start of this article. David Pincus is one of a group of psychologists working towards application of complexity (chaos) theory in psychology. They represent a move away from the elaborate “object-relations” theories of early psychoanalysis, and towards a much simpler basis for understanding what goes on between people and within people.

Perceptual Scope and Categories: Re-simplifying NLP

In 2006, my friend Steve Andreas published a fascinating reformulation of NLP based on two very simple concepts: Scope and Category (The two volume set “Six Blind Elephants”: 2006a and 2006b).

Scope (the range of sensory experience that we attend to) profoundly influences what choices we can make of course, and we are usually unconscious of what choices we have made about this scope. Experimentally, several negative illusions have been described in which areas or aspects of a stimulus field go unnoticed even though they are clearly present. For example, the phenomenon of change blindness is the inability of viewers to observe changes in those parts of a scene on which they are not focused (Milner & Goodale, 1995). Tschacherand and Junghan explain “When reading text from a monitor, readers frequently fail to notice changes in the unattended regions, even if all letters, except those in the line that is being read, are exchanged for meaningless pseudo-letters.” (Tschacherand and Junghan, 2008, p. 320). The famous Gorilla suited man who becomes invisible in a video, once people are asked to attend to the ball throwing in the human group he walks through (Andreas, 2006, p. 5, video below) is another example. Many NLP interventions broaden scope by focusing on the “context” within which a problem occurs or within which it began. By metaphorically “noticing the gorilla” you may get much better ideas.

Categorisation involves the classification of experiences within our scopes, and of course these two variables interact. To make sense of what we experience, our brain classifies “things” we interact with into categories like “living” and “inanimate”, “desirable” and “undesirable”. Steve notes (2006a, p. ix) “Scope and category interact with each other in several ways. A change in scope often changes the way we categorize an experience. As I was writing this, my wife asked me for a “sticky” for a note to put on a letter, and when I offered her a pink one, she said she wanted a yellow one. I categorized this as “picky” and unreasonable, thinking that a pink one would surely do just as well, and felt irritated as I searched for a yellow one. Then I saw that the letter was on bright pink paper; a pink sticky would be nearly invisible on it, so her request for a yellow one was quite reasonable after all! A larger scope changed how I categorized her request, the resulting meaning I made, and my response to her.”

Changing Category Criteria: Our categories are “bound together” by “criteria”, and again many criteria are hidden from conscious evaluation in our daily life. Consider the categorisation of discussions as “friendly” chats vs “arguments”. What criteria make an interaction an “argument”? Bill O’Hanlon (quoted in Andreas, 2006a, p. 150-151) discusses a couple whose marriage was in danger from repeated nasty conflicts. “The counselor suggested that the next time they began an argument that seemed to be getting out of control, they should take a brief break and then meet in the bathroom. The husband should take off all his clothes and lie down in the bathtub. The wife was to stay fully clothed and take a seat next to the bathtub on the toilet. They were then to continue the argument where they had left off. As you might imagine, it was difficult to have an argument that way. The husband felt absurd and exposed and wasn’t his usual self. The wife thought it was hilarious and couldn’t quite work up her usual head of steam. But, as the counselor suggested, for the next several weeks they dutifully performed this task each time they had an argument. After a few times of heading for the bathroom, however, they learned to modulate an argument so that it never went out of control. When things would start to get heated, one of them would glance toward the bathroom, and the other would say, “Okay, okay, let’s just calm down and see if we can talk this out.” (47, pp. 18–19)” Steve gives another example of recategorisation in individual change work (Andreas, 2006a, p. 172) “A young woman once said to me, “NLP is a crock.” I was particularly curious about her statement, because she worked for an NLP training center. When I asked her why she thought NLP was a crock, she replied, “Because I can’t use it on myself.” When I said, “Yeah, I guess brain surgery is a crock, too,” she threw up her hands and said “Ohhh!””

Iteration: Using scope and category iteratively (applying categories to the same categories) adds even more opportunities for both creating problems and creating solutions. “For instance, one man’s son regularly came home from school saying, “Everybody hates me.” Finally, one day his father said, “Well, if everybody hates you, then you must hate you, and don’t you think you should have at least one person on your side?” The father’s pointing out the self-reference in the boy’s statement made a big difference to him. Of course, the father’s statement implicitly also put himself on the son’s side.” (Andreas, 2006b, p. 118).

A sense of certainty is an example of an iterative process that can lead to a client being locked in their problem. Certainty is a belief about a belief. I believe something, and I believe that my belief is “waterproof”. Once you understand that certainty is iterative, you understand that you can simply repeat the iteration one more time. Here’s an example (Andreas, 2006b, p. 248): “Read the following interesting exchange between Richard Bandler, one of the original developers of NLP, and a participant in a seminar who is very sure about something that is messing up his life.
1. Bandler: Are you sure of that?
Participant: Yes.
2. Bandler: Are you sure you’re sure?
Participant: Yes.
3. Bandler: Are you sure enough to be UNsure?
Participant: Yes.
Bandler: OK, Let’s talk.”

Don’t get caught up in the “content”: notice what are the scopes and categories: Many people, when they read such stories as those in the last section, are impressed by the complexity of what the therapist seems to have done. However, by explaining Scope and Category, Steve made it clear that far from being complex, these interventions are disarmingly simple. By altering one or both of these two variables (scope and category), to use a metaphor from above, they alter the basic equation and thus the entire Mandelbrot set of the client’s problem disappears. It is not necessary to believe in the complexity of the problem (the Mandelbrot picture), let alone to try and understand and find a solution within that complexity. An effective therapist simply notices the scopes and categories that generate the image, and invites the person to change them. “blame” is a sure sign that we are attending to the Mandelbrot picture and not understanding that it is a spandrel of the underlying scopes and categories (OK, I did mix my metaphors there). It is only necessary to ask, with the innocence of a child, what the scopes and categories are that make up the basic equation. The result is a kind of psychological equivalent of gene therapy (changing a single gene may change thousands of chemical interactions in the body and heal a disease like Huntington’s disease), where previous psychotherapy was more like toxic chemotherapy (accepting the genetic base and trying to exterminate all the expressions of a particular gene using a chemical poison).

In fact, the whole idea of complexity vs simplicity is a kind of new category system through which we can understand how to live more elegantly. If this is true, then all NLP interventions can be understood simpler as variations of scope and category. We use the submodalities of an event (in a sense it’s psychological DNA) to alter its category, or we use the triggers to alter the category by anchoring. We change the scope and / or category by reframing. What seemed like a vast range of choices can be understood as variations on the most fundamental two variables that our brain uses in perception (remember that categorisation and scope are not mere human amusements, but, as Chomsky discovered, they are fundamental to all animals’ interaction with the world).

As Sir Isaac Newton said “Truth is ever to be found in simplicity.” (Bergey, 2025, p. 23).

Bibliography:

• Andreas, S. 2006a and 2006b, “Six Blind Elephants: Understanding Ourselves and Each Other” Volume I: Fundamental Principles of Scope and Category. Volume II: Applications and Explorations of Scope and Category. Real people Press, Moab, Utah
• Bergey, D. 2025, “Isaac Newton: Workman of God’s Word: The Radical Faith of the World’s Greatest Scientist” Independently published (KIndle Amazon), New York
• Francis, D. 2025, “Ask a Nerd: The Mandelbrot Set” accessed 20/12/2025 online at https://tildesites.bowdoin.edu/~dfrancis/askanerd/mandelbrot/
• Gould, S.J., and Lewontin, R. C. 1979, “The spandrels of San Marco and the Panglossian paradigm: a critique of the adaptationist programme”. Proceedings of the Royal Society B: Biological Sciences. 205 (1161): p. 581–598
• Hauser, M. D., Chomsky, N., and Fitch, W. T. 2002. “The faculty of language: what is it, who has it, and how did it evolve?”. Science, 298(5598), p. 1569-1579.
• Maturana, H.R. and Varela, F.J. 1992. “The Tree Of Knowledge” Shambhala, Boston
• Pincus, D. “Coherence, Complexity, and Information Flow: Self-Organizing Processes in Psychotherapy” p. 335-369 in Guastello, S.J., Koopmans, M. and Pincus, D. eds. 2008, “Chaos and Complexity in Psychology: The Theory of Nonlinear Dynamical Systems” Cambridge University Press, Cambridge
• Sagan, C. 1995, “The Demon-Haunted World: Science as a Candle in the Dark”, Random House, New York
• Tschacherand, W. and Junghan, U. “Psychopathology” p. 307-334 in Guastello, S.J., Koopmans, M. and Pincus, D. eds. 2008, “Chaos and Complexity in Psychology: The Theory of Nonlinear Dynamical Systems” Cambridge University Press, Cambridge
• Watzlawick, P. 1976, “How Real Is Real” Vintage Books, New York