Fractals, turtles, and lying eyes

Today’s words are fractals, turtles and lying eyes. Let’s see what we can do with these.

Fractal

Here’s the first two sentences of the Wikipedia entry for “fractals”: 

In mathematics, a fractal is a subset of a Euclidean space for which the Hausdorff dimension strictly exceeds the topological dimension. Fractals appear the same at different levels, as illustrated in successive magnifications of the Mandelbrot set.

Got that? Fractals, like so much in math, are utterly cool…and mostly beyond my ability to understand in anything other than the most superficial level. For the purposes of this post, though, we’re going to think of fractals as a pattern that recurs at multiple levels: from the large to the tiny. Why and how isn’t something to worry about right now — just the idea of recursive repetition from the tiny to the large. And just to set your mind at ease: no, “recursive” and “repetition” are not identical concepts.  Recursive means to define a thing in terms of itself, while repetition is the carrying of a pattern across time and/or space. Tricky things, words.


“Mod” by kevin dooley is licensed under CC BY 2.0

Turtles

So, that’s fractals. What about turtles? Turtles amble in to the post with the phrase “turtles all the way down.” This is where we connect fractals to belief. “Turtles all the way down” is what results when a mischievous 4-y.o. is put into a blender with a pompous priest: the fractal question of “but why” linked to doctrine. The expression apparently originates from beliefs about the earth. What supports the earth? Well, the earth has nine corners that hold up the heavens, and each corner rests on the back of an elephant. And what supports the elephants? Why, the elephants stand on the back of a turtle. And what supports the turtle? Why, another turtle. And what does that turtle stand on? Well, another turtle… And so it goes – turtles all the way down the teleological rabbit hole. A free-floating, authoritative assertion of scales, carapace and reptilian eyes. Maybe the reptilian overlords conspiracy theory is correct after all. Or dinosaurs did drown in the flood of Genesis. It’s like the internal logic of a dream, a language of pure emotion overlaid and painted with the imagery of our internal eye.

However, I am going to suggest that there is a deeper significance here – that our beliefs are…well, not “nothing more” than fractals, but rather are constructed at a profoundly deep level. So much so, that as with turtles all the way down, our psychological living (which is the only living any of us know), is constructed on beliefs that are constructed on beliefs that are constructed on beliefs, …all the way down. It’s not that there is no “there, there” when it comes to belief, but rather that all we are is belief, and that this goes all the way down, all the way up, all the way back, and all the way forward. It’s more than just the narrative constructions of doctrine – those delivered stories that make us smile in disbelief. Those we mostly grow out of, or as the famous quote from 1stCorinthian puts it:

When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things.

The point I’d like to make here is that putting away “childish things” is not as easy as all that, and the reason is that there is never any “putting away.” That is not how the mind works, and more to the point, that is not what a mind is. Each of us are turtles all the way down. Put aside one turtle, and there are infinite more chomping away, carapace to plastron, one supporting the other. The “I” never separates itself from its own construction, and here’s where the final phrase comes in: “lyin’ eyes.” 

Taking a rest from supporting all of your fake news

“Lyin’ Eyes”

A man is caught in bed with another woman; a group of thieves are caught rustling cattle; a man sees his sweetheart with another man; an actress jokes about her age – and the common refrain is some version of “who are you going to believe, me or your lying eyes.” As blatantly, absurdly, gutsy, and desperately as this phrase is, there is no getting away from its nugget of truth. When CAN you trust your eyes? Or to put it differently, does perception feed up facts that are “out there” or does it construct beliefs of what is “out there.” Because let’s face it, if you are going to put aside childish things and embrace the truer, authoritative, responsible, practical beliefs of adulthood, there is the assumption that one can be distinguished from the other – that eyes don’t lie, and that perception and its echoes (i.e., memories) are the bedrock of our truth.

But of course eyes do lie. In fact, they do nothing but lie day in and day out. The psychological science on this couldn’t be any clearer. The processes of perception don’t relay reality to us, but rather construct a reality for us. These perceptual beliefs might have utility, but they are still beliefs, which isn’t to say that these “lies” constructed by our perceptions are “wrong.” It’s simply a matter of mechanism. Let’s see if we can’t untangle this.

The dress

A few years ago in 2015 a meme swept through the internet that involved a photo of a dress. Here is the photo:

And here’s the question that accompanies the photo: what color is the dress? If you are like me, and approximately 60% of viewers, you answered something along the lines of “gold and ivory.” If you are like the other approximately 30% of viewers, though, you answered “blue and black.” Which is correct? Well, the actual dress is indeed blue and black. Here’s a photo of it:

No question there, right? Blue and black, which means that all of you that see it as “gold and ivory” in the first photo are wrong. Wrong or lying. The dress is blue and black, after all. If you were being interrogated by the police, maybe you’d be indicted for perjury. Locked away for spreading falsehoods. A public menace.

But of course, the dress in the first image IS “gold and ivory.” That is what I see, and I can’t unsee it. You can tell me that you see blue and black all you want, but it makes no difference. This I/eye that is me sees what it sees. 

Thankfully, science being science can offer up a belief-preserver of sorts. Here is a wonderful deconstruction of what is going on with “the dress.” And here is a write up of that deconstruction written for a more general audience. Basically, the way that we perceive color depends on many contextual variables that our brains filter and interpret in various ways. For example, did you know that the light of mid-day contains more blue in it than the light of, say, morning? Our brains filter that information out in order to keep colors constant. Or take shadow. If an object is back-lit and in shadow, our brains take that information into account in order to provide us with a perception of color. Mid-day or morning, back-lit or front-lit, our brain maintains for us the red of the apple. So, let’s get back to the dress. Is it in shadow or not? Is it mid-day or not? These are some of the questions that our brain is asking, whether we realize it or not, and the assumed answers change the psychological filters that are slotted into place in order to provide us with the belief that the dress is either blue/black or gold/ivory. Our brains even factor in whether most of our visual experience occurs in the morning (e.g., if you are an early riser) or late in the evening (i.e., a night owl). The former are biased to see the dress as gold/ivory, while the latter are biased to see the dress as blue/black.

It just so happens that the photo of the dress cleverly provides multiple, ambiguous perspectives embedded within its static field. In a sense, it is no different from a Necker cube. There is no cube, just as really there is no dress, just wavelengths of light differentially absorbed and reflected. But we see a cube, and not only that, but we see two potential cubes – the image rebounding from one to the other, depending on our point of reference.

You, too, can build one these at home!

I can’t emphasize enough, either, that there is no choice here. There’s no “putting aside the childish gold/ivory” of the dress for the truer, more adult blue/black of the dress, any more than one can put aside the filled in blindspot that sits a little off to the left and right of our eye’s field of vision. Yes, we see a complete field of vision and do not see the empty holes where our optic bundles exit the back of our retinas. Those empty holes are there, but our brains fill them in for us, providing us with a belief in a complete image. Or take the vision so many of us have experienced of a huge moon sitting just at the horizon. That is what we see, even if we know that the size of the moon does not change as it traverses the sky. Magnification of the atmosphere? No, not at all. Once again our brains are using assumptions to construct a visual reality – a set of beliefs about how distance and size are related to one another. On the back of our retinas the projected image of the moon is the same, whether on the horizon or overhead, and yet what we see in our mind’s I/eye differs. This so-called moon illusion, is related conceptually to many illusions, one of which I’ve tried to create below. Both cylinders are the same size, but our brains make one appear slightly bigger. 

An even simpler version can be found here, and is called the Ponzo illusion. Two objects, both the same size, and yet our mind offers them up as different. This is a difference predicated on assumptions, on beliefs offered up at the very start of our interaction with reality. There is no escaping these beliefs, nor are these beliefs of perception the bottom. They, themselves, are constructed by processes that are constructed by processes that are constructed by processes…. and on down it goes.

It reminds me of a quote from Graham Swift’s Waterland. Waterland is a meditation on history and memory – their tributaries, swamps, and recursive repetitions. Here is the protagonist, a high school history teacher, relating the ambiguities of the French Revolution and dealing with a student who wants facts.

“So where does it lie, this revolution? Is it merely a term of convenience? Does it really lie in some impenetrable mesh of circumstances too complex for definition? It’s a curious thing, Price, but the more you try to dissect events, the more you lose hold of them – the more they seem to have occurred largely in people’s imagination …’

‘Should we be writing this down, sir? The French Revolution never really happened. It only happened in the imagination.’

Laughter.

‘Don’t be literal, Price.’

 ‘I’m speculating, it’s true, Price. But we’re all free to interpret.’

‘You mean, so we can find whatever meaning we like in history?”

I’m taking that from my digital version of the book, but it’s right at the end of Chapter 14. The quote nicely summarizes the point of this particular blog post, and really the series of posts that I’ve made so far. A psyche is a constructed thing — processes strung together across history, and this “I” that each of us inhabits is a unique, particular and utterly confounded thing. A thing to hold lightly. A thing to hold humbly. Because just like there is no French Revolution, not really, there is no “I” beyond the confluence of processes that temporarily uphold it. And yet, just as the horrors of revolution emerged from processes of belief, so too do our own beliefs emerge from their own hidden furnaces. 

*****

I don’t want to end so heavily, though, so here’s a personal story to close out this post. It’s a story about belief and perception.

When I was a kid, growing up in the South, I went to a school that required all seventh graders to take “bible.” Our teacher was nicknamed “Yo” by all the students at the school. Yo Strang. Yo was one of the kindest souls I’ve ever met. A prisoner of war during WW II, he wore a heavy coat even on the hottest of days. The rumor was that it had something to do with the suffering that he had seen and experienced as a P.O.W. Yo was totally devoted to the kids in his classroom. Whether they were drawing pictures of penises in their notes or grade-anxiously writing down every word, Yo always projected a simple goodness.

Anyways, the seat that I sat in during Yo’s bible class was right next to a bulletin board.  On the bulletin board was a cut-out clipping from a newspaper with a caption that read something like: “Photographer takes photo of wooded scene only to discover the miraculous face of Jesus looking back.” The paper was yellowed, and the photo was in black and white. As a kid in a bible class, I sat next to this photo for most of our journey through the Old Testament, and all I saw was a photo of a some trees and snow. Jacob fighting the angel? Trees and snow. Moses up on Mount Sinai? Trees and snow. David having a husband killed so that he could sleep with his wife? Trees and snow. I wasn’t particularly devout in my thinking about Christianity, but I was a bit concerned that here I was with a 99.4 average in the class, but I couldn’t make out the face of Jesus in a newspaper photo. Finally, I asked one of my friends about the photo. They pointed to one blotch after another, “Here’s the beard. Here’s the eyes,…” 

and the face popped out.

A bit anti-climatic, actually, even then. Anyone who has looked at clouds in the sky knows that we “see” objects that aren’t there. A dragon. A train. And when it comes to faces, well, we see faces everywhere. Mars. Queen Elizabeth’s hair. The side of a mountain (until recently). In fact, “seeing” or “hearing” specific objects or words in an ambiguous sensory environment is so common that psychologists have a word for it: pareidolia. The basic idea isn’t so complicated: when you’ve got a hammer, everything looks like a nail. Or in other words, when you are so used to interpreting particular combinations of stimuli in a particular way, that’s the way you’ll tend to interpret new combinations.

By the way, if you are curious about where the word pareidolia comes from, it’s a combination of greek bits. Para (“before”) combined with eídōlon, which means “image” or “representation.” So the word means a sort of pre-representation of what is actually there. An image of expectation, rather than an image of reality. The large moon on the horizon, or the gold/ivory dress. Like I say, it’s turtles all the way down.

Perhaps you believe in God

Perhaps you believe in God. You believe that global warming is happening and open to human agency. You believe that hard work pays off, that you are more valuable than at least some other people. Or perhaps not. Perhaps you believe that everyone else has their act together, and you do not. You believe that your spouse is cheating on you, and you believe that your boss is out to get you fired. You believe that music is soul, or that there is such a thing as a justified murder, or that vaccines are dangerous or unholy or life-saving. We could go on…and on, and on. We have beliefs about proper clothing, about racial groups, about inanimate objects. We have perceptions of belief that we hold as “true”; we have perceptions of belief that we hold as functionally “true” – that in the absence of the belief particular outcomes would not happen. For instance, if I believe that the child is capable, that belief makes future outcomes by the child more likely. Conversely, if I believe that the child is incapable, then my belief tilts the child’s behavior in a different direction. In both cases our belief would be “justified” and “true.” After all, I knew all along that child was no good, and look, she turned out that way!

I always knew that’s where she was headed

This idea that our beliefs actively impact the world — that they reverberate outward and affect others — is not a new thing to psychologists. William James, who arguably was the father of U.S. psychology, wrote an essay entitled “The Will to Believe,” in which he allowed for unanchored belief. It’s a complex essay. One that requires a careful reading in order to unpack the many points that James is attempting to articulate. For instance here he is stating as obvious that everyone essentially believes in what is useful for them to believe (within the unique, specific needs or their life):

As a rule we disbelieve all facts and theories for which we have no use. Clifford’s cosmic emotions find no use for Christian feelings. Huxley belabors the bishops because there is no use for sacerdotalism in his scheme of life. Newman, on the contrary, goes over to Romanism, and finds all sorts of reasons good for staying there, because a priestly system is for him an organic need and delight. Why do so few ‘scientists’ even look at the evidence for telepathy, so called? Because they think, as a leading biologist, now dead, once said to me, that even if such a thing were true, scientists ought to band together to keep it suppressed and concealed. It would undo the uniformity of Nature and all sorts of other things without which scientists cannot carry on their pursuits.

William James was 20 at this point

Keep in mind that James is expressing his thoughts from a mind that did not know cars or television, and which had developed through a period of time in which the ghosts of hundreds of thousands of Americans, dead from the Civil War, haunted the social fabric that had been left behind. Within in that context James’ essay takes on a new urgency. Given the scars of those horrors, given the unrelenting “march of technology and industry” (and yes the sciences of which he was a part) what can be held on to? James’ answer is a generous and humble one. One that defends an individual’s unique feelings, as well as the careful accumulation of authoritative evidence. He writes:

A whole train of passengers (individually brave enough) will be looted by a few highwaymen, simply because the latter can count on one another, while each passenger fears that if he makes a movement of resistance, he will be shot before any one else backs him up. If we believed that the whole car-full would rise at once with us, we should each severally rise, and train-robbing would never even be attempted. There are, then, cases where a fact cannot come at all unless a preliminary faith exists in its coming. And where faith in a fact can help create the fact, that would be an insane logic which should say that faith running ahead of scientific evidence is the ‘lowest kind of immorality ‘ into which a thinking being can fall.

Two Experiments

Whether one accepts James’ defense of “faith” is beside the point (and I wouldn’t term it a defense so much as an allowance). Psychologists have enough science behind them to show that beliefs are not neutral things. They actively impact and shape the world of not only our own perceptions but those of others, as well — ants and termites busily at work in a psyche’s foundations

Let me describe two classic examples. 

Rosenthal and Fode, 1963

The first used rats, but really it used undergraduate students. The students were in a psychology laboratory class, and as part of the class they were assigned the task of training rats to run a T-maze. In a T-maze, an animal scurries down a runway, and then is presented with a single choice: go to one arm (painted white) or go to the other (painted gray). One of these will contain food. Give the rat enough experience, and they’ll figure the choice out. In order to “know” that their rats were figuring out which choice led to food, the students tracked the number of “correct” responses the rats made and also the amount of time it took the rats to make their choices. 

Taken from Rosenthal and Fode (1963).The effect of experimenter bias on the performance of the albino rat. Behavioral Science, 8(3), 183-189.
Notice how the average for the “Bright” rats is much better than for the “Dull” rats. Must be really smart rats, right?

The reason why this experiment is famous, though, is because the researchers, Rosenthal and Fode, introduced a very simple manipulation. The students were told at the start of the training that one set of rats were “maze bright.” These rats were “known” to solve mazes quickly. The students were also told that another set of rats were “maze dull,” i.e., had been bred such that they were slow learners in mazes. Sure enough, the average performance of the two groups showed clear differences. The only problem with these results is that there was no such thing as “maze bright” and “maze dull” rats. All of the rats had been selected at random, divided into two groups, which were labeled by Rosenthal and Fode (for the unwitting students) as “maze bright” and “maze dull.”

Loftus and Palmer, 1974

Now, its doubtful that the rats in the Rosenthal and Fode experiment came to see themselves as either “smart” or “dull.” All we can say is that instilling a belief in the trainer impacted the behavior of their subjects (rats). That said, psychologists do know that beliefs are directly shaped by experience, and we can point to many, many examples. For example, here is one that falls under the category of “false memories.”

False memories are subjective memories for events, objects, words, etc., that can objectively be shown to never have occurred. There are reasons to use the word “memory” rather than the word “belief,” but for our purposes I am going to conflate the two. A memory is a particular sort of belief about the past. To be more specific, let’s restrict ourselves to what are termed “declarative memories.” These are memories for events that we can verbally describe. Crudely, they are the normative memories that most people think of when they use the word “memories.” However, like I say, we can reasonably consider declarative memories as a belief about an event that took place in the past. It’s the classic “I know what I heard, because I’m the one that heard it.”

Taken from Loftus and Palmer (1974). Reconstruction of Automobile Destruction:
An Example of the Interaction Between Languageand Memory. Journal of Verbal Learning & Verbal Behavior, 13(5), 585-589. Notice how the words influence reported perception.

For this experiment, the researchers Loftus and Palmer had college-age subjects watch videos of traffic accidents. They were then asked to rate the speed of one of the cars when it __________ into the other car. The clever bit, or if you are a lawyer, the leading question bit, involved the word that was slotted into the blank. For some subjects the word was “hit.” For others it was “smashed.” For others it was “bumped.” And so on. All in all, Loftus and Palmer used five different words. What they found was that the word influenced the speed ratings. “I know what I saw, because I saw it!” Except in this case, it was more “I know what I saw, because you asked me to see it.”

Now, reporting different speeds based on particular questions isn’t necessarily evidence of a false memory. We’ve all had the experience of “going along” with another person’s opinion, even when our own opinion is different. “Doesn’t that sweater look good on him?” “Sure!” So, students asked to rate the speed of a car after a “crash” might rate the speed higher than after a “bump” merely to please the person asking the question – the authority figure / experimenter. In order to deal with this problem, Loftus and Palmer conducted another experiment. 

Here is where words became memory.

Once again students watched a car accident. 1/3 of the student were asked how fast the cars were going when they “hit” each other. 1/3 were asked how fast the cars were going when they “crashed into” each other. 1/3 were not asked any questions at all. Finally, a week later, the students were brought back to the lab and asked 10 questions about the video they had watched the previous week. One question was “Did you see any broken glass? Yes or No” More subjects reported seeing broken glass when the cars had “crashed into” one another (16/50), rather than “hit” one another (7/43) or when no question had been asked (6/44). Just to complete the scene, in the objective reality of the actual video, there was no broken glass evident.

James was right, then. Beliefs are not neutral things that have been constructed by our history. Yes, they have been constructed. But, they also construct. They change the landscape of our experience, and in so doing, alter the potentials of that experience for both “good” or “bad.” 

Look! There is a psyche peering out of these foundations.

 This post has been an especially long one, and believe it or not, we are just getting started on unpacking some of the currents – the river that William James called the “stream of consciousness.” There is just one more construct that I want to quickly introduce, though, because it actually pops up from time to time in the current cultural zeitgeist. It’s a construct that is deeply connected with the topic of beliefs: their origins and their shapings. The construct is gaslighting.

Gaslighting

Gaslighting is a colloquial term that refers to a form of psychological manipulation in which a targeted victim is led to doubt their own perceptions and beliefs. Up becomes down. Down becomes up. Memory can’t be trusted. Previously trusted sources of information and validation are doubted or removed. The stress of uncertainty is alleviated by a “supplier” who just so happens to be the manipulator. In the end the victim is so hollowed of agency and psychological certitude that they spiral into despair, depression, and madness. That is the dramatic read, and it’s not a bad place to start because the term “gaslighting” originates from a stage play and then movie, “Gas Light.”

Gaslighting is not a joke for individuals who have experienced its effects. At the same time, it is important to be aware that from a certain perspective “gaslighting” is what the world does to all of us in the construction of our psyche. Illusions, false beliefs, emotional assumptions, phylogenetic beliefs (i.e., cognitive “reflexes”) sprout within all of us, vines planted and spreading like southern kudzu. These processes are normal, true, but we ignore the malleability of our beliefs at our own peril. Victims of gaslighting could be any of us, just as the victims of a scam could be any of us.

“PICT0013”by The_Doodler is licensed under CC BY-SA 2.0

(modified from the original)

So, to wrap up this post, I’d simply like to point out three common techniques of gaslighting. I’m doing so in the same manner as Screwtape from C.S. Lewis’ Screwtape Letters. Yes, do think about the current political situation in the U.S. with its proclamations of “fake news.” But also realize that we all engage in “manipulations” of belief so some small extent. Sometimes without realizing it. Sometimes with cause. Sometimes for selfish reasons. Sometimes for what we would like to think of as positive reasons. With that said, if you wanted to start upping your game into the political big leagues three guidelines from a “gaslighters handbook” might look something like this (and remember, there are many more than just three):

  1. Establish confusion as to what qualifies as evidence! Trusted sources of information must be discredited or at the very least established as no different from any other source of information. Yes, it’s a long-standing newspaper, but it’s run by a bunch of liberals. Yes, they are your priest, but haven’t you read that priests are pedophiles? By the way, your parents called to check in on you. Are they ever going to let you be your own adult? And, I don’t know, they just seem to have it in for me. Easy peasy. While you’re at it. Reify, reify, reify. A reaction is never a natural result of the environment you’ve created. It’s because they distrustful or prone to depression. Bonus points for turning that characterization into a fixed “personality trait” that your target begins to accept about themselves! 
  2. Create distress, but do be sure to become the immediate solution to that distress. Chaos is your special sauce! Unpredictably trigger arguments! Publicly humiliate, if you have to. Just be sure to quickly follow this up with a way of releasing the stress that you’ve caused. Maybe it involves an abject “apology.” Maybe it involves producing a “plan” for both of you to fix the relationship. Maybe it involves wild “make-up sex.” Be creative! But be sure that you are central to the solution to the mess you’ve created, and bonus points if your “solution” subtly interacts with point number 1. “I hate that I get so angry, but maybe it has to do with the fact that I feel unwelcomed by your family. I think maybe it’s because I’m always so honest.” 
  3. Make yourself the center of attention! You can’t have your target’s attention wandering out of your control. Attention is a limited resource, so fill that sucker up with your shenanigans. Remember, there is no such thing as bad publicity, when it comes to your target’s attentional audience. Text. Create a scene. Demand gifts. Act helpless. Show up on their doorstep. Call their parents. Your goal is that of any advertiser: crowd out all other brands! Like the hypnotist, you need their identity to be wearied out and replaced by your own. Good luck!!