Month: November 2019

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.

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 1^stCorinthian 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.” 

“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.

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.