Search Term Friday: Strange Loops and Theology

Recently these search terms

strange loops and theology

brought someone to the blog.

Those search terms go back to a very old series I did in 2007 in the early years of this blog. In that series I shared some theological reflections on Douglas Hofstadter's book I Am a Strange Loop.

I have not thought about that series for years, but after seeing those search terms I was interested in going back to see how those reflections held up. Feel free to give your assessment.

Initially these reflections were broken up over five posts. I've edited and pulled them all together into this single post.

Yes, that makes this post very long. But if you get to the end I hope you'll feel rewarded with some really interesting ideas. Ideas that may change how you think about free will, love, life, death, resurrection, Jesus, narrative theology and the Eucharist.

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One of my favorite authors is Douglas Hofstadter. I first encountered his work when I picked up his 1979 Pulitzer-Prize winning Gödel, Escher, Bach: An Eternal Golden Braid (henceforth, GEB). In GEB, Hofstadter meditates on the idea of self-reference and how it seems central to consciousness and meaning.

In his book I Am a Strange Loop Hofstadter picks up those themes he left off in 1979. In what follows like to offer some theological reflections on I Am a Strange Loop, touching on issues related to identity, resurrection and the ritual of the Lord's Supper.

1. We Are "Little Miracles of Self-Reference"

The book GEB is mainly a reflection on Kurt Gödel's famous incompleteness theorem. Simplifying greatly, Gödel was able to embed self-reference in what was then considered to be a mathematical system of iron-clad logical rigor, Russell and Whitehead's Principia Mathematica. Today, Gödel's theorem is considered to be one of the most important logical, philosophical, and epistemological breakthroughs in the history of world.

The idea of self-reference is common enough. It even has biblical roots. Paul in Titus 1:12 says,

Even one of their own prophets has said, "Cretans are always liars..."

Given ancient sources we know the person Paul is referring to: The Cretan philosopher Epimenides. Consequently, the self-referential paradox surrounding Epimedides' statement is called The Epimedides Paradox or The Liar Paradox.

The paradox is easy to see. If Epimenides is a Cretan and he utters the statement p--"Cretans are always liars"--then what is that truth-status of p?

If p is true then Cretans are not always liars which means p is false: A contradiction.

The contradiction is due to self-reference. The simplest way to see this is in the old-standby:

This sentence is false.

You see the paradox. If the sentence is false then it's true. If it's true then it is false.

Again, the paradox is due to self-reference, the sentence points to itself. The point about Gödel's theorem was that Gödel was able to embed self-reference into the system of Principia Mathematica, making the logical system presented in that book speak about its own truth/proof status.

But Gödel's breakthrough was not just simply about self-reference. Rather, Gödel's proof was able to create a new level of analysis. That is, Gödel's paradox came via a higher-order coding system, a new level of meaning, which could "speak about" a lower level of meaning. The outcome was still paradoxical and self-referential, but it came via a higher-order, nested structure. A structure, Gödel later proved, that would continue on ad infinitum. Kind of like a set of logical Russian dolls.

Okay, all very interesting, but what does any this have to do with being a human being?

Well, Hofstadter contends that this idea of nested self-reference is what gives rise to human consciousness, our symbols, and our sense of self. It is our ability to reflect on reflections that pulls us up, cognitively speaking, from being simply stimulus-response creatures. That is, I can have a thought, then wonder about that thought, then wonder about that wondering.

It's like Gödel's self-referential Russian Dolls, with new meanings produced at each new level of nested self-reference. Hofstadter has some great labels for this process. He calls it the "Gödelian swirl of self." But mainly he calls us Strange Loops: Self-reference looping back on itself to create new meaning. In the words of Hofstadter we Strange Loops are "self-perceiving, self-inventing, locked-in, mirages [which] are little miracles of self-reference."

2. The Self as a Symbol and Attunement with the World

Beyond the idea of self-reference there is another idea in Douglas Hofstadter's book I Am a Strange Loop that we need to get under our belts. This involves the relationship between symbols, the self and the causal aspect of symbols.

Again, Hofstadter calls us "Strange Loops" due to the self-referential nature of human consciousness. If self-reference is the "loop" part, what does "strange" mean?

As we saw in Hofstadter's discussion of Gödel, a strange loop is not simply a feedback loop like audio feedback through a speaker and microphone leading to that ear-piercing screech. Rather, a strange loop produces higher-order structures which create meaning through their reference to lower level structures. These higher-order structures are called symbols. In the words of Hofstadter,

What I mean by 'strange loop' is...not a physical structure but an abstract loop in which, in the series of stages that constitute the cycling-around, there is a shift from one level of abstraction (or structure) to another, which feels like an upwards movement in a hierarchy.

This ability for level-crossing (higher-to-lower and lower-to-higher) and for loops of self-reference is what creates the vast complexity of human symbol acquisition and development. Again from Hofstadter,

Concepts in the brain of humans acquired the property that they could get rolled together with other concepts into larger packets, and any such larger packet could become a new concept in its own right. In other words, concepts could nest inside each other hierarchically, and such nesting could go on to arbitrary degrees.

Now, and this is the big point, what sits at the top of these higher-level structures? What is the big "nest" that "contains" all the levels of reference and all the symbols?

Hofstadter says it is the Self-Symbol, the "I" sitting in your mind. This Self-Symbol begins acting on the world and the world, in turn, sends input back through the levels of the Self-Symbol causing it to adjust, harmonize, and synchronize. The Self-Symbol becomes "attuned" to the world. Hofstadter describes this whole process:

The vast amounts of stuff that we call 'I' collectively give rise, at some particular moment, to some external action, much as a stone tossed into a pond gives rise to expanding rings and ripples. Soon, our action's myriad consequences start bouncing back at us, like the first ripples returning after bouncing off the pond's banks. What we receive back affords us the chance to perceive what the gradually metamorphosing 'I' has wrought. Millions of tiny reflected signals impinge on us from outside, whether visually, sonically, tactilely, or whatever, and when they land, they trigger internal waves of secondary and tertiary signals inside our brain...

And thus the current 'I'--the most up-to-date set of recollections and aspirations and passions and confusions--by tampering with the vast, unpredictable world of objects and other people, has sparked some rapid feedback, which, once absorbed in the form of symbol activations, gives rise to an infinitesimally modified 'I'; thus round and round it goes, moment after moment, day after day, year after year. In this fashion, via the loop of symbols sparking actions and repercussions triggering symbols, the abstract structure serving us as our innermost essence evolves slowly but surely, and in so doing it locks itself ever more rigidly into our mind. Indeed, as the years pass, the 'I' converges and stabilizes itself just as the screech of an audio feedback loop inevitably zeros in and stabilizes itself at the system's natural resonance frequency...

...but there is a key difference...in any strange loop that gives rise to human selfhood, [in] contrast [to the audio feedback loop], the level-shifting acts of perception, abstraction, and categorization are central, indispensable elements. It is the upward leap from raw stimuli to symbols that imbues the strange loop with "strangeness". The overall gestalt 'shape' of one's self--the 'stable whorl', so to speak, of the strange loop constituting one's 'I'--is not picked up by a disinterested, neutral camera, but is perceived in a highly subjective manner through the active processes of categorizing, mental replaying, reflecting, comparing, counterfactualizing, and judging.

The important point here is that in the process of attunement the Self-Symbol isn't passively absorbing the world. The Self-Symbol isn't a blank slate. The Self-Symbol is triggering events in the world. The symbols have causal potency. In turn, events in the world can trigger changes in in the symbols and how they are organized in the Self.

3. "Who Pushes Whom Around in the Population of Causal Forces that Occupy the Cranium" or Can an Idea Push Around an Atom?

The reason for focusing on this give and take between Self and World is that if the Self is primarily a symbol we'll have to wrestle with how symbols are locations of causality, how symbols can trigger other symbols and trigger events in the world.

Such questions bring us to the issue of how the Self might be "free" in a physical universe governed by the laws of physical causality. That is, are symbols controlling their own triggering or are these symbols being pushed around by the lower level particles? Do the symbols have any causal power of their own, able to push around the atoms and molecules? Or are the atoms and molecules pushing around the symbols in a deterministic and reductionistic manner?

Framed crudely, can an idea push around an atom?

In approaching this question Hofstadter takes inspiration from the thoughts of Roger Sperry, the pioneer of split-brained research fame (all our talk of "right-brained" versus "left-brained" traces back to Sperry). Here is the Sperry quote that has inspired Hofstadter:

In my own hypothetical brain model, conscious awareness does get representation as a very real causal agent and rates an important place in the causal sequence and chain of control in brain events, in which it appears as an active, operational force...

To put it very simply, it comes down to the issue of who pushes whom around in the population of causal forces that occupy the cranium. It is a matter, in other words, of straightening out the peck-order hierarchy among intracranial control agents. There exists within the cranium a whole world of diverse causal forces; what is more, there are forces within forces within forces, as in no other cubic half-foot of universe that we know of...

To make a long story short, if one keeps climbing upward in the chain of command within the brain, one finds at the very top those over-all organizational forces and dynamic properties of the large patterns of cerebral excitation that are correlated with mental states of psychic activity... Near the apex of this command system in the brain...we find ideas.

Man over the chimpanzee has ideas and ideals. In the brain model proposed here, the causal potency of an idea, or an ideal, becomes just as real as that of a molecule, a cell, or a nerve impulse. Ideas cause ideas and help evolve new ideas. They interact with each other and with other mental forces in the same brain, in neighboring brains, and, thanks to global communication, in far distant, foreign brains. And they also interact with the external surroundings to produce in toto a burstwise advance in evolution that is far beyond anything to hit the evolutionary scene yet, including the emergence of the living cell.

The big point Sperry is making is that it is perfectly legitimate to see ideas and symbols as causal forces. That is, a causal description of the brain does not have to be a description as a biologist and physicist would give it, at the level of molecules on down. It is legitimate to see ideas pushing around molecules and not the other way around. To quote Hofstadter:

Do dreads and dreams, hopes and griefs, ideas and beliefs, interests and doubts, infatuations and envies, memories and ambitions, bouts of nostalgia and floods of empathy, flashes of guilt and sparks of genius, play any role in the world of physical objects? Do such pure abstractions have causal powers? Can they shove massive things around, or are they just impotent fictions? Can a blurry, intangible 'I' dictate to concrete physical objects such as electrons or muscles (or for that matter, books) what to do?

Have religious beliefs caused any wars, or have all wars just been caused by the interactions of quintillions (to underestimate the truth absurdly) of infinitesimal particles according to the laws of physics? Does fire cause smoke? Do cars cause smog? Do drones cause boredom? Do jokes cause laughter? Do smiles cause swoons? Does love cause marriage? Or, in the end, are there just myriads of particles pushing each other around according the the laws of physics--leaving, in the end, no room for selves or souls, dreads or dreams, love or marriage, smiles or swoons, jokes or laughter, drones or boredom, car or smog, or even smoke or fire?

But beyond these rhetorical questions, Hofstadter tries to explain how there might be a scientifically valid way of viewing the causal power of symbols and mental states. The issue, according to Hofstadter, goes to levels of description. For example, consider the question: Why did World War II begin?

You could try to answer the question at the level of particle physics, trying to explain the swirl of particles that we labeled "World War II." Or you could try to describe WWII with a higher-level description, referring to larger-scale patterns. You might, for example, talk about a causal force labelled "Hitler."

To illustrate how ideas can have causal potency on physical objects Hofstadter offers up this metaphor.

Imagine a huge array of dominoes ready to fall. However, this array of dominoes is special. It is set up to do a calculation. Logically, you figure out an array of dominoes that can take a numerical input (e.g., knocking down X rows of dominoes in various spots to correspond to different numbers) and make a calculation. Specifically, the dominoes are set to fall to create two outputs, a red domino will fall in the end if the input number is prime and a blue domino, in a different area, will fall if the input number is not prime. So, we input our number--641--by knocking down the correlated rows of dominoes. We then watch the cascade of dominoes fall. The cascade goes in all directions dictated by the computational structure we've arrayed. Some cascades split and rejoin. Others stop. In the end, the red domino drops and the blue is left standing. Verdict: 641 is prime. (Computer people will recognize that this domino array is simply a computational algorithm, no different in application then what goes on in a computer or calculator.)

Given this example, Hofstadter asks the question: Why did the red domino fall?

Well, we could try to give the explanation in terms of particle physics. And that would be a valid but unfeasible and incomprehensible explanation. Or, we could scale up a bit and say, "Because the domino next to it fell." Again, that is a legitimate explanation but still too myopic. So, we could back up further and say that the red domino fell due to long complicated chains of dominoes falling, an appeal to the array. Again, this is accurate enough as far as it goes but it still misses a great deal, like the fact that this array isn't arbitrary or random. It has a pattern. So, in the end, it is perfectly legitimate to say that the red domino fell "Because 641 is prime."

Hofstadter's conclusion:

The point of this example is that 641's primality is the best explanation, perhaps even the only explanation, for why certain dominos did fall and certain other ones did not fall. In a word, 641 is the prime mover. So I ask: Who shoves whom around inside the domino chaninium?

To clarify, this isn’t a route around determinism. Rather, it is simply an acknowledgment that appeals to ideas and symbols as causal forces are scientifically legitimate. That is to say, if I love my wife I need not fear that a reductive appeal to biology, chemistry, or physics discounts or trumps the simple fact that I love my wife and it is this love that is the causal agent. Just like prime-hood was the causal agent in the domino example. And it is this love that pushes the molecules around in my mind rather than the other way around. Particle physics didn’t make the red domino fall. Prime-hood did. This is not to say that the particle physics picture and the prime-hood picture disagree. They are describing the same event. It is just that the particle physics picture, being at too low a level, can’t reach up and describe the higher-order pattern that is running the show. In the same way, brain function cannot reach up and explain love. Conversely, neither can love be reducible to brain functioning. Once the higher-order pattern is in place it gains a causal potency that does not exist when particles are random and patternless.

Pattern is everything. And you are a pattern.

4. The Self as a Curious Collage of Human Souls: How We Live Inside Each other

Having unpacked all this we can now start discussing some interesting theological implications which have to do with what Hofstadter calls the "blurring of selves."

Let me get to his thesis directly.

If the Self is a symbol--a pattern--that interacts with the world and other minds via feedback loops, then parts of the pattern of that symbol leave copies of itself, mainly upon other minds.

Let me give an example. When I say about my wife, "Jana would like that dress," I know this because Jana's Self-Pattern--her Strange Loop--has been using my Self-Pattern--my Strange Loop--as a feedback source for years. Thus, parts of Jana's pattern--her Selfhood--have left traces on my mind. Succinctly, my internal pattern/representation/symbol of Jana is due to the original pattern of Jana. Thus, parts of Jana's Self live in me. I say "live" because we've noted that symbols have causal potency. To some degree the patterns of Jana's Selfhood in me have the same causal potency they have in her. Thus, when I act or think in a way that reflects "Jana would do this" or "Jana would like this", I have these responses because, to a very real degree, Jana's pattern in me is causing those responses. I am not the cause. Jana is the cause.

In short, my Self, my Pattern, is not solely located inside me. Rather, my pattern is distributed, shared, and blurred across many minds. And, if symbols have causal potency, then my soul is affecting the world via that distribution.

Let me let Hofstadter make this point:

What is really going on when you dream or think more than fleetingly about someone you love (whether that person died many years ago or is right now on the other end of a phone conversation with you)? In the terminology of this book, there is no ambiguity about what is going on. The symbol for that person has been activated inside your skull, lurched out of dormancy, as surely if it had been an icon [on a computer screen] that someone had double-clicked. And the moment this happens, as much as with the game that opened on your screen, your mind starts acting differently from how it acts in a 'normal' context...The activation of the symbol for the loved person swivels into action whole sets of coordinated tendencies that represent that person's cherished style, their idiosyncratic way of being embedded in the world and looking at it.

Some more...

If you seriously believe, as I do..., that concepts are active symbols in a brain, and if furthermore you seriously believe that people, no less than objects, are represented by symbols in the brain..., and if lastly you seriously believe that a self is also a concept, just an even more complicated one..., then it is a necessary and unavoidable consequence of this set of beliefs that your brain is inhabited to varying extents by other I's, other souls, the extent of each one depending on the degree to which you faithfully represent, and resonate with, the individual in question.

Thus, we are, in Hofstadter's words, "curious collages" of human souls:

Every normal adult human soul is housed in many brains at varying degrees of fidelity, and therefore every human consciousness or 'I' lives at once in a collection of different brains, to different extents.

5. Jesus as Strange Loop: Symbols, Causality and Resurrection

If this is true, if causally potent self-symbols and self-patterns are distributed across persons--that is, you can change the world through me and I through you--then it stands to reason that this can happen across time as well. That is, the patterns of those who have died continue to affect the world through the patterns they originally created, the ripple they set off in the pond.

For example, in Chapter 1 of I Am a Strange Loop Hofstadter begins with a poignant autobiographical story involving the death of his father. A couple months after his father's death Hofstadter's mother was looking at a photograph of her husband and declared, "What meaning does this photograph have? None at all. It's just a flat peice of paper with dark spots on it here and there. It's useless."

In response Hofstadter writes, "The bleakness of my mother's grief-drenched remark set my head spinning because I knew instinctively that I disagreed with her."

Why? Hofstadter goes on to recount his response to his mother:

In the living room we have a book of the Chopin etudes for piano. All of its pages are just pieces of paper with dark marks on them, just as two-dimensional and flat and foldable as the photograph of Dad--and yet, think of the powerful effect that they have had on people all over the world for 150 years now. Thanks to those black marks on those flat sheets of paper, untold thousands of people have collectively spent millions of hours moving their fingers over the keyboards of pianos in complicated patterns, producing sounds that give them indescribable pleasure and a sense of great meaning. Those pianists in turn have conveyed to many millions of listeners, including you and me, the profound emotions that churned in Frederic Chopin's heart, thus affording all of us some partial access to Chopin's interiority--to the experience of living in the head, or rather the soul of Frederic Chopin. The marks on those sheets of paper are no less than soul-shards--scattered remnants of the shattered soul of Frederic Chopin. Each of those strange geometries of notes has a unique power to bring back to life, inside our brains, some tiny fragment of the internal experience of another human being--his sufferings, his joys, his deep passions and tensions--and we thereby know, at least in part, what it was like to be that human being, and many people feel intense love for him. In just as potent a fashion, looking at that photograph of Dad brings him back, to us who knew him intimately, the clearest memory of his smile and his gentleness, activates inside our living brains some of the most central representations of him that survive in us, makes little fragments of his soul dance again, but in the medium of brains other than his own. Like the score to a Chopin etude, that photograph is a soul-shard of someone departed, and it is something we should cherish as long as we live.

When I read this passage I immediately thought of Jesus of Nazareth. To see the connection let me slightly edit Hofstadter's speech to his mother. Read this and ponder its implications for how we might come to see the Imago Christi--The Image of Christ--causally potent in our lives today, still changing us and the world:

In the living room we have a book that contains the stories and words of the life of Jesus. All of its pages are just pieces of paper with dark marks on them, just as two-dimensional and flat and foldable as the photographs of the people we love who have died--and yet, think of the powerful effect that those stories have had on people all over the world for 2,000 years now. Thanks to those black marks on those flat sheets of paper, untold thousands of people have collectively spent millions of hours shaping their lives to imitate his life, producing communities and actions that give indescribable pleasure and a sense of great meaning. These saints have conveyed to many millions of people, including you and me, the profound emotions that churned in Jesus’ heart, thus affording all of us some partial access to Jesus’ interiority--to the experience of living in the head, or rather the soul, of Jesus of Nazareth. The marks on those sheets of paper are no less than soul-shards--remnants of the soul of Jesus. Each of those letters and words has a unique power to bring back to life, inside our brains, some tiny fragment of the internal experience of Jesus--his sufferings, his joys, his deep passions and tensions--and we thereby know, at least in part, what it was like to be like Jesus, and, thus, many people feel intense love for him. In a very potent a fashion, when the saints celebrate the Eucharist, sharing the stories of those who knew Jesus intimately, what is activated inside our living brains are some of the most central representations of Jesus that survive, making little fragments of his soul dance again.

In the shared memory of the Eucharist the Strange Loop known as Jesus of Nazareth is shared, spread, and passed along. Generation after generation. Century after century.
Theologians often emphasize the narrative heart of the Christian faith, The Story sitting at the Center. I think Hofstadter's work provides a whole new way of thinking about this. In light of Hofstadter's analysis the "story" isn't just a story, remembered, retold and reenacted in the Eucharist, it is the soul-pattern of Jesus that continues to causally affect and change the world.

Think of what happens during the Eucharist while you read this quotation from I Am a Strange Loop:

Though the primary brain has been eclipsed, there is, in those who remain and who are gathered to remember and reactivate the spirit of the departed, a collective corona that still glows. This is what human love means...the more deeply rooted the symbol for someone inside you, the greater the love, the brighter the light that remains behind.

6. Causality, Miracles and a Strange Loop Theology of Transubstantiation

If Jesus was God he represents a Causal Dead End. Jesus would be a causal force in history that could not be reduced to or traced back to anything prior. Jesus, then, would be causally unique.

But once "inserted" into human history, once that Strange Loop takes up its place in the causal whirlpool of history, it begins to affect things, causally speaking. Like a rock thrown in a pond which sends out ripples in all directions. And all those effects, all those ripples of the Incarnation, are, in a strict sense, supernatural. Because when they are "reduced" they trace back to the Causal Dead End.

In short, if Jesus is the cause then God doing it. Think of it like a Time Machine. If I, today, give a cup of cold water in the name of Jesus, then, in a very miraculous way (and I mean that literally), Jesus is doing it. Jesus is transported into the present. The Strange Loop of Jesus, like the Chopin songs discussed above, is inhabiting my mind, causing things to happen in the world. He was Dead. But now he is Alive.

To my mind, this seems to be an interesting convergence between causality and the miraculous, the two being, in this vision, the same thing. The view here suggests that causal events in the world, locally explainable via the scientific method, might actually be "supernatural" in their origin. God might not then need to intervene time after time after time, always fiddling with the cosmos. God may have intervened just once, inserting His Pattern into the causal flux. And everything traced back to that pattern is a miracle. Or, phrased another way, Jesus is the Only Miracle. A miracle that is still sending ripples across the pond.

But this miracle, if it plays out in the causal flux, needs a means of self-sustainment. A means to re-energize, propagate its influence, and avoid dissipation. Thus, the Incarnation, prior to death, ritualizes a means to accomplish those ends: a narrative, communal remembrance. In the words of Hofstadter: "in those who remain and who are gathered to remember and reactivate the spirit of the departed, a collective corona that still glows."

Eucharist.

And if this is so, then maybe Catholics and Protestants are both right about the Eucharist.

Maybe Jesus really is present, in a miraculous way, as the Catholics believe. And maybe Eucharist just is a corporate remembrance as the Protestants believed.

But maybe these two things--the presence of Jesus and the remembrance of Jesus--really are, in the end, the exact same thing.