For some time, I have been thinking about a piece by Bach as the opening to a general course on artificial intelligence: Canon per Tonos from The Musical Offering. My choice was initially more intuitive than deliberate. Before speaking about models, data, and neural networks, I wanted to play something that could show how a very simple structure, through repetition, can come to seem more complex than its individual parts.
But repetition is not the only interesting feature of this piece. The canon is constructed so that when one cycle ends, the music has arrived one whole tone above where it began. It can then travel the same path again, following the same rule but beginning from a new position. Each time, we feel that we have returned to the beginning, yet we have not returned to precisely the same place. The pattern has repeated, but the state has changed.
This small difference matters to me. A circle that returns to the same point each time is not the same as a path that carries something from one return into the next. The first may be a closed cycle; the second is more like a spiral. Seen from above, the movement is circular. Seen from the side, its height has changed.
Perhaps this is why the piece remained in my mind after the course. It was no longer merely a metaphor for explaining AI. I began to think about how much of nature, mind, and human life is built upon this same pattern: return with a small difference; repetition that retains something from the previous cycle.
Then a more personal question occurred to me: if what I call “myself” is also the product of such loops, what am I to do with the painful repetitions of my own mind?
When Does a Loop Create Something?
When we say that a phenomenon has “emerged” from simpler components, we usually do not mean that something magical has appeared out of nothing. The components still exist, and the larger phenomenon still depends on them. Yet properties become visible at the level of the whole that cannot be found by examining each component in isolation. Philosophical discussions of emergence often bring these two aspects together: a higher-level phenomenon depends upon its underlying components, while also possessing a degree of explanatory independence at its own level.
A single note is not music. A single neuron has no memory. A single ant does not hold a complete map of the colony in its mind. Yet through the relationships and exchanges among these parts, something appears at another level, and to understand it we are forced to use a different language: melody, memory, colony.
Still, we should not rush from these examples to the conclusion that “repetition creates meaningful complexity.” Mere repetition often reproduces only what was already there. If a program executes the same instruction millions of times without its state changing from one cycle to the next, nothing new has happened. For a loop to create something, it usually requires at least one of the following: a memory that retains the effects of the previous cycle, a difference that enters the next one, feedback that adjusts the path, or an environment that allows some outcomes to continue while eliminating others.
Perhaps the more precise statement, then, is this: complexity arises not from repetition alone, but from repetition accompanied by change and accumulation.
This is what we hear in Bach’s canon. The piece returns to its original form, but the musical key has changed. The rule remains the same while the position shifts. The movement is closed and open at once.
Stairs That Do Not Ascend
In Escher’s lithograph Ascending and Descending, groups of people walk around a staircase on the roof of a building. Those moving in one direction appear to be climbing forever, while those moving in the other seem to be descending without end. Yet both groups eventually return to the same point. Created in 1960, the work belongs to Escher’s series of “impossible constructions.”
What we see is locally plausible but impossible as a whole. Each step appears slightly higher than the one before it, yet together they form a closed path. Here, unlike in Bach’s canon, no real ascent is taking place. There is movement, there is exhaustion, and there is even the experience of climbing, but the final height never changes.
These two images—Bach’s canon and Escher’s staircase—seem to concern the same thing, and that is precisely why their difference matters. In both, the movement reconnects with its point of origin. But in one, the return is accompanied by change; in the other, the very feeling of change is part of the structure’s illusion.
Not every loop takes us higher.
In Gödel, Escher, Bach, Douglas Hofstadter writes about “strange loops”: structures in which, after passing through several levels, we somehow return to where we began—sometimes through self-reference, and sometimes through the collapse of a hierarchy that was supposed to have a clear top and bottom. Gödel gives this possibility a formal expression, Escher gives it an image, and Bach gives it sound. The book, at least in the reading that has mattered to me, asks whether what we call the “self” might also emerge from a complex system repeatedly turning back upon itself: a brain that constructs not only the world, but also an image of itself within that world, and then acts again on the basis of that image.
I am not claiming that this is a final explanation of consciousness or the mind. There is still no consensus that consciousness can be explained entirely through the idea of emergence. The term itself has both weak and strong meanings in the philosophy of mind, and the degree to which the mind can be considered independent of brain processes remains disputed. For me, the strange loop is less a definitive answer than a possibility for thought: perhaps the “self” is not a fixed object located somewhere inside the brain, but a pattern that the brain sustains by continually referring to the world, the body, memory, and its own image of itself.
If that is so, then I am not something that was created once and thereafter merely receives whatever happens. I am made and remade within these exchanges.
Nature Does Not Repeat Itself Exactly Either
Evolution is another example that easily tempts us to attribute everything to “repetition.” Generation after generation, life repeats a familiar cycle: birth, survival, reproduction, and death. But the diversity and complexity we see today were not produced by reproduction alone. Differences exist within populations; some of those differences are passed to the next generation; and environmental conditions allow certain traits a greater chance of persisting. Natural selection is only one mechanism of evolution, operating alongside mutation, migration, and genetic drift.
Nature had no plan to arrive at the human brain. We cannot say that every round of this cycle necessarily moved “upward,” because outside our own needs and values, upward and downward have no clear meaning in evolution. An adaptation that is useful in one environment may be useless or harmful in another. Many species have neither become more complex nor progressed towards a predetermined destination. They have simply endured under certain conditions—or disappeared.
Nevertheless, evolution demonstrates something important: when a relatively simple local rule is applied repeatedly, and when the result of each cycle remains present in the next—or when the environment accepts only some of each cycle’s outcomes because of their interaction with other cycles—it can, over a very long time, produce things that were visible in none of the individual stages. Eyes, wings, nervous systems, and eventually a creature capable of thinking about its own evolution did not emerge from a central set of instructions. They are accumulated histories of change.
We can see a limited version of the same image in machine learning. During one cycle, a model makes a prediction, its error is measured, and its weights are adjusted slightly. It predicts again and changes again. No individual cycle produces understanding, just as no individual generation explains evolution. What we later call a “model” is, to some extent, the sediment left by a vast number of small corrections.
The Loops That Turn Within the Mind
Repetition in the mind is not always so beautiful. Sometimes a piece of news, an image, or a sentence activates something we thought had ended. Anxiety returns. The body shifts into a state of alarm. Thoughts circle around the same problem and, on each pass, discover new evidence for an old conclusion: there is no future; nothing will change; I will not be able to endure this.
For me as an Iranian, these loops are not fed only by personal memories. War and the shadow of war, economic instability, rising prices, the collapse of any ability to plan, and a feeling that might best be described as “having no future” are not abstract events taking place outside the mind. Each can repeatedly enter everyday life and reactivate the same circuits of anxiety and depression. Under such conditions, it becomes difficult to distinguish how much of my suffering is an understandable response to the world outside, and how much has become an internal loop that now continues to operate even in the absence of its original trigger.
Psychology uses the term rumination for one form of this repetition: a recurring and passive preoccupation with the causes and consequences of feeling bad. Research regards it not as a solution but as a factor associated with intensified negative mood, greater difficulty in solving problems, and the persistence of depressive symptoms. Thought may feel as though it is investigating the problem, while in practice it keeps travelling the same path. Here we are closer to Escher’s staircase than to Bach’s canon: there is a great deal of mental movement, but no necessary change in level.
This raises a serious doubt about my original idea. Can I say that depression, and the events that repeatedly activate it, are ultimately creating meaning within me and producing a different, higher version of myself? Or are they keeping me trapped in a fruitless cycle? Could they even be pulling me downward through a loop of erosion and decline?
I think that if I make the first claim without qualification, I will be speaking with more certainty than the science permits—and with less humanity than the subject demands. Suffering is not necessarily a teacher. I want to say that once more. Suffering is not necessarily a teacher. The truth is that sometimes we may learn something from suffering and still deceive ourselves into believing that what we learned was useful. Some forms of suffering merely diminish a person’s strength, wear away their relationships, and take years that no virtue can ever replace. Depression is not a philosophical metaphor. It can be a serious disorder that disrupts sleep, concentration, work, relationships, and the desire to live.
If we tell someone living under the pressure of war, poverty, grief, or depression that “this had to happen for you to grow,” we place another burden on their shoulders. Now, in addition to enduring their pain, they must prove that they emerged from it as a better person. And if they cannot, it is as though they have failed even at suffering.
That is not what I want to say.
Meaning Is Not Within Suffering Itself
There is a fundamental difference between saying “suffering has meaning” and saying “meaning can be made from suffering.” The first statement assigns suffering a purpose and a necessity, as though what happened to me had been given a mission from the beginning: to carry me somewhere higher. The second is more modest. What happened may have been cruel, accidental, and meaningless, yet I may later be able to give it a place in the story of my life, change my relationship to it, or draw a decision from it.
We carry broad beliefs about the world, justice, control, identity, and our goals. A painful event may conflict with this larger picture and create a rupture. If the world is predictable, why did this happen? If effort leads to results, how could everything be undone by a political decision or a war? The mind tries to change either the meaning of the event or its general beliefs in order to narrow this gap.
Even the concept of “post-traumatic growth” is neither simple nor certain. Some people who have lived through severe experiences describe changes in their priorities, relationships, or understanding of life. Perhaps, at times, the narrative of growth is itself a way of enduring. That does not necessarily make the narrative false, but it is different from claiming that suffering has truly and inevitably made us better.
If meaning does take shape, then, it is not the automatic product of repeated pain. It is the result of a change introduced into the loop. That change might be naming the experience, speaking with someone, therapy, writing, grieving, recognising an old pattern, building a safe relationship, or taking one small action to change some part of the external reality. The next cycle may still pass through the same place, but something from the previous one travels with us.
Here I return to Bach—not because every repetition ascends, but because ascent requires a structure of return capable of retaining change.
The Mind Is Not Merely an Internal Problem
We should not overlook a cognitive danger here. If we reduce all suffering to psychological loops, we may ignore its real external causes. The anxiety of someone whose savings lose value every day is not merely a cognitive distortion. Fear of war cannot be turned into a solved problem through a few breathing exercises. A person who has lost the ability to construct a future does not necessarily suffer only from a “negative perception.”
Mind and environment form a loop. External conditions affect the mind; the mind changes our behaviour and choices; and those choices reshape our relationship with the environment. Sometimes breaking a loop requires inner work. Sometimes it requires security, money, treatment, relationships, migration, solidarity, or political change. Most often, it requires some combination of these.
For this reason, making meaning from suffering should not become a forced reconciliation with something that should never have happened. I can learn something from a wound while still wishing it had never been inflicted. I can be changed by an event without justifying it. I can have become more resilient and still retain the right to be tired.
These statements do not contradict one another.
Once, a friend told me about a great loss and suffering that had changed the course of his life. He emphasised that many years had passed and that he was now satisfied with the person he had become and the life he had. He said this to show me that the result of the suffering I was experiencing would not necessarily be bad. I took him back to the day it happened and asked: if, on that day, you had been able to prevent it—and if you had known that doing so meant you would not become the person you are today—would you have stopped it?
What about you? You have endured some great suffering. Would you have stopped it? However painful these cycles may be, they leave something behind, and what they leave may satisfy you in later cycles. It may give you greater strength. But it may also weaken you.
I know that life does not actually give us the right to make such a choice. Yet we can see how, in the world we inhabit, two opposing statements can both be true—and how each can transform the repetitions that follow.
The Next Cycle
When I think about loops now, I see two images at once. In one, Escher’s figures continue to walk and, despite their perpetual ascent, never rise any higher. In the other, Bach’s canon returns to its beginning, but one whole tone above where it started. The difference is not in the circular movement itself. It is in what the loop retains from the past and carries into the future.
Depression can also form a loop: an event, a thought, withdrawal, loneliness, and then a return to feeling bad. There is no guarantee that travelling this path will create meaning. But perhaps we have an opportunity to introduce a change somewhere within the loop—not necessarily a dramatic or heroic change, but something that makes the state of the next cycle slightly different. A simple act of companionship. A decision. Asking for help. Writing down precisely what keeps repeating. Or even accepting that today I cannot ascend, and that my only task is to remain alive.
I find this more comforting than the claim that “all suffering happens for a reason.” It does not require me to love my suffering or invent a cosmic plan for it. I need only avoid treating the possibility of change as completely closed.
Perhaps we are products of loops, but not every loop is destiny. Some loops must be broken. Some must be readjusted with the help of another person. And some, if they can carry something from one cycle into the next, may return us to the same place—but not as the same person.
The Spring of Colour and the Delight of Turning
هزار گل، ز چمن رفت و باز برگردید
A thousand flowers left the garden, then returned once more.
بهارِ رنگ چه مقدار ذوقِ گردش داشت.
How deeply the spring of colour delighted in turning and returning.— Bidel Dehlavi, Ghazal 815