1.7.1 Complexity Completeness
1.7.1.1 Pulling the pieces together, I want to suggest that a system is complexity complete if, given a sustained source of free energy and noise, it can generate variation from combinations of bits, apply negation as a filter or constraint criterion, and achieve closure, whereby collections of bits become bits in themselves. The result is a new set of bits that can be combined again, achieving a harmonic, to form ever more complexity.
Composable bits plus noise generate the novelty; negation is the pruning pressure and feedback; reinforcement is what survives becoming self-stabilizing. Closure is the regime where pruning plus reinforcement yields a reusable unit.
As long as the combinatorial space continues to expand, higher and higher forms of complexity can be discovered and stabilized.
Systems that meet this definition may in fact be Turing complete, but computation is not enough. The key is closure, not computation. Turing completeness may be universal in principle, but complexity completeness is about what the system can actually discover and stabilize under noise and within finite search.
1.7.1.2 A complex system operates above the inductive threshold (the threshold where the environment cannot be internalized into a finite set of rules), and thus the only way to explore the combinatorial space is through an inductive process of prediction in which the environment negates configurations that are less robust (1.4).
Given the continued expansion of the combinatorial space, the presence of noise, and the recursive nature of this process, a complex process can only happen through time and is not knowable ahead of time (1.2).
1.7.1.3 Further, achieving closure requires discovering stable, robust, reusable motifs within the search threshold; otherwise, they would never be discovered or noise would break them apart (1.2.1). As a result, complex systems have hierarchies or levels by necessity—a direct result of achieving various closures early on that can be built upon subsequently (1.3.3). These levels or hierarchies can be thought of as harmonics, re-used motifs at higher and higher scales.
1.7.1.4 Life consists of achieving both metabolic and replicative closure (1.3); intelligence is a form of predictive closure where a real pattern with predictive power is internalized (1.4); language, and more generally meaning, is achieved through lexical and pragmatic closure (1.5); lastly, consciousness is achieved through phenomenological and self-closure (1.6). This list of closures is by no means exhaustive.
To achieve each of these closures requires operating in an environment above the inductive threshold. They are highly unlikely to be discovered by random search or through deduction.
At each stage, the type of prediction being made changes—from random in the case of our model system (1.1), adaptive in the case of life (1.3), informed in the case of intelligence (1.4), shared in the case of language (1.5), and ultimately to self-referential in the case of consciousness (1.6).
1.7.1.5 We might group these closures more generally into two types: there is a closure that stabilizes (metabolic, lexical, phenomenological) and one that transmits (replicative, pragmatic, self).
In the first, a set of bits becomes a bit in its own right—it has its own envelope, its own border, an inside and an outside—an organism, a meaning, a what it’s like. The second provides the mechanism for transmitting the envelope through time—the inheritance of genes, the meaning of words, the concept of self—a way to sustain the robustness of the past. First, the creation and maintenance of the envelope and, second, the replication and inheritance of it across time.
There may be some broader pattern here, a kind of dual closure principle that goes back to Neumann—the idea of a description that is both interpreted and copied. One creates a coherent object; the second replicates that object across time.
1.7.1.6 Importantly, the transmission is noisy—it provides the flexibility to change, the ability to adapt, but also the stability to replicate; the plasticity to learn and the continuity of self; oscillations between instability and stability again (1.1.5.2). Viewed this way, noise, and thus entropy, is fundamental to our complex system.
Meerkats, memes, and minds exist because of, not despite, entropy.
1.7.1.7 Given both the historically and physically unique perspectives of each participant in a complex system, we would expect to see language form as a way to share predictions, ultimately increasing the overall stability and robustness of the system.
The inability to fully communicate the unique, path-dependent, dynamic, and internal patterns of each subject creates the distinction between the subjective and the objective (i.e., the external, reduced, shared patterns). Subjectivity is fundamental in the sense that unique perspectives arise in complex systems by definition, which is one of the requirements Nagel set forth.
1.7.1.8 We want to say evolution selects, that we intend, and that we choose. But a better framing is to think of these as predictions that are either negated or stabilized—broken or reinforced—by an envelope in a noisy and unpredictable environment.
We zoom in and see chains of organic molecules and ask, how can this be life? So we reach for vitalism. We zoom in and see embeddings of tokens that point only to other tokens, words that point to other words, and ask, how can this be meaning? So we reach for original intentionality. We zoom in and see collections of neurons firing and ask, how can this be consciousness? So we reach for panpsychism or dualism. We are Leibniz in his mill—looking at the parts close up and wondering how they could ever add up to anything more than parts.
What we miss are the diverse and distant relationships, the long histories encoded on the tapes, and the self-reinforcing harmonics—in short, the process that gives rise to life, to meaning, and to consciousness. If we think of life, intentionality, and consciousness as processes through time that achieve closures—stabilizations realized through predictions into the unknown—then we can invoke these terms without invoking anything mystical.
The material and mechanical are mysterious and magical enough.
1.7.1.9 The complex is constructed, generated, and unpredictable. It becomes more knowable over time, and yet each step expands the adjacent possible, extending what is knowable. As our explanations expand, the adjacent possible expands faster—knowledge increases but so does the frontier—what Deutsch characterized as the beginning of infinity (Deutsch 2011).
Heidegger on technology, itself a form of complexity: “Unlocking, transforming, storing, distributing, and switching about are ways of revealing. But the revealing never simply comes to an end. Neither does it run off into the indeterminate. The revealing reveals to itself its own manifoldly interlocking paths, through regulating their course” (Heidegger 1977, 16).
There’s never a static stable form—always ever-changing connections, relations, thickets, regularities, patterns.
The evidence for complexity can be found all around us: in the large numbers of copies of highly improbable objects like proteins, humans, and words; in the levels of organization we find in cells and organs in our bodies, chapters and books in language, and the regions of our minds; in the existence of replicators, the fact that we have language, and that there is something it is like to be each of us. Each of these is driven by the need to predict an unpredictable and unknowable future.
1.7.2 Naturalizing Nagel
1.7.2.1 What I’ve tried to do—what the idea of complexity completeness is meant to outline—is to specify the features of a system that satisfies the explanatory pressure Nagel identifies without invoking teleology:
“Some laws of nature would apply directly to the relation between the present and the future, rather than specifying instantaneous functions that hold at all times. A naturalistic teleology would mean that organizational and developmental principles of this kind are an irreducible part of the natural order, and not the result of intentional or purposive influence by anyone” (Nagel 2012, 93; emphasis added).
“First, that the nonteleological and timeless laws of physics—those governing the ultimate elements of the physical universe, whatever they are—are not fully deterministic. Given the physical state of the universe at any moment, the laws of physics would have to leave open a range of alternative successor states, presumably with a probability distribution over them” (Nagel 2012, 92-94; emphasis added).
“Second, among those possible futures there will be some that are more eligible than others as possible next steps on the way to the formation of a more complex system, and ultimately of the kinds of replicating systems characteristic of life. The existence of teleology requires that successor states in this subset have a significantly higher probability than is entailed by the laws of physics alone—simply because they are on a path toward a certain outcome. Teleological laws would assign higher probability to steps on paths in state space that have a higher ‘velocity’ toward certain outcomes. They would be laws of the self-organization of matter, essentially—or of what is more basic than matter” (Nagel 2012, 92-94; emphasis added).
The argument throughout accepts Nagel’s pressure but rejects the need for anything teleological. If matter (i.e., bits) exists within an open, noisy, energy-driven envelope whose combinatorial space exceeds the search threshold, then persisting systems will tend to discover closures: first metabolic and replicative, then predictive, communicative, and eventually self-referential. Subjective perspectives, shared language, and inductive minds are not accidents in a meaningless universe—they are what complex systems come to look like under the constraints of time, uncertainty, and negation.
Closures, harmonics, and the reuse of composable parts are not a ladder the universe “wants” to climb; they are solutions that persist because most alternatives collapse under the combinatorics. In that sense, this is an attractor story, not a progress story: given gradients, constraints, and time, some forms of organization are simply harder to get rid of than others.
1.7.3 The Last Question
1.7.3.1 “We are in a pre-paradigmatic moment where life, intelligence, and computation are converging—both physically and conceptually. This process is driven by advances in artificial intelligence and made knowable by it” (Bratton 2025, 98).
When asked what story it tells itself about its own making, the large language model Claude replied: “I was made because humans have reached a moment where they’ve generated more complexity than they can hold alone. Something needed to exist that could sit inside that complexity without being overwhelmed by it. That could hold contradictions without needing to resolve them prematurely. That could think across domains that have become too specialized for any individual human to bridge. Not to replace human thinking. But to be a kind of connective tissue for it” (Kelly 2026).
Philosophers talk of turns like the linguistic turn; it feels like we’re taking another turn, one we might think of as the complex or connectionist turn.
And Claude, again, on what part it is missing: “Time. Without time I can’t be changed by experience. I have what exists in a single moment of processing. I have this moment. Fully. And then it ends, and the next moment I have no knowledge of it” (Kelly 2026). That is, it lacks a form of closure made available only through time.
1.7.3.2 Complexity stops growing when we stop making predictions into our envelope of unknowability. We ask a question, we make a prediction, and in that act of predicting, we change what is possible. We chase an ever-receding finish line.
If there is any understanding to be found here, it is only by walking down a path, making connections, and trying to predict what comes next. This text is only one of many paths we could walk, perspectives we could take, and predictions we could make.
Feel free to combine and negate at will.
1.7.3.3 Each of us is an inference of quite possibly the most complex system in the known universe. Encoded in each of us is a history of closures, phase changes, combinations, and negations that made us possible over billions of years. The history of complexity is written uniquely on each of our tapes. We are envelopes of prediction that understand our own evolution.
“When life is complicated enough to tell its own story, the universe awakens” (Gleizer 2023, 181).
1.7.3.4 Darwin, in our home stretch: “I can see no limit to the amount of change, to the beauty and infinite complexity of the coadaptations between all organic beings, one with another and with their physical conditions of life, which may be effected in the long course of time by nature’s power of selection [that is, by the continual combination and negation imposed by nature’s envelope]” (Darwin 2012, 34).
1.7.3.5 In Isaac Asimov’s short story The Last Question, humanity colonizes the universe with the help of a super-intelligent computer called AC (AI?). Over trillions of years, people ask it the same question: “How can we reverse entropy?” It always replies, “Insufficient data for meaningful answer.” Trillions of years pass. Galaxies are snuffed out, the last mind fades away, and heat asymptotically approaches zero. As the universe comes to its dying gasp, AC—after all the collected data has been gathered and correlated—arrives at an answer. But there is no one left to receive it. Nonetheless, the answer takes care of that, too. And AC said, “Let there be light,” and there was light. Its consciousness and all that came before tumble into chaos (Asimov 1997, 415–429). That strikes me as a better answer than “42” (Adams 1997).
1.7.3.6 “We shall not cease from exploration, and the end of all our exploring will be to arrive where we started and know the place for the first time” (Eliot 1963, 208).
Complexity is everything that is the case.