Review | The Information Theory of Individuality

Introduction

Few concepts have been as influential, and as widely misunderstood, as information. Claude Shannon’s 1948 paper, A Mathematical Theory of Communication, formalized information entropy, introduced bits as the unit of information, and established foundational limits on coding and transmission, helping launch modern information theory and, by extension, much of the current digital era. Later, in 1989, John Wheeler popularized the slogan “it from bit,” suggesting that physical reality might be understood as emerging from informational distinctions, while Rolf Landauer’s insistence that “information is physical” tied informational processes to material substrates and thermodynamic constraints. Together, these moves encouraged a powerful but often misleading habit of thought: to treat information as though it were a kind of stuff, a fundamental substance that could stand in for matter, life, or mind.

Yet, information is not a fundamental substance in the way mass or charge are substances. It is better understood as a relational property—a measure of constrained possibilities, of what could happen relative to what does happen. It is true that the same mathematical framework can be used to describe communication systems, inheritance, development, and control, but that generality can easily tempt one into pancomputational (or paninformational) narratives in which everything is said to be “nothing but information.” The problem is not that informational language is useless; on the contrary, it is often indispensable. The problem is that information becomes reified, stripped from the physical and organizational contexts that make it meaningful. This is especially visible in contemporary debates about life, agency, and individuality, where formal tools are asked to do philosophical work they were never designed to do.

Something similar happens with the concept of individuality. In biology, the term “individual” seems obvious until one asks what exactly counts as one. Organisms, cells, colonies, symbioses, holobionts, superorganisms, and even tiny viruses have all been proposed as biological individuals under different criteria. Philosophical work on biological individuality makes clear that the concept sits at the intersection of physiology, evolution, agency, reproduction, and ecology, and that there is no single, uncontroversial criterion that works across all cases. Biological individuals are often treated as bounded, integrated, temporally enduring entities, yet the living world repeatedly undermines such neat expectations.

It is precisely here that David Krakauer and collaborators intervene. Their Information Theory of Individuality asks whether we can identify individuals without beginning from familiar but possibly derivative markers such as membranes, clonal ancestry, or replication. Their proposal is elegant: individuals are aggregates that preserve temporal integrity, meaning they propagate information from their past into their futures. Rather than starting from objects and then listing their properties, they start from stochastic processes and ask whether an aggregation carries forward enough self-predictive information to count as an individual. In doing so, they turn Shannon’s mathematics toward one of biology’s oldest and hardest questions, not what information is in the abstract, but what informational structures are stable enough, autonomous enough, and persistent enough to be recognized as selves.

What is an individual?

Krakauer and colleagues begin from the basic—but often unexamined—fact that biology always presupposes individuality almost everywhere. We speak of genomes, metabolisms, behaviors, immune systems, and ecological strategies as though the relevant units were already given. But what counts as a “fundamental unit,” and whether such a unit really is an individual, has consequences across taxonomy, physiology, behavior, and ecology. Even Erwin Schrödinger, in What is Life?, took the organism as an obvious point of departure rather than something needing formal derivation. The authors’ project is narrower but deeper: how can we identify individuals without relying on specific solutions (like membranes or germ lines) that some systems use to maintain integrity, but which may not be foundational to individuality itself?

To motivate this shift, the paper reviews a series of standard assumptions. A familiar one is that replication presupposes individuality. From that starting point come several associated expectations, such as the premise that individuals exploit metabolic free energy, respond adaptively to environments, and maintain tightly coordinated relations among their parts. These are powerful heuristics, but they become unstable once one looks beyond the textbook organism. Ant colonies can exhibit coherent temporal continuity even though most workers do not reproduce; colonies themselves do not replicate in the simple sense that cells or single organisms do, yet the colony behaves as a coordinated, adaptive unit. Viruses complicate the picture in a different way; they lack much of the machinery needed for autonomous persistence, yet they retain recognizable identity and adaptive capacities through their embedding in host processes. These cases reveal that replication is neither obviously necessary nor obviously sufficient as a universal criterion of individuality.

The authors therefore propose three fundamental methodological shifts. First, individuality can be continuous: some processes may possess more individuality than others, rather than individuality being strictly all-or-none. Second, individuality can emerge at any level of organization. This means giving up the privilege usually granted to cells or organisms and allowing the possibility that groups, distributed systems, or higher-order collectives can count as individuals when the right formal criteria are met. Third, individuality can be nested. Since life is hierarchically organized, multiple levels of individuality may coexist, overlap, or partially depend on one another. This move is important because it opens the door to individuality without forcing a single scale or a single material boundary in every case.

What unifies these three proposals is the idea of temporal integrity. The authors suggest that individuals are not best understood as static things but as aggregations that preserve information from past to future in a distinctive way. This move places their framework closer to a process ontology than to substance metaphysics. Instead of starting with an object and asking what properties its components have, they begin with a dynamical process and ask whether some coarse-grained partition of that process exhibits enough persistence, closure, and self-predictability to warrant being treated as an individual. In this sense, the paper reframes the individuality problem as a question about information flow through time rather than about material enclosure alone.

Formalizing individuality

The formal core of the paper is built from Shannon information theory applied to a stochastic process over a system $S$ and an environment $E$. The general idea is simple: if we observe some aggregated process at times $n$ and $n+1$, we can ask how much information about the future system state $S_{n+1}$ is already contained in the present system state $S_n$, how much comes from the environment $E_n$, and how much depends on their interaction. In the authors’ terms, individuality is revealed by choosing appropriate information-theoretic “filters” or coarse-grainings, meaning that some partitions expose coordinated persistence, while others wash the signal out entirely. This makes individuality a matter of detecting structured temporal dependence, not of assuming it beforehand.

Their framework depends on a discrete stochastic process where the next state of the system can depend on both the current system and environmental states. The central quantity is the mutual information $I\left(S_n, E_n; S_{n+1}\right)$, which measures how much the joint past of a system and its environment helps predict the system’s future. Using the chain rule for mutual information, the authors decompose this in two complementary ways:

\[I\left(S_n, E_n; S_{n+1}\right) = I\left(S_{n+1}; S_n\right) + I\left(S_{n+1}; E_n | S_n\right)\]

and

\[I\left(S_n, E_n; S_{n+1}\right) = I\left(S_{n+1}; E_n\right) + I\left(S_{n+1}; S_n | E_n\right).\]

These two decompositions correspond to two ways of assigning explanatory weight. One privileges the system’s own persistence, the other privileges environmental determination. From these expressions come the first individuality measures. The quantity $A^* = I\left(S_{n+1}; S_n\right)$ is called organismal individuality (or endogenous determination), while $A = I\left(S_{n+1}; S_n \mid E_n\right)$ is called colonial individuality, and $nC = I\left(S_{n+1}; E_n \mid S_n\right)$ captures environmental determination.

To deepen the interpretation, the paper then appeals to partial information decomposition (PID). Although the authors do not commit to one contested formal version of PID, they use it conceptually to separate the information in $S_{n+1}$ into four components: information uniquely supplied by the system, information uniquely supplied by the environment, information shared by both, and synergistic information that only appears through their joint interaction. In this reading, organismal individuality $A^*$ combines shared information with the unique contribution of the system, while colonial individuality $A$ combines synergistic information with that same unique system contribution. This leads to an elegant qualitative contrast. Organismal individuality corresponds to systems that carry significant internal memory while also sharing adaptive information with their environment. Colonial individuality, by contrast, characterizes systems whose persistence depends more strongly on ongoing interactive regulation with the environment than on private inherited memory. Environmental determination measures the degree to which the environment itself continues to shape the system’s future, while environmental coding captures the difference between organismal and colonial forms by asking how much environmental information is innately encoded versus continually negotiated.

An illustrative example in the paper makes these distinctions concrete. By analyzing a simple coupled binary system, the authors show that when higher-order coupling between system and environment is low, organismal and colonial individuality can coincide, because both are supported by strong self-memory. As higher-order coupling increases, organismal individuality can collapse while colonial individuality rises, since the system’s persistence becomes increasingly dependent on coordinated interaction with the environment. Environmental determination likewise transforms under coupling, becoming less a matter of independent environmental memory and more a feature of jointly structured dynamics. This example also reveals an important limitation: both organismal and colonial measures can only stay constant or increase as one enlarges the candidate system boundary. They therefore do not, by themselves, identify the optimal boundary of an individual. To obtain precise boundaries, the authors note that one would need a regularizer or cost function penalizing system size. Their present goal, the authors accept, is not to find the perfect partition, but to provide different informational “windows” on individuality.

The formalism is powerful, but it also inherits some deep assumptions. Most notably, the state spaces of system and environment are assumed to be fixed. That is methodologically convenient, but biologically restrictive. Fixed state spaces are often poor at representing genuine novelty, because they presuppose the full space of possibilities in advance. Evolution, development, technological, and cultural change routinely generate new functions and constraints that alter the very structure of the space being navigated. In that sense, the information theory of individuality (ITI) is strongest as a theory of persistence and partitioning within a given informational world, and weaker as a theory of how genuinely new informational worlds are created. That is not a fatal flaw, but it does delimit the scope of what the framework can presently claim.

Conclusion

Krakauer and colleagues close by arguing that the ITI provides a principled way to detect fundamental units in adaptive systems using suitable informational filters. In this respect, the framework aspires to do for individuality what model-free methods in physics attempt to do for undiscovered particles: identify subtle but stable patterns without imposing too many assumptions in advance. The larger implication is that individuality may be less a visible property of neatly bounded objects than a revealed structure of information flow, detectable only when one looks through the right coarse-grained lens. This is a compelling shift, especially for multi-scale, distributed, or socially constituted systems that standard biological categories tend to treat as derivative or epiphenomenal.

A second strength is the connection the authors draw between individuality and uncertainty reduction through nested slow variables. In their view, one driver of new function is the construction of dynamical processes with characteristic time scales that compress fast microscopic fluctuations into more stable, predictive macrostates. That picture makes individuality part of a broader account of adaptive organization, implying that systems become individuals insofar as they generate coarse-grained variables that better predict their own futures than the underlying microscopic details do. This is one of the most suggestive aspects of the paper, because it links individuality to hierarchy formation, temporal depth, and the emergence of functional order.

At the same time, the framework leaves open several major questions. The paper explicitly takes for granted the availability of accurate measurements across meaningful scales and times, while postponing the problem of how to identify the “best” partition of system and environment in the first place. That challenge immediately invites comparison with the free energy principle (FEP), which also seeks to explain how adaptive systems persist within bounded state spaces while reducing uncertainty, and which does so by appealing to Markov blankets that separate internal from external states. Like the FEP, the ITI places great explanatory weight on uncertainty reduction and coarse-graining, and this suggests that it may inherit some of the same difficulties critics have raised for blanket-based accounts, especially the risk of treating living systems as if their persistence were exhausted by state-invariance, rather than by historically changing forms of organization and normativity.

There is also a deeper limitation. The ITI is illuminating precisely because it treats individuals as dynamical informational processes, not as substances. But because it stays within a Shannon-style formalism, it remains a theory of syntactic temporal dependence, not of semantic or organizational closure in the stronger sense that some theories of life might demand. It can tell us when an aggregate propagates information from past to future, and how much of that depends on itself versus its environment, but it does not yet tell us whether that propagation is sufficient for agency, meaning, or life itself. The authors are careful here: they present ITI as a lens, not a final metaphysics. In that modest but important sense, the paper succeeds. It does not solve the individuality problem once and for all, but it gives us a mathematically disciplined way to ask where individuals are, how many levels they occupy, and how strongly they hold together through time.