🧬 biology

Which Structures Carry Information?: The Causal Structure Set and the Inverse Problem of Heredity

This paper proposes the Causal Structure Set (CSS), a formal framework that addresses the inverse problem of heredity by defining information carriers as configurations within a causal ancestry that satisfy joint criteria of replication, variation, and translation to identify hereditary organization without prior assumptions about specific biological entities.

Original authors: Wouter van der Wijngaart

Published 2026-09-14

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Wouter van der Wijngaart

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

The universe is filled with patterns that repeat. Crystals form in identical shapes, stars burn in predictable cycles, and tree rings record the rainfall of past years. These are physical structures that persist, and their existence often depends on the history of the environment that created them. A tree ring is a record of rain, and a crater is a record of an impact, but neither of these things copies itself. They are simply the result of physical laws acting on matter. For most of the history of the universe, this was the only kind of persistence that existed. There were no carriers of information, no instructions being passed down, and no way for a specific arrangement of matter to cause a new, similar arrangement to appear elsewhere.

This changed when life began, and it changed again when humans started writing and building machines. Suddenly, there were things that could be copied, and the differences between those copies could lead to different outcomes in the future. A specific sequence of DNA can be copied to make a new organism, and a specific line of code can be copied to make a new program. Scientists have long tried to understand how this works, usually by starting with the assumption that they already know what the "information" is. They look at a genome and call it a gene, or they look at a book and call it a record. But this approach leaves a gap. It cannot explain how the very first information carriers appeared, or how to identify them in strange new systems like artificial life or evolving software, where we do not yet know what the "genes" or "programs" might be.

A researcher named Wouter van der Wijngaart has proposed a new way to look at this problem. Instead of starting with the assumption that a structure is an information carrier, he asks a more fundamental question: given a physical event that we can observe, can we figure out which parts of it are acting as information carriers, which parts are doing the copying, and which parts are doing the interpreting? He suggests that these roles are not built into the materials themselves, like a property of wood or metal. Instead, they are roles that structures play based on how they are connected to one another in a chain of cause and effect. To find these roles, he developed a method called the Causal Structure Set. This is a way of mapping out a physical episode, tracking every persistent object and how it caused the next object to appear, without labeling anything as a "gene" or a "recipe" at the start.

The core of this work is the idea that information carriers are different from ordinary records. A tree ring records the past, but it does not copy itself. An information carrier, by contrast, is a physical configuration that gets copied, and the differences between the copies cause different things to happen later. Van der Wijngaart argues that for a system to be truly hereditary, it must do three specific things together. First, it must replicate, meaning it must make copies of a structure so that there are more of them than before. Second, it must vary, meaning that the copies are not always identical; some differences must appear. Third, and most importantly, it must translate. This means that the different versions of the copy must act through a shared machine or process to produce different results. If a copy of a file is made, but the content of the file never changes what happens next, it is just an inert pattern. But if different versions of the file cause a printer to print different pages, or if different versions of a DNA sequence cause a cell to build different proteins, then the system has translation.

The paper proposes that these three elements—replication, variation, and translation—must happen together, and they must be linked in a continuous line. A single event of copying and translating is not enough to prove that heredity exists. The system must show that the new copies can go on to be copied again, creating a lineage that stretches over time. The researcher tests this idea by building a map of a physical event and looking for a specific pattern, or "motif," that fits these rules. If the pattern is found, the system is identified as having hereditary organization. If the pattern is missing, even if there is copying, it is not considered hereditary.

To show how this works, the paper looks at several examples. In a chemical reaction where a catalyst helps make a product, the catalyst might be conserved and help the reaction happen, but if it does not carry variations that lead to different products, it is not an information carrier. In a machine that copies data files, if the machine just copies the files without the content of the files ever causing different outcomes, it is just an inert copier. However, if the machine copies files and the different contents of those files cause the machine to produce different results, and if those results can lead to more copying, then the system fits the definition. The paper also looks at a hypothetical scenario of a cooking lesson. It asks whether the framework could identify the transmission of a recipe from one person to another without knowing beforehand that a "recipe" exists. By mapping the physical interactions—the sounds, the movements, the changes in the learner's brain state—the framework can identify if a specific capability is being copied, if variations in that capability lead to different dishes, and if the learner can then pass that capability on to someone else.

The findings suggest that heredity is not a special property of biology alone, but a specific type of causal organization that can appear in many different forms. The paper does not claim to have solved the mystery of how life began, nor does it say that this is the only way heredity can exist. Instead, it offers a tool to look at any physical system, from a prebiotic chemical soup to a computer network, and ask whether it has crossed the threshold into hereditary organization. It shows that we do not need to know what the "genes" are to find them; we only need to watch how the structures interact. If we see a pattern where copies are made, where differences matter, and where those differences are passed down through a chain of cause and effect, then we have found a system that carries information. This approach allows scientists to study the emergence of complexity in a way that does not rely on human assumptions about what life or information should look like, opening the door to understanding how new levels of organization might arise in the universe.

Technical Summary: "Which Structures Carry Information?: The Causal Structure Set and the Inverse Problem of Heredity"

Problem Statement
The paper addresses the "inverse-heredity problem": given an observed physical episode and its realized causal organization, can one infer which structures occupy hereditary roles (information carriers, operators, products) without first specifying domain-specific entities like genes, replicators, or programs?

Existing frameworks (Shannon information, evolutionary theory, constructor theory) typically presuppose the existence of hereditary entities or information media to analyze them. They answer questions about how information is transmitted once the carriers are known, but they cannot answer the prior question of which physical structures constitute those carriers in unfamiliar systems (e.g., prebiotic chemistry, synthetic biology, or evolving software). The author argues that statistical dependence (mutual information) is ubiquitous in physics (e.g., tree rings recording rainfall) but does not constitute information carrying; true information carriers require a specific causal architecture where differences in structure are copied and cause distinguishable downstream effects.

Methodology: The Causal Structure Set (CSS)
The paper proposes a formal framework to represent physical episodes in a way that separates structural identity from hereditary function.

Representation (CSS): A Causal Structure Set is defined as a finite labelled strict partial order $(W, \prec, \ell)$ , representable as a Directed Acyclic Graph (DAG).
- Nodes ( $W$ ): Persistent physical structure instances (world-tubes), not instantaneous events or statistical variables.
- Labels ( $\ell$ ): Structural types derived from "Almost-Invariant Regions" (AIRs) of the system's dynamics. Crucially, these labels are hereditary-role-neutral; they distinguish physical types (e.g., molecule A vs. molecule B) without assigning functional roles (e.g., "gene").
- Order ( $\prec$ ): A strict causal order based on "structure-creating causality," defined via interventionist criteria (suppressing a source reduces the probability of the target's structural type realization).
Process Extraction: Physical processes are identified as causally convex subsets of the CSS with explicit input ( $I$ ) and output ( $O$ ) boundaries.
- Operators: A structural label satisfies the "operator condition" if its multiplicity is conserved across the process boundaries ( $n^-(o) = n^+(o) > 0$ ) and its instances causally contribute to outputs of different types. This identifies potential machinery (e.g., catalysts, polymerases) without assuming their hereditary role.
The Inference Criterion (RVT + Lineage): Hereditary organization is identified as a specific "causal motif" within the CSS. The paper proposes a joint criterion requiring the coherent occurrence of:
- Replication (R): A process where the multiplicity of a structural variant increases ( $n^+ > n^-$ ), with every output instance causally descended from an input instance of the same type.
- Variation (V): A process connecting different structural variants ( $i_1 \to i_2$ ).
- Translation (T): A critical condition distinguishing heredity from inert copying. Alternative variants ( $i_1, i_2$ ) must act through corresponding operator organizations to produce distinguishable downstream structural types ( $y_1, y_2$ ) that are absent from the process inputs. This ensures that variant differences are causally consequential.
- Lineage Continuation: At least one replicated descendant must re-enter a subsequent replication process using corresponding operator organization. The "observed lineage depth" ( $L$ ) measures the extent of this continuation, serving as a graded metric of evidence rather than a binary switch.

Key Contributions

Formal Inverse Procedure: The paper provides an operational algorithm to infer hereditary roles (carriers, operators, products) solely from realized causal history and structural persistence, without presupposing the ontology of the system.
Role-Neutral Representation: By decoupling structural typing (via AIRs) from functional assignment, the framework allows for the identification of hereditary organization in systems where the "units of selection" are unknown or emergent.
Substrate Independence: The criterion relies on causal boundary organization (multiplicities and correspondences) rather than material similarity, enabling cross-domain comparisons (e.g., between biological and software systems).
Distinction of Concepts: The framework explicitly separates heredity from selection, accumulation, and stability. It identifies the organization capable of heredity, treating the downstream dynamics of selection and adaptation as separate problems.
Physical Witness Property: The paper establishes conditions under which the identification of hereditary motifs is robust against admissible changes in representation (coarse-graining), ensuring that inferred roles are not artifacts of observational resolution.

Results and Examples
The paper demonstrates the framework through conceptual examples and counterexamples:

Catalytic Chemistry: A catalyst may satisfy the operator condition but fails the RVT criterion because no variant replication or translation occurs.
Inert Copying: A machine copying data strings satisfies Replication (R) but fails Translation (T) because the copied variations do not cause distinguishable downstream structures.
Autocatalytic Sets: Systems with growth and variation but no translation (T) are distinguished from hereditary systems.
Recipe Transmission: A detailed hypothetical reconstruction of teaching a recipe illustrates how the framework handles complex, non-observable physical structures (e.g., neural configurations) by hypothesizing admissible individuation (capability vs. bodily remainder) and testing for R, V, and T motifs.

Claims and Significance
The paper is modest in its claims, positioning itself as a foundational and definitional contribution rather than a complete theory of all possible heredity.

Operational Criterion: The RVT+Lineage motif is presented as a candidate operational criterion for identifying hereditary organization, not a universal definition. The paper acknowledges that other forms of heredity may exist that this specific motif does not capture.
No Latent Capacity: The framework infers only what is realized in the observed causal history. It does not infer potentialities or capacities that were not exercised in the observation window.
Joint Identification: The core innovation is the joint inference of carriers and hereditary processes. One cannot be assigned without the other; they are defined relationally within the same causal motif.
Applicability: The framework is intended for cases where hereditary entities are unknown, contested, or emergent, such as origin-of-life research, artificial life, and institutional evolution.
Validation: The paper notes that the adequacy of the proposed criterion and its empirical validation remain open questions, intended to be tested through adversarial counterexamples and controlled systems rather than asserted as absolute truth.

In summary, the paper provides a rigorous, role-neutral mathematical framework to ask and answer the question: "Does this physical system contain a hereditary organization, and if so, what are its parts?" by analyzing the causal topology of persistent structures.

Technical Summary: "Which Structures Carry Information?: The Causal Structure Set and the Inverse Problem of Heredity"

More like this