Contribution
It gives downward causation an operational form that avoids the charge of non-materialism: the higher level acts only through components that estimate it and tune to the estimate, so “the components are tuning to patterns they perceive and hence are ‘doing the work’” (§1). It splits the notion into a weak form (apparent downward causation) and a strong one (effective downward causation), lists criteria for each, and ties the strong form to the origin of a new organizational level (§1, §7). It proposes information-theoretic measures for how far an aggregate is built by the collective rather than mirroring the environment, and for whether a level is consolidating (§6). The macaque power example (§3) is a review of the author’s earlier work ([9,10,26,27]); no data are presented here.
Key insight
The cause is the members’ estimate, not the aggregate. “I propose we move from simple feedback to downward causation when components tune behaviour in response to estimates of coarse-grained, aggregate properties” (§1). The aggregate is itself computed by the components (“endogenous coarse-graining”, §2), so the loop runs from microscopic behaviour, through the components’ own integrations of it, to a slow variable they estimate and condition on. Slowness is what makes the tuning possible: “for tuning to be possible the coarse-grained variables need to have a slow time scale compared with (i) the microscopic behaviour producing them and (ii) the computation used to estimate them” (§1, citing [8–10]).
Assumptions
- Adaptive systems are collective, heterogeneous and noisy (§1): “It is not necessarily (it is perhaps rarely) the case that all components perceive similarly the aggregate properties describing the system or tune to them in the same way.”
- Coarse-graining has two defining properties (§2): it is “lossy but true”, introducing no outside information, and it is “an integration over component behaviour”, which is what sets it apart from lossless compression. §6 then concedes that in Nature it “is unlikely to be a ‘true’ simplification of the microscopic details as it is the physics sense”, because components are imperfect.
- The causal notion is operational, not a definition of causation. “I will not discuss in this paper when the operational concept of downward causation I am proposing conforms to strict definitions of causality (e.g. [13,14])” (§1). [13] is Ay’s refinement of the common cause principle, [14] Janzing et al. on quantifying causal influences.
- An idealized observer “with perfect information about the regularities in the system or environment” supplies the benchmark value of S (§6, §7).
Key results
Two forms of downward causation (§1)
- Apparent (weak). “I use the term apparent downward causation when tuning is partial and imprecise. In this weak or minimal form, only a few components need to be tuning their behaviour to estimates of aggregate properties for there to be some downward causation in the system.” It “does not demand that estimates of aggregate properties be correct or even good predictors”, and “components do not need to agree in their estimates”.
- Effective (strong), when (citing [8–10]): “aggregate properties are predictive of the future state of the system (slow variables); aggregate properties are robust to small perturbations; estimates of these variables are used nearly universally by all components to tune decision-making; components largely agree in their estimates of these variables; and as estimates converge there should be an increase in mutual information between the microscopic behaviour and the macroscopic properties.”
- Agreement in estimates is not agreement in strategy. Components “need not be in agreement about how to best to tune to these variables”, and “High agreement—high homogeneity—in strategy would likely make the system sensitive to perturbations and move it towards a critical point” ([12]).
- Level. “from an operational perspective it makes sense to start talking of a new level of organization when the criteria for effective downward causation are met” (§1). In its strong form downward causation “locally reduces entropy and creates order, which facilitates extraction of energy to do work” (§1); the paper does not return to the energy point.
Coarse-graining (§2)
Temperature as the example; effective theories “by definition are agnostic to system mechanics”, and the ones of interest “have a basis in mechanism but nonetheless ignore many of the details”. “To distinguish coarse-graining in Nature from coarse-graining by scientists, we call coarse-graining in Nature endogenous coarse-graining [8].”
The macaque power example (§3)
- Power “is operationalized as the degree of consensus among group members that an individual can win fights”, encoded in “a network of subordination signals”. The species is not named in this paper (“a well-study macaque society model system”).
- Two coarse-grainings. A subordination signal is “a coarse-grained representation of the history of fight outcomes over some period”, sent only when the sender perceives “a large asymmetry in fighting ability in its opponent’s favour”. A power score is “a course-grained representation of the signalling network” (sic). “The power distribution (DSP) results from the collective computation by all individuals of their power scores.”
- Fighting continues at a reduced rate after signalling, “a mechanism by which the relationship might reverse in the future”, likened to “a ‘background process’ running on your computer”.
- Two phases: “an information accumulation phase in which the individuals, like sensors, gather information semi-independently”, and “a consensus or aggregation phase” in the signalling network.
- Why coarse-grain. Memory minimization: after signalling, the fight series “can (in principle, we do not yet know exactly how this works) be deleted from memory”. And “uncertainty reduction through slow variable construction”: “even though the coarse-graining is lossy, from a functional perspective information is gained because the signal to noise ratio is higher”. “There is not yet a good language for discussing this transition.”
- Function. A DSP predicts interaction cost “if it has mutual information with the underlying (and not directly observable) distribution of fighting abilities and changes slowly [27]”. Its right skew makes policing accessible to those in the tail, who “are perceived to be disproportionately powerful and are unchallenged when they intervene”.
- Apparent downward causation in the system “when the DSP has consolidated enough so that it changes more slowly than the microscopic fight behaviour producing it and at least one individual uses estimates of its power scores or other properties of the DSP … to make predictions about interaction cost and tune behaviour”.
- Effective downward causation “when/if (i) the collectively estimated DSP is robust to small perturbations in signalling patterns and has a slower time scale than the fight outcome network (many fights per hour with a per individual time scale on the order of hours [29]) underlying it and the signalling network used to compute it, (ii) the DSP predicts the cost of social interaction, (iii) individuals’ estimates of properties of the DSP begin to converge … and (iv) the mutual information between DSP and the underlying distribution of fighting abilities is high”.
- Convergence (iii) is more likely with a fully connected fight network, similar dataset sizes, social learning, disparity in fighting ability, incentives to estimate accurately [27], similar computational capacity, “and as a result of positive feedback induced by the downward causation itself”.
- Pairwise effective downward causation. Signal exchange “strongly predicts for signal sender tolerance by the receiver around resources” and reduces uncertainty about the relationship for both; “signal senders spend greater time in proximity to signal receivers than in the absence of signal exchange”.
Other systems (§4, §5)
- Fontana and co-workers’ internal coarse-graining of molecular signalling into “fragments”, “patterns that the system recognizes and uses” ([24,25]). “It is not yet clear however whether this work has anything to say about downward causation”; it does not say how fragments are produced.
- Mehta and Schwab’s mapping between variational renormalization and deep networks via restricted Boltzmann machines ([35]), and Shwartz-Ziv and Tishby’s information bottleneck with “a fast fitting phase” and “a slow generalization or compression phase” ([36]). Flack reads (§5) the layered networks as “each layer consolidated through coarse-graining and effective downward causation, such that the coarse-grained output one layer up, influences the microscopic behaviour one (and in some cases two layers) down”. The difference she notes: “in our work the fitting phase is slow and the generalization phase is relatively fast”. Her own open question: “whether effective downward causation in adaptive systems can increase symmetries at the microscopic level making the system as it consolidates increasingly amendable to coarse-graining”.
Measures and mechanisms (§6)
- Figure 1’s variables. “E is the state of the environment. Mi are the strategies/behaviour/opinions of the microscopic components about E (and S…), S is the coarse-grained, aggregate variable. P is the algorithm that maps the environment onto component behaviour in M. C is the collective computation that aggregates the information in M and outputs S. D is the algorithm that captures both how the components, i, in M estimate S and use the estimate to tune their behaviour.”
- Constructed or mirrored. Compare the collectively computed S with the idealized one, and “By calculating the conditional mutual information for these variables we can determine the contribution of the environment/some underlying constraint versus the collective computation to S.” Where the environment contributes little, “components are effectively constructing their macroscopic worlds through collective behaviour and information processing”. Power and stock price are “loosely tied” to a ground truth.
- Predictions, stated as expectation: where information processing dominates, macroscopic variables “will scale superlinearly”; with strong energetic constraints they will have high conditional mutual information with the environment and “scale sublinearly”, as mass and metabolic rate do ([42]).
- Consolidation. “we can also quantify the extent to which a new organizational level is consolidating out of S by asking if the I(S;M|E) is increasing over time.”
- Time-scale separation as a mechanism. “If the time scale associated with a coarse-grained or aggregate variable is very slow compared to the microscopic behaviour producing it, it effectively becomes the ‘social’ environment … and components can tune to it regardless of whether it actually does a good job of summarizing the regularities in E or now in M—think of social institutions that are highly constraining and very hard to change or the power distribution in the monkey case study.” It “facilitates learning and hence coordinated and organized behaviour”. But “it seems likely the system will fail at some point if the aggregate properties components rely on for prediction do not capture the regularities in M or E—failure may just take longer if the time scale separation is very large.” “In the monkey case study, both the signalling network and power structure have a much slower time scale than the fight dynamics.”
- Collective estimation as a second mechanism, a wisdom-of-crowds variant that Flack calls “a somewhat trivial insight”; the interesting questions are the aggregation’s details, since collective computation “may, as a result of higher order interactions and synergies, produce aggregate properties that bare little relation to the environmental states or underling constraints they are supposed to summarize” (sic).
Conclusion (§7)
- Coarse-grained variables “promote accelerated rates of microscopic adaptation [8]”: they let components fine-tune and “free components to search at low cost a larger space of strategies”. RNA neutral networks: “structure changes more slowly than sequence” ([55]).
- The level criteria restated ([8,10]): estimates are “(functionally) good approximations of the idealized aggregate properties”; aggregates “sufficient to predict system dynamics at the macroscopic scale”; components “rely to a greater extent on the coarse-grained descriptions … than on microscopic behaviour”; estimates “largely in agreement”; and “mutual information between the consolidating higher level/layer and the microscopic behaviour one level down”.
- “the consolidation of a new level of organization requires, in addition to downward causation (§1), that component estimates of aggregate properties … are functionally good approximations of the aggregate properties as computed by an observer with perfect information”. “an open and system dependent question is what constitutes ‘good enough’.”
- “the increase in correlation is due to the components increasingly perceiving the world in the same way—an effect that amplifies itself through effective downward causation.”
- “The result is the slow variables become fundamental macroscopic properties that are a public good of sorts”.
Claims
| id | claim | strength | support |
|---|---|---|---|
| C1 | Downward causation can be operationalized as components tuning behaviour to their estimates of collectively computed aggregate variables, which meets the materialist objection | moderate | conceptual argument (§1); the paper sets aside whether it meets a definition of causation |
| C2 | A coarse-grained variable can be tuned to only if it is slow relative to the behaviour producing it and to the computation estimating it | weak | asserted, citing [8–10]; no argument in this paper |
| C3 | In the macaque group, the power distribution is slower than fight dynamics, predicts interaction cost and is used by individuals | moderate | reviewed from [9,10,26,27,29]; the paper reports no data and gives no measured time scale for the DSP |
| C4 | A new level of organization begins when the effective-downward-causation criteria are met (and, per §7, estimates are good approximations of the idealized aggregate) | weak | proposal, “from an operational perspective” (§1, §7) |
| C5 | A very slow aggregate becomes a social environment components tune to whether or not it summarizes regularities well, facilitating coordination, with failure delayed by larger separation | weak | argued informally with institutions and the macaque DSP as illustrations (§6) |
| C6 | I(S;M|E) rising over time measures the consolidation of a new level | weak | proposed (§6); not computed for any system |
| C7 | Information-processing-dominated aggregates scale superlinearly, energetically constrained ones sublinearly | weak | ”I further predict” (§6); no data |
| C8 | Deep networks are layered coarse-grainings with effective downward causation between layers | weak | the author’s reading of [35,36]; neither paper is said to show downward causation |
Concepts
- Endogenous coarse-graining — coarse-graining “performed by the system (as opposed to a scientist) as an inference mechanism” (§1, §2, after [8]); Fontana’s “internal coarse-graining” is the molecular counterpart.
- Apparent downward causation — at least some components tune to estimates of an aggregate that is slower than the behaviour producing it; estimates may be wrong and may disagree (§1, §3).
- Effective downward causation — the five §1 criteria: predictive (slow), robust, nearly universal use, agreement in estimates, rising micro–macro mutual information.
- Slow variable — an aggregate “predictive of the future state of the system” (§1); in §3 a variable that “changes more slowly than the microscopic fight behaviour producing it”.
- Power — “the degree of consensus among group members that an individual can win fights” (§3).
- Two-phase collective computation — information accumulation, then aggregation or consensus (§3, §5).
- ‘Social’ environment — an aggregate slow enough that components treat it as their environment, as distinct from the exogenous E (§6).
Connections
- Flack 2012 ([9]; LIT-1122, unread) and “Life’s information hierarchy” ([10], not held) carry the detail of the example and of the criteria; this paper defers to them (“For further important detail, I refer the reader to [9,10]”). The criteria are attributed to Flack, Erwin, Elliot and Krakauer 2011 ([8], not held) as well.
- Brush, Krakauer and Flack ([26], [27]) for the consensus algorithms and the claim that conflict improves collective computation; Daniels et al. ([11], [12]) for collectivity and criticality.
- Campbell 1974 ([1,2]; the reference list gives the same chapter twice) for downward causation; Ellis, Walker and Davies, Laughlin et al. ([3–7]).
- Simon’s near-decomposability is not cited, though §6’s time-scale argument is close to the result the record holds as THEORY-661.
Bearing on the record
- CLAIM-327: two of its three stages are Flack’s; the third is not. Stage 1 (an observer finds a stable statistic) has no separate place in Flack. Her aggregate is computed by the members from the start (“endogenous coarse-graining”, §2), so the observer enters only as the idealized benchmark (§6). Stage 2 (members recognize and use it) is her apparent downward causation, with two refinements the claim lacks: what members condition on is their estimate, which may be wrong and need not be shared (§1), and one member tuning is enough (§3). Stage 3, use that “preserves, transforms or regenerates” the variable, is not among Flack’s criteria in either list (§1, §7). What reinforces itself in Flack is agreement: “positive feedback induced by the downward causation itself” makes estimates converge (§3), and correlation “amplifies itself through effective downward causation” (§7). Her stage beyond use is convergence, robustness, near-universal use and rising mutual information, and for a level, estimates good enough against the idealized aggregate (§7). The variable is maintained by members in Flack’s example, since the signals that compose it are their behaviour and fighting continues as a “background process” (§3), but she does not make that a criterion. So CLAIM-327 is the exchange’s synthesis, with regeneration where Flack puts convergence. It also differs on what makes the variable a level: CLAIM-327 says only the third stage does, and Flack says use alone is already (apparent) downward causation and a level needs the effective criteria. This paper does not settle whether Flack 2012 says otherwise. Its own deference to [9] suggests the 2012 paper has the same criteria. LIT-1122 remains unread. THEORY-1061 states Flack’s criteria.
- CLAIM-331: Flack builds slowness into the definition. For her, slowness relative to the producing behaviour is a condition even of apparent downward causation (§3), and “slow variables” is the first effective criterion (§1). Its stated reason is enabling: “for tuning to be possible” (§1), asserted, citing [8–10]. That is stronger than CLAIM-331’s “a mark of a level and not its definition”, and it is support of the kind CLAIM-331’s note of 2026-10-20 sets aside for slow feature analysis: slower by construction. The one empirical time scale given is the fight network’s (“many fights per hour with a per individual time scale on the order of hours [29]”, §3); the DSP’s is only “much slower” (§6). The claim’s caution “Not that a slow variable is a level” is Flack’s too: slowness alone gives no downward causation without tuning.
- CASE-116. Arm A, slow and unread, has no downward causation in Flack’s sense, since nobody tunes (§1, §3), which agrees with the case. Arm B, read and rewritten and fast, falls outside Flack’s account by definition, since she requires the variable to be slower than the behaviour producing it (§3) and than the computation that estimates it (§1). So arm B’s “slowness is not necessary” contradicts a stipulation, not a finding. Flack’s reason for the stipulation (that estimation needs a variable stable over the estimation window) is the thing arm B would have to meet: its members read Z_t directly, with no estimation step, so her reason does not bite there. Arm C, transmission without running, is not addressed.
- CLAIM-478: Flack states its first half for social systems. §6: a very slow aggregate “effectively becomes the ‘social’ environment … and components can tune to it regardless of whether it actually does a good job of summarizing the regularities”, with institutions “highly constraining and very hard to change” as the example, and separation “facilitates learning and hence coordinated and organized behaviour”. That is separation making a constraint, made effective only through tuning, which is the claim’s “available, not effective”. Flack adds a limit the claim lacks: a poorly summarizing aggregate will likely fail eventually, “failure may just take longer if the time scale separation is very large”. On the second half (organization makes separation) she has only an open question: whether effective downward causation “can increase symmetries at the microscopic level making the system as it consolidates increasingly amendable to coarse-graining” (§5). Filed as THEORY-1073 (Proposed).
- CLAIM-277: the macaque case is an instance of endorsement summarizing a track record, but not of trust in its sense. A subordination signal is a coarse-graining of fight outcomes, sent by the party that perceives itself weaker; power is the group’s consensus aggregated from those signals; and fighting continues at a reduced rate so that the relationship can reverse (§3). That is CLAIM-277’s “right a lot” loop with fights as the track record, a refresh process in place of a memory kernel, and memory minimization (the fight series can be dropped once signalled, “we do not yet know exactly how this works”) as the forgetting of raw history. The tail’s access to policing (§3) is durable, differentiated authority. Flack does not discuss early advantage, and the reliability side rests on mutual information with fighting abilities [27], which is not shown here. What is endorsed is the ability to win fights, not the competence of a policy, so the case is a structural analogue.
- CLAIM-334, TERM-051 and CLAIM-158: a fourth sense of “downward causation”. Flack’s is neither Seth’s Granger sense, nor ΦID’s D, nor the interventional one. She leaves its relation to “strict definitions of causality” aside (§1). Its causal path runs through the members’ estimates, which are states of the members distinct from S. That is the route CLAIM-334 leaves open: one can intervene on what members believe of S without holding S’s micro base fixed. Flack does not put it that way. “Downward causation” in Flack should not be compared with D or with Granger measures without saying so. Her apparent-to-effective gradation is a strength of tuning, not a spectrum of who drives (CLAIM-158).
- QUESTION-033: a proposed apportionment. §6 proposes conditional mutual information to apportion S between the environment and the collective computation, and I(S;M|E) over time to track consolidation, which is the “how the apportionment changes over time” the question asks for. They are proposals and are computed for no system here.
- NOTE-153’s C8 cites Flack for higher-level causal power. This paper gives that power only through components’ estimates (§1), which is compatible with Rizi’s “not a metaphysical extra cause”.
- No instruction for machine-learning practice is made; §5 reads two deep-learning papers for analogy only.
Limitations
- No data. The macaque results are summarized from [9,10,26,27,29] and are not reproduced; no time scale is given for the DSP or the signalling network beyond “much slower” (§6).
- The two lists of criteria differ. §1’s effective criteria include robustness and near-universal use. §7’s level criteria drop robustness, replace near-universal use with relying “to a greater extent” on the coarse-grained description, and add that estimates be good approximations of the idealized aggregate. §7 says the level “requires, in addition to downward causation (§1)” the approximation condition, while §1 had said a level begins when the effective criteria are met. The paper does not reconcile them.
- “Good enough” is left open (§7), and the idealized observer’s S is not defined for any system.
- Physics slips. “Temperature is the average speed of particles” (§2, rather than mean kinetic energy), and BCS theory is called a theory “of high temperature superconductivity” (§2). The XML also has typos (“course-grained”, “bare little relation”, “underling”). None bears on the argument.
- Figure 1 was not seen; its content is known only from the caption and §6.
- The causal notion is not tied to any account of causation (§1), so whether apparent downward causation is causation at all is not argued.
- The deep-learning section reads the cited papers through the author’s framework. The information-bottleneck results it relies on ([36]) are reported as experiments that “suggested”, and the paper says no more for them.
Open questions
- Does Flack 2012 (LIT-1122) include regeneration of the variable by its use among its criteria, or only convergence? A reading of it would settle CLAIM-327’s attribution.
- Is slowness needed for downward causation, or only for estimation? A case in which members read a fast variable without estimating it (CASE-116 arm B) and tune to it would separate the two.
- Can I(S;M|E) be computed for the macaque data, and does it rise as the DSP consolidates (§6)?
- Do the superlinear and sublinear scaling predictions hold (§6)?