Source
Hoel, Albantakis and Tononi (2013, PNAS), LIT-1038, read in NOTE-726. Their title, “macro can beat micro”, and their discussion call the EI-optimal level the intrinsic causal scale and say the macro then excludes the micro.
What is asserted
That the level at which effective information is highest is the level at which the system’s causation is, so that a coarse-grained description can be causally privileged over the micro description it supervenes on.
What the record holds toward it
THEORY-222, Active, is the formal part: with uniform interventions at each level, a macro description of a known discrete mechanism can carry more effective information than its micro description, by 0.40 to 2.92 bits in four toy systems. The step from “EI is highest there” to “causation is there” rests on the uniform intervention distribution imposed separately at each level, which weights micro states differently at the two levels. QUESTION-204 asks whether the advantage survives a common intervention distribution and agrees with an independent interventionist test.
What this does not say
- Not that any real system has been shown to have causal emergence; the search over coarse-grainings is exhaustive only for toy sizes.
- Not the authors’ further claims about brains and the hierarchy of the sciences, which they offer as conjecture.
What would confirm or reject it
Confirmed by the promote_when: the EI-optimal level stays macro under the system’s own or another fixed intervention distribution, on systems not built for it, and agrees with an independent interventionist test. Rejected if the macro advantage disappears whenever the same intervention distribution over micro states is used at both levels.
Note of 2026-10-29: the “in trouble if” clause is met for effective information
The promote_when says this account is in trouble if the macro advantage disappears whenever the same intervention distribution over micro states is used at both levels. For effective information that condition is now met, and by proof, not by example. THEORY-1167 (Active): with one distribution over micro states at both levels, each macro intervention realized by that distribution within its block, the macro EI is I(f(X); f(Y)), which data processing bounds by I(X; Y), the micro EI. A macro can at most tie. By the same derivation, the positive causal emergence of LIT-1038 is the micro mechanism’s gain from changing the distribution, from the uniform one to the one Hoel’s macro interventions induce, less a non-negative loss.
Two readings of this date bear the same way.
- Comolatti and Hoel, LIT-1843 (NOTE-1416), concede the decisive case: under the system’s own stationary distribution, used at both levels, EI shows no emergence, “This was known”. Their reply, that other measures and individual transitions still show emergence, changes the measure, not the distribution. Those measures are pointwise or normalized by log₂ n, and data processing does not bound them. So the reply is not evidence for EI’s level, which is what this account asserts. Their only system is a bipartite chain built so that its macro is a deterministic NOT gate, a hand-built toy of the kind the promote_when says cannot settle it.
- Eberhardt and Lee, LIT-1839 (NOTE-1413), trace EI’s ambiguity and non-commutativity to the maximum-entropy distribution, “extraneous to the system”. They do not compute EI under a common distribution; the record’s derivation supplies that step.
The bound covers a coarse-graining of one transition. It does not reach LIT-1038’s temporal and spatio-temporal macros, and it says nothing about measures that data processing does not bound (THEORY-1167, “What this does not say”).
A move to Rejected, or a narrowing of this account to measures that data processing does not bound, is proposed and left to the owner. The status and the title are unchanged.
Note of 2026-10-29: the independent interventionist test, and what it can show
The promote_when asks, beside a common distribution, that the EI-optimal coarse-graining agree “with an independent interventionist test of which level the effects track (realization insensitivity under changes of realizer)”. Causal feature learning is that test: Chalupka, Perona and Eberhardt, LIT-1833 (NOTE-1420), and their overview, LIT-1834 (NOTE-1415). Two micro causes share a macro state iff manipulating to either has the same effect, and no distribution over interventions enters.
Its verdict bears on this account in two ways.
- It cannot confirm the account. On a transition matrix the causal partition is the coarsest description whose manipulations are unambiguous. The micro description is never worse, only finer: it “contains no more causal information”, and it loses none. So the test can confirm that a macro is proportionate, where micro rows are exactly equal, as in Eberhardt and Lee’s (11), Hoel’s example, and never that causation emerges at the macro or that the macro beats the micro. THEORY-1169 (Active) makes the link to EI exact: under one full-support distribution at both levels, the coarse-grainings that keep all of the micro EI are exactly the causal partitions and their refinements, whatever the distribution. The ties THEORY-1167 allows are these, and nothing exceeds them.
- It disagrees with the EI this account rests on. Hoel’s EI, uniform at each level, merges causes with different rows on Eberhardt and Lee’s (13) and (14), and on their note 6 it keeps identical rows apart. On those matrices the agreement the promote_when asks for fails. They are hand-built, which by the promote_when’s terms cannot settle it, and Hoel 2013’s own examples (THEORY-222) were not recomputed.
The test also needs exact equality. With estimated rows, causal feature learning merges by a distance threshold, a choice THEORY-1169 does not make.
Nothing here moves the account toward promotion. The status and the title are unchanged. The move to Rejected, or the narrowing, that the earlier note of this date proposed is still the owner’s call.