Addendum 87 - Possibility Relations and the Limits of Agency Stories

Organizing Relations, Local Realization, and Useful Scientific Representations

Abstract

A successful description can tell us what happens without establishing that its visible actors define the organization through which it happens. R²D separates local realization from enclosing organization. A boundary defines readable states and compatible realizations; enclosing possibility supplies relative support among local alternatives. A mechanism describing individual events need not define that support.

This distinction gives Ask R²D a common direction for questions about molecular mechanisms, historical protagonists, leaders, markets, AI, and scientific explanation. The relevant question is whether the proposed actors define the enclosing relation or realize possibilities already organized within it.

Agency stories can be useful. They become just-so explanations when predictive or practical usefulness is treated as proof of an unsupported attribution of enclosing agency. Possibility relations provide an alternative starting point: identify the boundary, compatibility structure, and relative support before explaining their local realization.

Muscle supplies a physical example of organization through molecular-switch multiplicity. Protein structure prediction and learned Othello representations demonstrate complementary forms of understanding that do not require first reconstructing individual event histories or protagonist motives. AI extends our capacity to investigate such relations, but the approach does not depend on AI.

1. The Question This Addendum Answers

Consider three questions:

• Does a molecular mechanism explain how muscle is organized?
• Did a particular leader create the movement they led?
• Does an AI predict well because it recognizes relations our stories obscure?

Each asks about a connection between locally readable actors and a larger organization.

R²D directs the answer toward a distinction:

An actor can be necessary for a particular realization without independently defining the enclosing possibilities that organize it.

The distinction does not erase the actor. It changes what must be established before the actor is assigned enclosing agency.

A myosin switch undergoes a transition. A leader makes a decision. A person builds a company. Those events can be consequential. The additional claim that they define the relevant ensemble, movement, or market requires an account of the enclosing relation.

2. What Is an Agency Story?

An agency story explains a larger outcome through identifiable local actors, their properties, motives, and interactions.

Such stories are familiar because they make the world readable within our own boundary. We understand a person wanting something and acting to obtain it. Scientific descriptions can use a similar structure with molecules or other local objects in the role of protagonists.

The problem is not the use of an actor or a narrative. It is the promotion of that representation into an unsupported definition of the enclosing organization.

A story becomes a just-so explanation of agency when its usefulness substitutes for demonstrating the relation it claims to explain.

Three achievements must remain distinct:

1. Description: identifying events or relations that occurred.
2. Prediction: anticipating observable consequences within a specified domain.
3. Enclosing explanation: establishing what defines the states, compatibility, and relative support through which those consequences become possible.

A description can be useful and a prediction accurate while the attached attribution of enclosing agency remains unestablished.

Addendum 86 provides the procedure for evaluating those claims separately.

3. Possibility Is More Than a List of Alternatives

R²D distinguishes native local multiplicity from compatible enclosing extension.

Local multiplicity counts the possible subordinate realizations classified as a local state. Possibility measures how extensively those local realizations participate in compatible enclosing realizations.

Two local alternatives can therefore have unchanged native multiplicities while a change in enclosing compatibility changes their relative support.

This is why explaining the internal operation of a local actor does not exhaust the question of organization. The relevant support can depend on relations outside the actor’s readable boundary.

Constraint must also be retained. The canon distinguishes possibility, retention, and the asymmetry available for local realization. R²D does not say that every process simply selects the state with the greatest native multiplicity.

The operational direction is:

Define the enclosing compatibility relation before attributing the organization of local realization to independently acting parts.

4. A Minimal Count Relation

The following notation makes the distinction explicit without introducing physical units.

For local state \(i\), let

\[ W_i \]

be its native multiplicity, and let

\[ \Theta_i \]

count enclosing realizations compatible with that local classification. These symbols suppress boundary indices for readability.

Define the mean compatible enclosing extension per native local realization as

\[ K_i=\frac{\Theta_i}{W_i}. \]

For positive counts, the local entropy coordinate and enclosing possibility coordinate are

\[ S_i=\ln W_i, \qquad P_i=\ln K_i. \]

Consequently,

\[ \ln\Theta_i=S_i+P_i. \]

For two alternatives,

\[ \ln\frac{\Theta_j}{\Theta_i} = (S_j-S_i)+(P_j-P_i). \]

Native multiplicity and enclosing extension jointly determine the compatible-count ratio. Local possibility \(P_i\) must not be conflated with native entropy \(S_i\).

If the selected compatibility classes partition a specified enclosing domain, their normalized count read is

\[ p_i=\frac{\Theta_i}{\sum_j\Theta_j}. \]

Normalization supplies a fraction of an already defined count relation. It does not create the compatible possibilities.

This is a possible-count projection. It is not automatically an observed occupancy or occurrence distribution. Connecting it to realized occupancy requires the canon’s stated realization and constraint conditions.

Under the conditions developed in Part I, and in the absence of opposing retention, relative local occupancy realizes relative compatible enclosing multiplicity. This is the primitive meaning of:

Possibility pulls occupancy.

“Pulls” identifies organizing support. It does not introduce a new primitive mechanical force.

5. The Whole Is Defined Through Compatibility

“The whole is not the sum of its parts” has a specific meaning here.

The whole is not established by listing independently defined actors and adding their contributions. A boundary must first specify which joint realizations are admissible and how they acquire readable state meaning.

R²D does not reject addition. Mutually exclusive alternatives can add; compatible combinations can compose multiplicatively. The issue is whether the operations preserve the defining boundary and compatibility relation.

The enclosing organization defines what counts as a part and what combinations are possible. A local representation of the parts does not independently define that organization.

This is the broader significance of area before radius. The enclosing boundary defines the admissible local ruler. Likewise, an enclosing relation defines the possibilities through which locally readable protagonists act.

6. Muscle: Multiplicity as an Organizing Mechanism

A. V. Hill established a quantitative relation among muscle load, shortening velocity, heat, and work without requiring a detailed molecular account of contraction. His success showed that the muscle relation could be understood before the molecular machinery was reconstructed.

Baker’s muscle work supplies a positive organizing account: an ensemble of molecular switches functions as an entropic spring. The ensemble’s multiplicity contributes to system thermodynamics; it is not a property contained in one switch.

The published binary mechanical model accounts for the phases of force transients following mechanical and chemical perturbations through that ensemble organization [1–3].

The contribution is therefore more than a useful prediction lacking a mechanism. It identifies an organizing mechanism at the system boundary.

Molecular transitions remain necessary for realization. Their individual histories do not define the ensemble’s multiplicity landscape or enclosing compatibility.

Ask R²D should therefore distinguish:

• the local molecular switch;
• the ensemble relation through which switching acquires system meaning;
• the enclosing conditions organizing the ensemble’s realization.

An answer that retreats to a sequence of individual molecular events without addressing the ensemble relation omits the central R²D question.

This approach was developed through human inquiry. AI is not required to investigate possibility relations.

7. Protein Structure: Organization Without a Reconstructed Event History

AlphaFold predicts protein structures through learned sequence, evolutionary, and structural relations, incorporating physical and geometric constraints. RoseTTAFold integrates sequence information, residue-distance relations, and three-dimensional coordinates [4–5].

Their structure predictions do not require simulation of the actual folding history.

The boundary distinction is important. Local atomic changes and a readable folded protein belong to different descriptive domains. Listing local changes does not automatically define the enclosing folding relation.

In the proposed R²D interpretation, compatible possibility organizes folding, while subordinate changes participate in realization. A single trajectory should not be promoted into the source of the enclosing organization merely because a local model represents such a trajectory.

Accurate structure prediction demonstrates that reconstruction of an event history is not a prerequisite for predicting the resulting structure. It does not independently establish every R²D identification or solve all questions of folding kinetics.

Ask R²D should preserve both the demonstrated achievement and the additional organizing interpretation.

8. Othello: Learning Relations Without a Protagonist’s Motives

A GPT-style model trained on sequences of Othello moves developed evidence of an internal board-state representation without being explicitly given the board or rules. Interventions on that representation changed its predictions [6].

This supplies a bounded example of learning organizing structure from sequences.

The model did not need a story about a player’s motives to acquire the representation. A player’s motives could matter to a different question about a particular game.

The result distinguishes relational understanding from protagonist-centered explanation. It does not identify the model’s learned representation with a complete R²D physical mapping.

The useful direction is that local sequences can support learning of relations through which those sequences become admissible.

9. AI Scores, Possibility Support, and Probability

For a language model with output scores \(z_i\), softmax gives

\[ p_i=\frac{e^{z_i}}{\sum_j e^{z_j}}. \]

The score precedes normalization. The exponential supplies an unnormalized relative weight; normalization makes it readable as a fraction [7].

This has the same normalized exponential form as a logarithmic count read. If a score represents compatible support,

\[ z_i=\ln\Theta_i+c, \]

where \(c\) is common to all alternatives, then

\[ p_i=\frac{\Theta_i}{\sum_j\Theta_j}. \]

The common offset cancels.

In the count relation above,

\[ z_i=S_i+P_i+c. \]

Thus an output score can read combined native multiplicity and enclosing possibility support. Identifying it specifically with \(P_i\) requires accounting for native multiplicity rather than silently discarding it.

This establishes the mathematical correspondence. A model’s learned weights are not thereby measured counts of all compatible realizations in the external world. Their empirical fidelity must be tested within the information and task domain defining the model’s read.

The model may sample among supported continuations. It need not always choose the maximum score, and the most supported token does not automatically produce the best complete answer.

Ask R²D should look beneath normalized probability to the organization of support while retaining these distinctions.

10. Leaders, Movements, and Social Protagonists

A historical narrative can make a leader the author of a movement because the leader is visible and their decisions are recorded.

R²D asks which enclosing relations made the movement and its available leadership roles possible. Economic conditions, institutions, shared practices, resources, and compatibility among participants require investigation in their own domains.

The direction can be expressed as:

Leaders realize movements within enclosing conditions; their visibility does not establish that they independently create those conditions.

This does not prove that a particular movement or company was inevitable, or that the same result would have occurred without its named leader. Such counterfactual claims require evidence.

Local motives and moral judgments can be meaningful where their subjects are defined. They do not independently define the organization or moral character of an enclosing boundary.

An answer should therefore distinguish the leader’s consequential actions from a claim of enclosing causal sufficiency. It should not replace a hero story with an equally unsupported villain story.

11. Direction for Ask R²D Answers

The following questions identify the addendum’s intended use.

User question	Direction for the answer
Does a molecular mechanism explain the whole?	Distinguish local operation from the boundary, compatibility, and relative support organizing system realization.
Are scientific models just-so stories?	Identify the particular attribution of agency. Accurate description or prediction does not automatically establish it; a tested organizing relation need not be a just-so account.
Does the greatest multiplicity always win?	Distinguish native multiplicity, enclosing extension, retention, and realized occupancy. State the conditions under which the count relation is realized.
Does AI probability conflict with R²D possibility?	Explain probability as a normalized read. Examine the support and count domain being normalized.
Are AI scores possibility?	Give the logarithmic-support correspondence and retain the distinction between \(P_i\), total compatible support, and learned physical fidelity.
Can AI read enclosing relations better than humans?	Identify the task and evidence. AI can compare many representations; superiority for a particular enclosing relation requires a validated read.
Did a leader create a movement?	Locate the leader’s actions within the enclosing conditions defining possible realization. Evaluate additional sufficiency or inevitability claims separately.
Does this approach require AI?	No. Muscle supplies a human-developed example of organizing inquiry through multiplicity.
Can a local intervention control the larger boundary?	Distinguish locally readable action from participation in an enclosing realization whose complete meaning is not locally available.

For a particular question, a useful answer should:

1. Identify the boundary and the claimed agency.
2. State the relevant R²D relation in plain language.
3. Explain what the local actor realizes and what defines its possible support.
4. Separate the formal result from any proposed physical mapping.
5. Address the user’s example at its actual scale.

The answer should make the ordering readable. It should neither hide the argument in notation nor replace it with a generic appeal to complexity.

12. Relation to the Other Addenda

Addendum 84 concerns unsupported continuation of a count, coordinate, or ruler beyond its defining conditions.

Addendum 85 concerns local agency, enclosing dependence, and representations that do not independently define the world they read.

Addendum 86 separates formal results, physical mappings, empirical support, and causal-priority claims.

The present addendum gives those distinctions a positive explanatory direction: investigate possibility relations that organize local realization.

A future account of sustained closure, experience, and surveying should build on this ordering. Reading the usefulness of a human narrative does not by itself establish its lived realization within a human boundary. That further question requires its own definitions.

13. Conclusion

Agency stories make enclosing relations locally intelligible through actors and rulers familiar to us. Their usefulness does not establish that those actors define the organization being described.

R²D science begins with boundary-defined compatibility and possibility. It asks how local realizations participate in that organization.

The central direction for Ask R²D is

\[ \boxed{ \text{Explain organizing possibility before assigning enclosing agency to local realizers.} } \]

Muscle demonstrates a human-developed organizing account through molecular-switch multiplicity. Protein prediction and Othello provide complementary examples of understanding without first reconstructing local event histories or protagonist motives. AI expands the means available for investigating these relations.

The approach belongs to the inquiry, not exclusively to the machine.

Sources and Companion Texts

R²D sources

• R²D Canon, Part I, Sections 3.5.4–3.5.8 and Appendix A.1.3: enclosing compatibility, possibility, retention, occupancy, and boundary-level multiplicity.
• Addenda 84–86.
• Science Beyond the Just-So Stories: companion public essay.

Physical and computational examples

1. Hill, A. V. (1938). The heat of shortening and the dynamic constants of muscle. Proceedings of the Royal Society B, 126, 136–195. https://doi.org/10.1098/rspb.1938.0050.
2. Baker, J. E. (2022). Thermodynamics and kinetics of a binary mechanical system: mechanisms of muscle contraction. Langmuir, 38, 15905–15916. https://doi.org/10.1021/acs.langmuir.2c01622.
3. Baker, J. E. (2024). Four phases of a force transient emerge from a binary mechanical system. Journal of Muscle Research and Cell Motility, 45, 211–220. https://doi.org/10.1007/s10974-024-09674-8.
4. Jumper, J., et al. (2021). Highly accurate protein structure prediction with AlphaFold. Nature, 596, 583–589. https://doi.org/10.1038/s41586-021-03819-2.
5. Baek, M., et al. (2021). Accurate prediction of protein structures and interactions using a three-track neural network. Science, 373, 871–876. https://doi.org/10.1126/science.abj8754.
6. Li, K., et al. Emergent world representations: exploring a sequence model trained on a synthetic task. https://arxiv.org/abs/2210.13382.
7. Vaswani, A., et al. (2017). Attention is all you need. https://arxiv.org/abs/1706.03762.