Objectivity After Babel

A Mythopoetic Reading of Observer-Equivariance

Most of my recent work on observer-equivariance has moved in the direction of greater precision. I have tried to separate formal results from physical calibration, and physical calibration from philosophical interpretation. That discipline matters. A suggestive idea can otherwise acquire the appearance of a theorem merely by being placed next to mathematics.

Here I want to pause that work and let the imagination move more freely. The thought that prompted this essay was that the forgiveness of sins might be recognizable as an archetypal pattern within my interpretation of observer-equivariance. If no part is finally isolated from the whole, perhaps guilt cannot simply be expelled onto an alien part. The whole must somehow bear what has happened within it.

I still think this intuition contains something important. It also carries a serious moral risk: it can erase differences in responsibility that must remain visible. This essay is an attempt to discover what remains of it after the necessary distinctions have been made.

I use archetype in a modest sense: a recurrent narrative pattern that can serve as a heuristic for thought. I am not claiming to demonstrate Jungian universals, a collective unconscious, or a hidden influence of mythology on the mathematics. Mythology will not be evidence for observer-equivariance, nor observer-equivariance evidence for theology. Pattern recognition is powerful but permissive, so the limits of a resemblance matter as much as the resemblance itself. I will therefore keep three levels distinct:

1. The formal level: perspective-bound presentations, admissible transformations, shared structure, and possible obstructions to global coherence.
2. The interpretive level: my relational and partly Bayesian reading of that structure, including its possible application to a plurality of agents.
3. The mythopoetic level: images of Babel, incarnation, scapegoating, forgiveness, mourning, and polyphony.

Only the first belongs to the mathematical core. The second is a philosophical proposal. The third is an experiment in disciplined imagination.

The formal floor

In the strict categorical model developed in my formal work, there is a functor

p: O → S.

Here O is a groupoid of perspective- or presentation-dependent descriptions and reversible admissible transformations between them. The category S carries the shared structure being presented. It is not a cosmic spectator with a view from nowhere. It records what can be publicly identified across changes of presentation.

Presentation-independence is not the same thing as a symmetry of a physical law. Under the hypotheses of the strict model, suitable assignments on O factor, with the required coherence, through p; a transformation is a symmetry of specified law data only if it preserves those data. More generally, objectivity need not require literally identical descriptions; it may consist in invariant content or in content that transforms coherently under justified changes of perspective.

The normal-form theorem in my first formal paper uses deliberately strong assumptions. In wider settings, compatible local descriptions may fail to descend to a global object. A groupoid need not be connected, and its arrows alone provide no gluing theorem. Obstructions are part of the story, not defects to be concealed.

The objects of O are formally presentations, not automatically persons, consciousnesses, or wills. I am nevertheless exploring an extension in which some presentation states are indexed by situated agents and carry Bayesian priors. This places the proposal between RQM, where quantum events are relative to interacting physical systems without any fundamental role for consciousness, and QBism, where quantum states and outcome probabilities are an agent's personal judgements constrained normatively by the Born rule.

This would be a groupoid of presentation states indexed by agents, not a claim that the agents themselves are mutually isomorphic. A developed version must specify coherent transport of the attached probability data; merely adding arbitrary priors to objects is insufficient. Nor should Bayesian updating be identified with a reversible change of presentation. It is an evidential update rather than a redescription, and depending on the update rule and support it need not define an invertible transformation on the chosen probability-state space.

Even with these extensions, observer-equivariance remains a constraint architecture rather than a new dynamics. Its formal grammar is plurality, admissible transport, shared structure, and the possibility that local coherence may still fail globally. I will use reconcilable plurality for a mythic possibility suggested by this grammar.

After Babel: unity without a single language

The first strong pattern appears when Babel and Pentecost are placed side by side.

Genesis 11 begins with the whole earth speaking one language. The language is confused and the builders are scattered. In Acts 2, by contrast, people from many regions hear the proclamation in their own native languages. Christian tradition has often read Pentecost as an answer to or reversal of Babel. Yet Acts does not describe humanity returning to one universal language. Shared understanding occurs through a plurality of languages.

Genesis does not explicitly identify monolingualism as the sin, and Acts does not cite Babel. Yet in the traditional typology they suggest a useful contrast between pre-Babel linguistic uniformity, post-Babel fragmentation, and multilingual intelligibility at Pentecost.

Observer-equivariant objectivity is not a return to the one language spoken before Babel. It is closer to the possibility that what is shared can become intelligible in more than one language. Read passively, a Lorentz transformation relates component descriptions in different inertial frames without making those descriptions identical.

Descriptions may differ while obeying a coherent transformation rule, and objective content may be recovered where the relevant identification or descent succeeds. Objectivity is not secured by choosing one local description and declaring it universal, but by specifying admissible passages and testing what survives or transforms consistently.

Not every standpoint is automatically translatable into every other. Admissibility requires physical, operational, or structural justification, and the groupoid need not be connected.

Still, the comparison suggests a concise archetypal formula:

No voice is the language of the whole, yet something shared may be heard through several voices.

Shared structure in a local form

Translation preserves plurality, but it leaves a deeper question. How can shared or universal structure be articulated locally without becoming identical to one local form?

At considerable doctrinal distance, the Christian image that suggests itself is incarnation: the eternal Word assuming human nature and living a particular human life without ceasing to be divine. A physical law, by contrast, is expressed through coordinates, frames, gauges, models, and experimental arrangements.

A representation may encode the law completely within its domain without thereby becoming a presentation-independent standpoint.

The two errors exposed by the analogy are Chalcedonian in form, though not in doctrinal content. The Definition of Faith of the Council of Chalcedon describes Christ as acknowledged in two natures “without confusion, without change, without division, without separation.” Borrowing only that logical rhythm, the relational interpretation must neither confuse a local presentation with the shared structure nor separate the shared structure from every concrete presentation.

The first error is therefore idolatry of the local form: one presentation is mistaken for reality itself. A preferred coordinate system, gauge, or observer's account silently becomes absolute. The second is disembodied abstraction: because a fact is local or relational, it is treated as less than real. The first abolishes plurality in favour of one representation; the second preserves an abstract unity by emptying its local appearances of significance. A local fact can instead be real as a local fact without becoming an absolute fact for every other system, while a shared law can be objective without requiring a privileged presentation.

Yet classical incarnation doctrine also marks where the analogy breaks. Jesus is not one interchangeable presentation among many. The incarnation is unique and revelatorily privileged: “Whoever has seen me has seen the Father” (John 14:9). Observer-equivariance, by contrast, grants no presentation automatic privilege; it asks which comparisons are justified and what is preserved or coherently transformed across them. Chalcedon helps name the twin risks of confusion and separation, but its Christological asymmetry has no counterpart in the formal plurality of frames.

The related Christian term kenosis—the “self-emptying” associated with Philippians 2:7—has a long and disputed theological history. Used here in an epistemic rather than a doctrinal sense, it names the discipline by which a human investigator remains situated while relinquishing the claim that this situation is the measure of all others: remaining local without making the local absolute.

Who bears the wound?

The most important analogy—and the one with the highest moral stakes—concerns forgiveness.

I initially expressed the intuition in a strong form. If no part of the universe is fully isolated, then no act belongs to one part alone. All wills must somehow be harmonized; the universe has no exterior to which disorder can finally be expelled. I therefore said that the universe as a whole must bear the guilt. In this image, the archetype of the forgiveness of sins appears because the whole cannot permanently disown any of its parts.

The formulation captures something that I still find important, but it also says too much.

Neither universal non-isolation nor the demand that all wills be harmonized follows from the formal core of observer-equivariance. Within my broader metaphysical interpretation, the argument still contains several additional steps. Non-isolation must first be connected to causal involvement; causal involvement must then be connected to responsibility for repair; and that responsibility must finally be connected to a hope of reconciliation. None of these transitions is automatic.

Relational dependence is not agency or control, and defining the universe as all-inclusive does not make it morally responsible. Even where the conditions and consequences of an act extend beyond the individual, culpability need not follow the same distribution. Otherwise perpetrator and victim disappear into an undifferentiated cosmic responsibility.

At least three notions must therefore be kept apart:

• causal involvement: the network of conditions from which an act arose;
• moral responsibility: the differentiated accountability of agents for what they did;
• the work of repair: what must happen if the consequences are to cease reproducing the injury.

A more defensible version of the original thought is therefore:

No individual exhausts the causal history of a wrong, and neither victim nor offender can be made metaphysically external to the world. Speaking metaphorically, the whole bears the wound insofar as the event and its effects remain within its history. This does not make every part equally affected or responsible.

This casts the scapegoat in a revealing role. In René Girard's influential but contested model, scapegoating can temporarily unite a community by concentrating its disorder on a presumed-guilty victim. Girard reads the Passion as exposing this mechanism by maintaining the victim's innocence—a specifically Girardian interpretation, not a neutral summary of Christian atonement.

An all-inclusive ontology does not make every form of social separation unjust. Exclusion or restraint may sometimes be necessary to protect others. The narrower point is that projecting a community's disorder onto a falsely blamed victim does not repair the relations or institutions that produced the violence. The source of injury has then been displaced rather than resolved.

On the account adopted here, forgiveness is not deletion, retrospective acquittal, or compulsory renewed intimacy. It does not make the perspectives of perpetrator and victim morally equivalent. Forgiveness may transform a person's relation to an irreversible wrong while retaining the judgement that it was wrong. Reconciliation is different: it concerns a relation between parties, requires protection against repeated injury, and should not be demanded unilaterally from the injured party.

None of this follows mathematically from p: O → S. It is a moral extrapolation prompted by the same resistance to isolated absolutes. In its most careful form, the archetype is not “the universe is equally guilty of everything.” It is this:

A wrong is not repaired merely by treating the injured party—or the wrong itself—as alien to the world's history.

The will that refuses

A Norse myth, in Snorri's telling, offers a vivid stress test for the idea that all wills must be harmonized.

In Snorri Sturluson's thirteenth-century Gylfaginning, Frigg takes oaths from things not to harm Baldr, but the mistletoe is overlooked as too young. Loki obtains it and guides the blind Höðr's hand; Baldr is killed. Later, Hel agrees to release Baldr if all things, living and dead, will weep for him. They do—except for the giantess Þökk. Her refusal prevents Baldr's return. Snorri adds that people believed Þökk to have been Loki in disguise.

The overlooked mistletoe breaks the supposed completeness of the protection; later, extensive agreement fails because of one refusal. The myth gives narrative form to two questions that any rhetoric of total harmony must face: who was omitted from the construction of the whole, and what happens to the voice that will not assent?

If harmonization means forcing Þökk to weep, harmony has become domination. If dissent can be removed merely by declaring the dissenter “inadmissible,” admissibility has become circular. Formal admissibility classifies transformations between presentations, not the moral standing of persons; the analogy is therefore a warning about a possible misuse of the interpretation, not a claim about the mathematics itself.

Conversely, preserving a will does not mean granting it everything it wills. Desires may be jointly impossible, and harmful actions must sometimes be prevented. Conflict must be representable and constrainable without being erased. The possible disconnectedness of O and the possibility of descent obstructions show only that the formalism supplies no guarantee of global reconciliation.

Within the mythopoetic register, I would therefore recast “all wills must be harmonized” as a defeasible ethical aspiration—or, in a theological register, an eschatological hope. A just order should not depend on denying the existence or moral standing of persons affected by it, even though it may legitimately restrict harmful actions and cannot guarantee agreement. Whether any fuller reconciliation is possible is precisely what the formalism does not decide.

History belongs to the perspective

The return to Bayesian language is deliberate. Here the technical extension tests and limits the mythopoetic motif.

A prior represents an agent's probability assignments within a specified model before the evidence currently under consideration is incorporated. It may reflect earlier information, modelling decisions, expectations, and experience, but need not encode a biography. A presentation enriched by a prior is indexed by an epistemic situation rather than an empty geometrical point.

For the proposed synthesis of QBism and RQM, this raises a further question: what comparison maps and coherence conditions would allow agents with different histories to compare assignments and identify shared content? Identical priors cannot be assumed, and Bayesian updating does not guarantee convergence without further conditions.

There is a limited analogy with forgiveness here. Bayesian updating does not return an agent to an epistemically blank state. Under a specified model and update rule, a posterior is obtained by conditioning a prior on evidence. But the posterior alone does not generally preserve a reconstructible record of either the prior or the full evidential history.

The analogy preserves only historical conditioning, not literal retention. A present perspective can be shaped by a prior state that cannot be recovered from present data. Likewise, forgiveness does not make a wrong unreal, although a person's relation to it may change. Forgiveness is not Bayes' theorem; the shared pattern is transformation from a situated history, not a common mechanism.

Not unison, but a fugue

For that reason, music offers a better final image than either a courtroom or a kingdom.

In a fugue, a theme enters in different voices and can reappear through transformations such as transposition, inversion, augmentation, or diminution. The entries are not identical strings of notes, yet their relations make the theme recognizable. No single voice is the whole composition. Nor does polyphony become coherent by forcing every voice onto the same note.

Musical consonance is not formal consistency or moral reconciliation. A theory could satisfy the relevant observer-equivariance constraints while describing a morally catastrophic world. The three meanings of “harmony”—mathematical, musical, and ethical—must not be collapsed.

Yet the fugue captures the governing pattern better than the image of an all-seeing observer. Difference need not be noise. A transformation need not destroy an independently specified identity. Dissonance need not be denied in order to belong to a larger form, and not every dissonance must be resolved on demand.

I would therefore call the central archetypal hope suggested by my interpretation of observer-equivariance reconcilable plurality. On the philosophical level, objectivity can be understood as invariant or coherently transforming content articulated across situated perspectives rather than as the result of removing perspective altogether. On the mythopoetic level, this becomes a hope: that plurality need not end either in Babel or in totalitarian unison.

The groupoid does not promise Pentecost. Its possible obstructions warn against easy closure.

What survives from the original forgiveness intuition is the claim that a wrong is not repaired by making the injured party—or the wrong itself—alien to the world's history. What must be surrendered is the inference from universal connectedness to shared guilt, the identification of causal involvement with moral responsibility, and any formal guarantee that all wills can or must be reconciled.

Myth adds no equations to observer-equivariance, and observer-equivariance verifies no myth. Myth can nevertheless bring the human questions around the structure into view: How can difference remain real without destroying shared meaning? How can a whole acknowledge injury without exporting all guilt to one part? How can conflicting voices belong to a future that none owns alone?

The whole, in this mythopoetic reading, is not a final voice speaking above all the others. It is the still-unfinished possibility that their differences may belong to one intelligible composition without being erased.

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References and notes

• Gustaf Ullman, A Strict Normal Form for Shared Physical Law: A Lean-Verified Classification Theorem for Observer Equivariance, 2026. The paper states the strict formal model and its limitations; the mythopoetic interpretation in this essay is not part of its theorem content.
• “Relational Quantum Mechanics,” Stanford Encyclopedia of Philosophy and “Quantum-Bayesian and Pragmatist Views of Quantum Theory,” Stanford Encyclopedia of Philosophy. These sources also make clear an important difference: RQM's observers need not be conscious agents, whereas QBism is explicitly agent-centred.
• Genesis 11:1–9 and Acts 2:1–13. For the traditional Babel–Pentecost comparison and the qualification that Acts retains linguistic plurality, see A. J. M. Wedderburn, “Traditions and Redaction in Acts 2.1–13”, Journal for the Study of the New Testament 17, no. 55 (1995), 27–54.
• The Definition of Faith of the Council of Chalcedon, 451, for the formula “without confusion, without change, without division, without separation”; and John 14:9 for the revelatory asymmetry that limits the incarnation analogy.
• Philippians 2:7 is the textual source of the language of kenosis. Its interpretation is historically contested; see Michael C. Magree, The Interpretation of Kenosis from Origen to Cyril of Alexandria: Dimensions of Self-Emptying in the Reception of Philippians 2:7, Oxford University Press, 2024.
• For the Girardian claim that the Passion exposes rather than simply repeats the scapegoat mechanism, see John Lechte, “Image, Violence, Victim and the Crucifixion: Girard's Version”, chapter 6 in Violence, Image and Victim in Bataille, Agamben and Girard (Edinburgh University Press, 2023), 163–182. Girard's theory and its theological application remain contested.
• For distinctions among forgiveness, excuse, forgetting, condonation, and reconciliation, see “Forgiveness,” Stanford Encyclopedia of Philosophy.
• Snorri Sturluson, The Prose Edda, Gylfaginning, commonly numbered chapter 49 (chapter XV, “The Death of Balder,” in the linked Rasmus B. Anderson translation, 1901), for Baldr's death and Þökk's refusal to weep.