Paimana

The report is repeated often enough that it has stopped functioning as a claim and started functioning as a slogan: al-tāʾib min al-dhanb ka-man lā dhanba lah, the one who repents of a sin is like one who has no sin. Read at conversational speed it sounds like a statement about the past. The act is undone, lifted out of the record, and the agent is returned to a condition in which the thing never happened. I want to argue that this reading is both physically incoherent and unnecessary, and that the doctrine becomes considerably more interesting once one asks what kind of identity claim it is actually making.

The incoherence first. An act deposits itself in the world along every channel available to it. It is in the person who was wronged and in the dispositions of the agent, reinforced by having performed it once, along with whatever else registered it. No operation available within the created order deletes any of this. One can of course reply that divine power is not constrained by the ordinary course of things and that the God who sustains the world moment to moment can simply decline to sustain a portion of it, and this reply is available to any Ashʿarī and to a good number of Imamis. I think it concedes too early. It treats the ḥadīth as making a claim that requires a miracle in order to be true, when a reading is available on which it makes a claim that is exactly and unmiraculously true, and on which the rest of the juristic tradition’s behavior around repentance stops looking like a set of embarrassing exceptions.

Microstates and macrostates

The distinction I discuss is the one that statistical mechanics uses to get thermodynamics out of mechanics. A microstate is a complete specification of a system, every position and momentum, the whole configuration down to the last degree of freedom. A macrostate is a class of microstates that agree on the values of a small number of variables that one is in a position to measure: temperature, pressure, volume, magnetization. Entropy counts the size of that class, the number of microscopic arrangements compatible with the same macroscopic description.

The underlying mechanics permits less than the erasure reading needs, and the constraint should be stated exactly. Liouville’s theorem says that the flow of trajectories through the space of microstates behaves like an incompressible fluid, so that a region of possibilities is carried along without shrinking or growing in volume. The evolution is also invertible, which Loschmidt put to Boltzmann as an objection in the 1870s: a mechanics indifferent to the direction of time seemed a poor foundation for a law that runs one way only. Poincaré added the recurrence theorem, that a bounded system returns arbitrarily close to any earlier configuration if one waits long enough, on timescales that remove the result from physical relevance while leaving its logical force undisturbed. What actually happens to a compact region of phase space is that it is stretched and folded into filaments at conserved volume, until the difference between it and its surroundings survives only at a resolution finer than any instrument that exists, and then finer than any instrument that could be built. Inaccessibility at every achievable resolution is the strongest form of loss the created order supports, and a doctrine of repentance that respects the grain of things has this much and no more to work with.

Two features of this construction are important. The first is that the partition into macrostates is not read off the system. It depends on which observables one has been given or is capable of resolving, and a different set of observables induces a different partition and therefore different entropies for the same microstate. Jaynes pressed this to its limit in his 1965 paper sorting out the Gibbs and Boltzmann entropies, crediting the epigram to Wigner: entropy is an anthropomorphic concept, fixed by the experiments one chooses to perform on a system. One can dispute how far the subjectivism should be pushed, and the literature has been disputing it for sixty years, but the minimal point survives every position in that dispute. The second is that the underlying dynamics destroys nothing. Microscopic evolution is invertible; the information about where the system came from is still there in principle, distributed into correlations too fine and too numerous to be recovered by anything short of the full description. Irreversibility is a fact about the coarse-grained account, and the past is not deleted in the process of becoming inaccessible.

I should add a third feature, since the theological use depends on it and the erasure reading implicitly denies it. Identity of macrostate is real identity within the partition, and it is not an approximation to some stricter sameness that the two systems fail to have. Two samples of gas at the same temperature, pressure, and volume are the same thermodynamic state, though their microstates differ in every particular, and every engine ever built has run on that sameness being good enough to calculate with. Thermodynamics is not a diminished science for trafficking in this kind of identity alone.

The proposal, then, is that “like one who has no sin” is a macrostate identity claim. Ka-man, like one who, asserts co-membership in a class and declines to say more. It says that the repentant and the never-guilty fall into the same equivalence class under some specified set of observables. It says nothing whatsoever about the microstate, and it does not need to, because nothing in the force of the consolation depends on the microstate having changed. What it does require is a specification of the observables, since an equivalence claim with an unspecified partition is not yet a claim at all.

Which observables

Here the tradition is more forthcoming than the slogan suggests, and what it says is restrictive in a way that reads as evasion under the erasure interpretation and as precision under this one.

Take the clearest case. Tawba does not clear ḥuqūq al-nās. A man who has taken property and then repents is required to return it, and no amount of nadam substitutes for radd al-maẓālim. If repentance produced erasure this would be inexplicable, since there would be nothing left to return and no one who had been deprived. Under a coarse-graining reading it is exactly what one expects: the equivalence is asserted over one set of observables, the ones concerning liability before God, and simply not asserted over another, the ones concerning what passed between two people and remains outstanding between them.

The sharper case is qadhf. The Qur’an assigns the slanderer the lash, rejects his testimony permanently, and names him among the corrupt, and then attaches an exception for those who repent and make amends. Jurists have disagreed for a very long time about the scope of that exception, specifically about whether it reaches only the designation of fisq or also lifts the disqualification from testimony. Abū Ḥanīfa held the narrow reading, on which the exception governs the final clause alone, so that repentance restores the man’s standing as a Muslim in good faith while the bar on his testimony holds permanently and abadan means what it says. Mālik, al-Shāfiʿī and Aḥmad held that the exception governs the whole sentence and the repentant slanderer testifies again. The Imami jurists sit with the second camp and attach a condition I find instructive, that the repentance takes the specific public form of takdhīb al-nafs, the man’s declaring himself a liar in the matter, so that what restores the observable is itself an observable, available to the court that has to rule on it. The disagreement is a dispute about the partition, conducted in the only vocabulary available before anyone had the vocabulary of partitions. Both sides agree that something is restored and something might not be. What they are arguing about is whether ʿadāla for purposes of testimony is one of the variables over which the repentant and the innocent are being equivalenced, or whether it belongs to a finer description on which they still differ.

I notice that I work with this structure every day without thinking about it. A patient’s problem list carries entries marked resolved. The entry is not deleted, and the whole point of retaining it is that the resolution is a status assigned to a record that persists, since the fact of a resolved infection changes what one expects on the next presentation. “Resolved” is a macrostate assignment made under a specified set of clinical observables, and it coexists without contradiction with a chart that remembers everything. Nobody experiences this as a hedge on the word resolved.

The cost of clearing a record

Landauer’s principle says that erasing a bit of information has a minimum thermodynamic cost, and that the cost is paid because the information survives, pushed out into the environment as heat. Resetting a register regardless of its prior content dissipates at least kT ln 2, and the discarded content survives in the correlations of the surrounding bath, where nobody reads it. Bennett used the principle to settle the case of Maxwell’s demon, which had resisted a century of attempts: the demon can measure and sort for free, and the account balances when it clears its memory to begin the next cycle, at a cost that matches exactly the entropy it appeared to have saved. The bound has since been confirmed in single-particle experiments, so it is no longer only a theorem. A logically irreversible operation performed on a physically reversible substrate has to export the difference somewhere, and the export is the price.

The tradition keeps this account too, and the place it keeps it most explicitly is a text I have known since childhood without hearing it in these terms. A man says astaghfiru Llāh in the presence of ʿAlī and is stopped. Do you know what istighfār is? It is a station of the elevated, and it is a name standing on six things. Regret for what has passed. Resolve never to return. That you render to creatures their rights until you meet God with nothing outstanding against you. That you discharge every obligation you neglected. That you go at the flesh grown on unlawful nourishment with grief until it melts and the skin adheres to the bone and new flesh grows in its place. That you make the body taste the pain of obedience as you made it taste the sweetness of disobedience. Then say astaghfiru Llāh.

The six things are a ledger organized by where the record sits, and the ordering does the organizing. The first two are conditions on the will, the one register whose contents the agent can rewrite by deciding to, and they are the only two that the kalām manuals require. The third and fourth are transfers, since where the record sits with other people or with obligations left undone, the outstanding difference is moved to whoever holds it, and this is the moral counterpart of Landauer’s export into the bath. The fifth and sixth demand a change of microstate, and they demand it in the only substrate over which the agent has anything like write access. Tissue grown on unlawful nourishment is to be melted off and regrown. A body that learned the sweetness of the act is to be retrained on the cost of its opposite. What the saying refuses is a repentance that consists in a change of description alone. Where rewriting is physically possible it commands rewriting, and where the record is held by others it commands settlement, and the word itself is withheld until the ledger has been worked through.

The rest of the juristic apparatus looks like the same accounting. Restitution moves the outstanding difference to the person who is owed it. Kaffāra fixes it as a prescribed act with a determinate cost, and the ḥadd discharges it into the body of the offender under public supervision, which is why the tradition treats a punishment undergone as expiation. In each case the tradition names a destination, and in each case the doctrine that repentance suffices by itself is qualified by the requirement that the difference go somewhere first. The Qur’anic clause exempting the muḥārib who repents before he is apprehended is the interesting boundary case, since there the transfer is waived, and the waiver is conspicuous enough that jurists treat it as a specific dispensation and decline to generalize from it.

I do not want to press the analogy past where it holds. Landauer’s cost is paid into a thermal bath that has no stake in the transaction, whereas restitution is paid to a person who does, and the entire moral content of the requirement sits in that asymmetry. What the physical principle contributes is a single constraint: creation permits the clearing of records and forbids their destruction. The two operations have been run together wherever repentance is described as erasure.

Who fixes the partition

The kalām tradition inherited from the Muʿtazila a dispute about whether God is obliged to accept a valid repentance or whether acceptance is an act of tafaḍḍul. The Muʿtazilī position came out of their doctrine of the promise and the threat, on which God’s declared consequences must fall, since failing to carry out a threat is as ugly as breaking a promise and therefore impossible for a just God, from which it follows that pardon without repentance cannot occur. The Baṣran school added that a valid repentance removes liability to punishment by rational necessity, in the way that a debt discharged is a debt gone, and they policed the validity conditions accordingly. Regret counts only if it is regret at the ugliness of the act as such, so that a man who regrets his sin because it ruined his health or his standing has repented of the damage and his register reads as it did. The Imami mutakallimūn adopted the rationalist apparatus wholesale and then declined to follow at this point, holding that pardon without repentance is possible and that intercession reaches sinners who never settled their accounts. In the position that came to prevail, even the fall of punishment upon a valid repentance is an act of grace, with no entailment behind it.

Put in the usual terms the dispute is about divine obligation, and it looks like one more instance of the general question about whether the intellect can bind God. Put in the terms I have been using it becomes a question about who fixes the partition.

If the observables are settled independently of the divine will, so that the class of the innocent is defined by facts about liability that hold whatever anyone decides, then the repentant’s membership in that class follows from the facts of his case and there is nothing left for God to do beyond recognizing it. Acceptance is then obligatory in the same sense that a correct sum is obligatory. If instead the choice of what to count belongs to God, then the repentant has done everything specifiable on his side and the equivalence still waits on a decision about which variables are being read. Acceptance is grace, in a precise sense, since what is being given is the coarse-graining itself.

Forgiveness as covering is coarse-graining performed as a favour. The Imami position has a consequence that its own vocabulary has been carrying all along, since a God who fixes the partition can decline to read a variable, and the root of ghafara is covering, the root that also names the helmet. The divine names built on it, along with Sattār by which the tradition addresses the concealer of faults, describe an operator whose action is a refusal of resolution, with the record left intact and the reading declined. Justice survives alongside it untouched, since reading a variable falsely and punishing an innocence that is there remains excluded, while declining to resolve a guilt that is there belongs to whoever owns the instruments.

This also explains why the conditions on repentance are stated as they are. Regret and resolve are conditions on the agent, and they are the only conditions that could be conditions on the agent, since he has no access to the description under which he will be read. The tradition’s insistence that one can never be secure about acceptance follows from the same structure without needing any additional pessimism about divine caprice.

The stronger claim

The Qur’an says something considerably stronger than the ḥadīth in the passage in Sūrat al-Furqān about those whose evil deeds God exchanges for good ones. Under the erasure reading this is difficult, since it is unclear why a record that could simply be deleted would instead be converted, and conversion of a past act into a different past act is a stranger operation than deletion.

Under the reading I am proposing it is the natural extension. Consider the Szilard engine, proposed in 1929, where a demon with information about which side of a partition a molecule occupies can extract work from a single-temperature bath. The molecule does nothing different. What changes is that a correlation now exists between the system and something that can act on it, and the same microstate that was useless becomes a resource. Access to a new observable converts heat into work without touching the underlying dynamics at all, and Bennett’s accounting shows the conversion to be honest, since the cost was paid when the correlation was established.

A sin that has been integrated into a life that knows what it was and what it cost is correlated with the person in a way that an innocence never tested is not. The tradition’s occasional and uncomfortable suggestion that the repentant sinner stands somewhere the untested innocent does not stand is a claim of this shape, and it is the same intuition that produces the warnings about ʿujb, on which self-admiration corrupts the obedient more reliably than remembered sin corrupts the repentant. The claim is about the record and not about the act. Once the record is available to the agent as knowledge it does work that it could not do while it sat there as unexamined history, and the exchange attaches to repentance because repentance is what builds the correlation.

Why the partition is never published

The tradition never issues the list of observables, and I have been treating that silence as a gap in the record. It may be a requirement of the doctrine. Any statement of which variables are read becomes a specification that an agent can satisfy directly, and an agent who has satisfied a specification has done something other than repent. Goodhart described this for economic indicators and Campbell for social ones, the case in which a measure adopted as a target stops measuring what it was chosen for, because the behaviour under observation reorganizes itself around the observable. A published partition would be a partition one could meet by construction, with the regret calibrated to the reading and the reading registering the calibration.

This predicts the pattern the jurists actually produce, and it accounts for the asymmetry I described earlier without appealing to divine reticence. Where the object of a ruling is public order the observables are stated with precision, since testimony and ḥudūd have to be administrable, and the cost of a man engineering himself into the criteria for restored testimony is bounded by what a court can check. The takdhīb al-nafs is a criterion built to be checked. Where the object is the man’s standing before God the tradition specifies nothing, and holds instead to formulas whose entire content is that acceptance may or may not have occurred. The refusal to publish keeps the variable diagnostic. It also explains the strictness of the Baṣran condition on the object of regret, since a doctrine worried about calibration has to insist that the regret be regret at the ugliness of the act, the one formulation nobody can satisfy while attending to the consequences of being read.

What this leaves standing

The reading resolves the appearance of contradiction between a doctrine that promises the condition of the sinless and a jurisprudence that keeps careful books on what repentance does not clear, and it does so without invoking a suspension of the ordinary course of things. It also preserves the phenomenology, since the repentant who continues to remember what he did is not thereby suffering from insufficient faith in the promise. His memory is a variable over which the equivalence was never asserted, the ḥadīth does not overreach into the claim that he should forget, and the six conditions suggest that the memory is the correlation on which the stronger promise runs.

What it does not resolve is the question of which observables God actually tracks, and this is the question on which everything else rests. The tradition’s confidence about the partition comes from report, and the disputes I have described turn on the interpretation of reports, with nothing derived from the structure of the case. If the Goodhart argument holds, the silence is a condition of the doctrine working at all, and no analysis will supply what has been withheld by design. The analysis I have given constrains what the doctrine could coherently mean, and it makes visible that the choice of partition is the whole of what is at stake in accepting a repentance. The procedure is subject to its own description. I have chosen observables here as well, the juristic residue and the kalām disputes, and left out the devotional life in which repentance is actually conducted, and a different choice would have partitioned the tradition differently. It supplies no independent access to the choice, and the sinner who wants to know whether the variable he is worried about is among the ones being read is in the position of a system that cannot see its own macrostate description.