The Emergence of Meaning from Encounter - A Generative Relational Theory of Serendipity 【（Preliminary）Draft】

ENGLISH

Abstract

Serendipity is ordinarily analysed as the sum of two independent quantities, a contingent event and a prepared mind, following Walpole’s pairing of accident with sagacity. Three developed traditions refine that analysis. The first locates the decisive factor in the observer, treating preparation as a cognitive property that some individuals possess in higher degree. The second locates it in the object or in the order that placed the object there, which is the form the question takes under doctrines of providence and under strong determinism. The third, in recent philosophy of science, locates it in the scientific community and in the retrospective recognition of value. This paper develops a fourth account. An encounter is a relation between a configured cognition and a contingent phenomenon, and the meaning that arises in a serendipitous event is generated at that relation, with neither relatum holding it in advance. Sagacity is accordingly reconstructed as the capacity to hold a relation unresolved for the interval required for an unforeseen phenomenon to couple to it, a capacity of sustained non-closure whose failure mode is early termination in a settled response. The encounter that terminates in an appreciative judgement is examined as the limiting case in which contingency arrives and generation does not follow. The account is extended to the structure of inquiry: disciplines are treated as relational crystallizations whose local coherence is productive, and whose foreclosure of encounter begins where local coherence is taken for independence. Cases are developed in physics, cosmology, intelligence analysis, economic interpretation, international practice, and cross-domain transfer, together with a survey of the existential, religious, and philosophy-of-science literatures on contingency.

Keywords: serendipity; contingency; encounter; meaning; relational ontology; preparation; interdisciplinarity; generative relational being.

A note on the standing of this paper. This is a preliminary discussion. It occupies the position between an ontology and a governance programme: if being is generative and relational, the epistemology that follows must say how meaning arrives, and serendipity is the case in which the arrival is most visible because nothing in the encounter was arranged in advance. The order of exposition follows the order of the argument. The existing accounts are set out first, across three literatures that have rarely been read together, and the relational account is introduced at the point where their common commitment becomes visible. Should the phenomenon prove fully described by preparation on the observer’s side, the central sections lose their ground. The cases are constructed for illustration and drawn from the published record; they carry the weight of illustration. Objection, correction, and counter-evidence are welcome at huangwanhong@serendip.ngo.

§1 Introduction

Two people stand before the same crystal. The first looks, finds it beautiful, and moves on. The second looks, and something opens: local rules of growth have produced a structure that is ordered throughout and uniform nowhere, whose grains meet at boundaries that hold difference in place while the whole retains its integrity. Within the hour this second observer is thinking about languages in a shared political order, and about whether a plurality of coherent worlds can be held together by the relations between them. The crystal was the same crystal. It sat in the same case, under the same light, for the same interval. Whatever happened, happened between the mineral and one of the two people looking at it.

The ordinary vocabulary for this is luck, and the ordinary refinement of that vocabulary is that luck favours the prepared. Pasteur’s formula from the Lille address of 1854 has become the settled wisdom of the sciences: in the field of observation, chance favours the prepared mind. Horace Walpole’s coinage a century earlier had the same two-part shape. Writing to Horace Mann in January 1754, he named after the heroes of a Persian tale a faculty for making discoveries by accidents and sagacity, of things one was not in quest of. The pairing has proved durable, and it names the two factors correctly. What the pairing leaves open is the relation between them. Accident and sagacity are joined by a conjunction, and a conjunction is the weakest connective available. It states that both were present and says nothing about how the presence of both produced what neither produced alone.

The question this paper takes up concerns that connective. Where does the meaning of a serendipitous encounter arise, and what kind of thing must sagacity be for the encounter to yield anything at all?

Three developed positions answer the question, and they divide by where they place the meaning.

The first places it on the side of the observer. Preparation is a property of a mind, distributed unevenly across individuals, and the serendipitous discovery is the yield of a well-stocked and alert cognition meeting an occasion. Merton’s serendipity pattern belongs here in its classical reading: an unanticipated, anomalous, and strategic datum becomes the occasion for extending a theory, and what makes it strategic is the theoretical equipment the observer brought. The position is sound as far as it reaches, and it grounds a large practical literature on how research environments should be arranged. Its difficulty is that it inherits a picture of the object as inert. The datum contributes its anomaly and contributes nothing further; the work is done inside the head that receives it. On this picture the crystal is a stimulus, and the polycrystalline account of plurality was already latent in the second observer, waiting for any sufficient trigger.

The second places the meaning on the side of the object, or on the side of the order that arranged for the object to be there. This is the form the question takes wherever a doctrine of providence, decree, or comprehensive determination is in force, and §4 treats it at length because the religious traditions have thought about contingency longer and harder than the sciences have. Calvin’s treatment in the Institutes is the sharpest version available: fortune and chance are terms that leave no place in human affairs once providence is understood, and what appears fortuitous to us is fortuitous only in respect of our ignorance of its cause. Aquinas preserves more, holding that providence extends to contingents in their contingency, so that chance is real relative to particular causes even where it is not real relative to God. The strength of the family is that it takes the meaningfulness of the encounter with full seriousness. Its cost, for the present question, is that meaning arrives at the encounter already complete. What the observer does is find it.

The third position, developed most carefully by Copeland in recent philosophy of science, moves the analysis out of the individual altogether. Serendipity is an emergent property of a discovery process distributed across a community, and its recognition is retrospective: a valuable outcome must be obtained before reflection on its significance can occur. Glăveanu, in the same research programme, presses further toward relation, proposing that the question of what lies inside the prepared mind be replaced by a question about what happens between mind and world. This literature is the nearest to the account developed here, and §3 states the points of contact precisely. The remaining distance concerns time and locus. On the social-epistemological account the meaning is conferred by a community looking back; the encounter itself is an event whose significance is settled elsewhere and later.

Across three literatures that do not read one another, a single commitment recurs. Meaning is taken to have a location. It sits in the observer’s equipment, or in the object and the order behind it, or in the community’s retrospective judgement, and the analytic task is to identify which. The alternatives are then arranged as a dispute over the address.

The present paper proceeds from a different starting point. Generation occurs between relata and is a property of neither. This is the governing commitment of Generative Relational Being, and serendipity is the case that displays it with least interference, because nothing in a serendipitous encounter was arranged to produce the outcome it produced. In the crystal case there is no prior fact about the mineral that contains a theory of multilingual democracy, and no prior state of the observer that contains it either. The second observer carried an unresolved question about how coherent particulars might compose a whole without being flattened into uniformity. The crystal carried a structure in which local rules produce ordered heterogeneity across grain boundaries. Neither was the theory. The theory was generated when the two came into relation, and the relation produced a third thing that was in neither.

From this starting point the two ordinary terms are reconstructed. The contingent phenomenon has a structure of its own that participates in what is generated, which is why the same prepared observer meets a thousand contingencies and generates from a few. And sagacity ceases to be a quantity of intelligence or a stock of expertise. It becomes a temporal capacity: the capacity to hold a relation open, unresolved, and unclosed for the interval required for an unforeseen phenomenon to couple to it. On this reading the first observer’s response to the crystal is the diagnostic case. Nothing was lacking in attention or in feeling. The response was appreciative and closed, and closure is what forecloses generation. Beauty arrived as a terminus. For the second observer, beauty was where the encounter opened.

The account developed from this starting point yields four contributions.

The first is the relational reconstruction of the serendipitous event, which places the emergent meaning at the coupling of a configured cognition and a contingent phenomenon and derives the observed features of serendipity from that placement (§6).

The second is the reconstruction of sagacity as maintained non-closure, together with its failure modes (§7). This is the paper’s principal original claim, and it converts a dispositional term into a temporal one. It also carries the practical consequence that the capacity can be cultivated, though the encounter it prepares for cannot be planned.

The third is the treatment of aesthetic closure as the limiting case of the non-encounter (§5), which supplies the negative diagnostic the field has lacked. Existing accounts explain why serendipity occurs. The question of why it fails to occur, in the presence of both a contingent event and an attentive observer, has not been posed in these terms.

The fourth extends the account from the individual encounter to the architecture of inquiry (§8). Disciplines are relational crystallizations, and their local coherence is what makes them productive. The foreclosure of encounter begins where local coherence is taken for ontological independence, at which point the boundary sorts a phenomenon away from a question before the two can meet.

The paper occupies a determinate position in a larger programme. Generative Relational Being supplies an ontology in which relation has priority over relata. A governance extension draws consequences for institutional design. Between them a question stands open: if being is generative and relational, by what route does new meaning enter, and what must a knower do to be available to it. Serendipity is the answer’s most legible case, and the account developed here is offered as the epistemological hinge of the programme.

These are pursued under three questions.

RQ1. Where does the meaning generated in a serendipitous encounter reside, given that neither the contingent phenomenon nor the observer’s prior state contains it?

RQ2. What capacity on the observer’s side allows an unforeseen phenomenon to couple to a question the observer carries, and what are the conditions under which that capacity lapses?

RQ3. What follows for the organization of inquiry, given that boundaries which make local coherence possible also govern which encounters can occur?

The first is treated in §5 through §6. The second is the centre of the paper and is treated in §7. The third is treated in §8 and its consequences in §11.

The account may be stated as a single claim.

Central claim (The two conditions of generation at an encounter). A serendipitous encounter is a relation between a configured cognition and a contingent phenomenon, and the meaning arising from it is generated at that relation, with neither relatum holding it in advance. Sagacity is the capacity to maintain a relation unresolved for the interval required for an unforeseen phenomenon to couple to it. The encounter that terminates in a settled response is a non-encounter, in which contingency arrives and generation does not follow. The conditions of serendipity are therefore two and jointly necessary: a configuration carrying live and unresolved relations, and an openness across the boundaries that would otherwise sort the phenomenon away from the question before they meet.

The remainder proceeds as follows. §2 surveys the treatment of contingency in the existential tradition, which has thought about the encounter with brute contingency more thoroughly than any other, and identifies the projection model it bequeaths. §3 surveys serendipity in the study of discovery, from Walpole through Merton to the recent social-epistemological turn, together with the theory-ladenness literature that bears directly on the configuration claim. §4 surveys contingency in religious and theological thought, where the strongest opposition to the account and several of its closest precursors are both located. §5 develops the configuration of the encounter and the case of aesthetic closure. §6 states the generative structure and distinguishes information from meaning. §7 develops sagacity as maintained non-closure. §8 treats disciplinary crystallization and the foreclosure of encounter. §10 develops cases across six domains. §11 draws consequences for the conduct of inquiry, and §12 states the limits of the account and the work it leaves open.

§2 Contingency in the Existential Tradition

The encounter with brute contingency is the founding scene of a whole philosophical tradition, and the tradition arrived at an answer that runs opposite to the one developed here. Setting out that answer with care is the first task, because the projection model it bequeaths is the position most likely to be attributed to this paper by a reader who moves quickly.

2.1 The Withdrawal of Meaning in Sartre

Roquentin, in the public garden, looks at the root of a chestnut tree. The words have gone, and with the words the meaning of things has gone; the root is there, entirely raw, and existence discloses itself as the absolute, perfectly gratuitous. Sartre (1964) makes this the paradigm encounter with contingence, and the philosophical apparatus of Sartre (1956) formalizes it: facticity is the perpetual contingency that the for-itself assimilates without founding, and it is altogether contingent that I be, since I am not the foundation of my being.

The structural feature to mark is the direction of the movement. At the encounter with raw contingency, meaning drains out. The in-itself is dense and significance-free; the for-itself confers such significance as there is; and the confrontation with contingency is the moment at which the conferral is exposed as conferral. This is the projection model in its strongest form, and it is the exact inverse of the account developed here. Where Sartre finds nausea at the encounter with the unconceptualized, the present account finds the site at which generation becomes possible.

A tension internal to the scene deserves note, since it has been observed by Sartre’s readers and bears on the argument. Roquentin arrives as something other than an unconfigured consciousness meeting a bare object. He is a historian in a specific crisis, having abandoned a biography, carrying a particular set of unresolved questions about existence and justification, standing in a French provincial park in the late 1930s. The encounter is thoroughly configured. What Sartre presents as the confrontation of consciousness with sheer being is itself a relational event with a determinate structure on the observer’s side, and the nausea is what that particular configuration generated. On the present account this is unsurprising. A differently configured observer, presented with the same root, generates differently.

2.2 Disclosure and the Prior Horizon in Heidegger

Heidegger (1962) holds that beings show up as something only within a referential totality already in place. The world is the relational whole in which an entity can be encountered as ready-to-hand, and presence-at-hand is the derivative mode obtained when that whole is suspended. Thrownness, Geworfenheit, names our being always already delivered over to such a situation; the later vocabulary of Ereignis reworks the same structure, which Sheehan renders as thrown-openness.

This is the closest thing in the existential tradition to the configuration claim, and it should be claimed as an ancestor of it. Preparation, in Heidegger’s idiom, is the prior disclosive horizon without which nothing appears as anything. The point of divergence concerns what the horizon does. Heidegger’s horizon governs disclosure: an entity shows up as what it already is within a world. The claim developed in §6 concerns generation: what arises at the encounter was in neither the horizon nor the entity, and the horizon’s contribution is to make coupling possible, with the coupling producing a third term. Disclosure and generation are distinct operations, and the difference is the paper’s principal debt-and-departure with respect to phenomenology.

2.3 The Chiasm in Merleau-Ponty

Merleau-Ponty (1968) develops the most nearly relational position the tradition contains. Meaning arises in the flesh, la chair, a primordial reversible tissue in which seer and seen, toucher and touched, are modes of one fabric; the intertwining resists resolution into a relation between two separate terms, and an écart, a thickness or divergence, holds the terms apart within their reversibility.

The overlap with the present account is substantial: meaning genuinely between, in neither alone. The divergence is precise and consequential. Merleau-Ponty dissolves the two-term structure into a single reversible flesh, so that the terms are modalities of one tissue. The account here retains two relata that are differently structured and independently describable, a cognition with a determinate configuration and a phenomenon with a determinate structure, and locates generation at their coupling. The distinction matters for the cases. Whether the polycrystal’s grain-boundary structure participates in what was generated, or merely occasioned an unfolding on the observer’s side, is a question with different answers under the two ontologies, and the cases in §10 are constructed to bear on it.

2.4 The Absurd as a Relation in Camus

Camus (1955) supplies the clearest statement in the tradition of the logical form this paper argues for. The absurd is essentially a divorce; it lies in neither of the elements compared; it is born of their confrontation. The absurd is not in the human being and not in the world, but in their presence together, and for the moment it is the only bond uniting them. It is born of the confrontation between the human demand for clarity and the unreasonable silence of the world.

The form is exactly the form of the central claim. A quality resides in neither relatum and arises from the relation between them. Two differences fix the position of the present account against it. Camus theorizes a negative relation, a divorce and a tension whose product is a permanent dissonance; the account here theorizes a productive relation whose product is new meaning. And Camus’s two relata are fixed and generic, a human demand and a silent world, so that the absurd is invariant across observers. The present account makes the observer’s configuration variable, which is what allows two people to stand before one crystal and generate differently.

Camus’s rejection of Kierkegaard’s leap is instructive on the closure question. The leap, on Camus’s reading, is philosophical suicide: a forced resolution that terminates the tension by an act of will. The vocabulary of §7 recovers this: premature closure resolves an open relation and forfeits what the relation might have generated. Camus and this paper agree on the discipline of staying open, and disagree about whether staying open is productive.

2.5 Contingency as First Philosophy in Kuki

Kuki (1935) constitutes the most sustained treatment of 偶然性 (gūzensei, contingency) in the modern non-Western literature, and it has been largely absent from the discussion in European languages. Kuki defines contingency by the negation of necessity, breaking the identity that necessity requires, and gives it a primary metaphysical position. The move that matters here is his grounding of the category in the contingent encounter: the presence one faces now, which need not have been faced, and whose necessity cannot be recovered.

Two features recommend Kuki’s treatment for the present argument. He takes the encounter, and not the isolated contingent fact, as the primitive, which is the same choice made in §6. And he extends the analysis into poetics, treating the beauty of fortuitous rhyme as the chance encounter of sounds, which begins to connect the aesthetics of the contingent to its metaphysics. The relation between Kuki’s account and the present one deserves a longer treatment than can be given here; what is taken from it is the licence to treat the encounter itself as the unit of analysis.

2.6 The Position Inherited from the Tradition

The existential tradition establishes the encounter with contingency as a philosophical problem of the first order, supplies the vocabulary of thrownness, configuration, and horizon, and in Camus supplies the logical form of a quality residing in a relation. What it bequeaths, in its dominant Sartrean line, is a projection model in which significance flows from consciousness onto a world that has none. The remainder of the paper develops the alternative that the tradition’s own resources make available and that the tradition did not take.

§3 Serendipity in the Study of Discovery

The literature that takes serendipity as its explicit object is younger and more empirical, and it has converged over seventy years on a position considerably closer to the one argued here. Setting out that convergence establishes what the present account inherits and what it adds.

3.1 The Original Pairing

Walpole’s letter to Mann of 28 January 1754 supplies the term and its two-part structure. The princes of Serendip made discoveries by accidents and sagacity, of things they were not in quest of, and Walpole adds a constraint that has been more often quoted than honoured: no discovery of a thing one was looking for falls under the description. The constraint does real work. It rules out the case in which a prepared observer finds what the preparation was aimed at, which is ordinary competence, and isolates the case in which preparation yields something the preparation did not target. Any account of sagacity must therefore explain how a configuration can be productive with respect to a phenomenon it was not configured for. The account in §7 is built to meet this constraint.

3.2 The Prepared Mind and the Serendipity Pattern

Pasteur’s Lille formulation of 1854 fixed the observer-side reading for the sciences, and Merton and Barber (2004), written in the late 1950s and published decades later, gave it its sociological development. The serendipity pattern is the experience of observing an unanticipated, anomalous, and strategic datum which becomes the occasion for developing a new theory or extending an existing one. Merton’s three adjectives repay attention. Unanticipated locates the contingency; anomalous locates a property of the datum with respect to a body of expectation, which is a relational property; strategic locates its bearing on theory, which is relational in the same way. Merton’s own analysis therefore already places two of the three conditions at the relation, while the explanatory weight continues to rest on the disciplined observer.

Yaqub (2018), working from Merton’s archives, supplies the field’s most useful taxonomy, distinguishing four types by the relation between search and finding and four mechanisms by the route through which the finding arrives, among them a network-emergent mechanism in which the connection is made across parties. The taxonomy is descriptive and compatible with several ontologies of the encounter; the account here can be read as supplying one.

3.3 The Relational Turn

Copeland (2019) moves the analysis decisively away from the individual. Serendipity in science is best understood within the context of the scientific community, and the insight of the individual is insufficient, since discovery processes depend on environmental factors and on the structure of the community. Copeland’s positive formulation treats serendipity as an emergent property of the discovery process, describing an oblique relation between the outcome of a process and the intentions that drove it.

Glăveanu (2022) presses the same programme toward relation in terms that come very close to the present thesis: the question of what is inside the prepared mind gives way to a question about what happens between mind and world in moments of creative serendipity, with surprise, curiosity, and wonder expanding the prepared mind into a system of open and dynamic relations between self and other, mind and culture, person and world.

The distance between this literature and the account developed here can be stated in two points. The first concerns when. Copeland’s serendipity is retrospectively categorized: a valuable outcome must be obtained before reflection on its significance can occur, so that the meaning is conferred by a later community judgement. The account here locates the generation at the encounter, with recognition and validation following as distinct operations. The second concerns what is maintained. Glăveanu’s system of relations is synchronic, a description of how a mind is relationally constituted at a moment. The claim in §7 is diachronic: what does the work is the maintenance of a relation in an unresolved state across time, and the activation of that maintained relation by an encounter that could not have been scheduled.

3.4 Configuration and the Observation Literature

One line in the philosophy of science bears so directly on the configuration claim that it must be stated before the claim is made. Hanson (1958) argues that observation is theory-laden and that there is more to seeing than meets the eyeball. The canonical illustration has Tycho and Kepler on a hill at dawn with identical retinal images: the geocentric observer sees a mobile sun over a fixed horizon; the heliocentric observer sees a fixed sun and a dipping horizon. Kuhn (1962) supplies the same structure in a bubble chamber, where the student sees confused and broken lines and the physicist sees a record of familiar subnuclear events.

The overlap with the configuration claim is close enough to require explicit handling. Hanson’s thesis is an epistemology of perception under theory: what an observer sees is conditioned by the theory the observer holds. The claim developed here is an ontology of generation: what arises at the encounter was held by neither party in advance, and the configuration’s role is to make coupling possible. The standard objection to Hanson, that the two astronomers see the same thing and interpret it differently, is a dispute about the perceptual level that the present account can leave open, since generation in the relevant sense occurs downstream of whatever the perceptual verdict turns out to be. What Hanson establishes, and what is taken from him, is that the differential response of two observers to one phenomenon is a serious philosophical datum with a long analysis behind it.

3.5 Abduction and the Surprising Fact

Peirce’s schema for abduction supplies the inferential correlate of the event under analysis: a surprising fact is observed; if a certain hypothesis were true, the fact would follow as a matter of course; there is therefore reason to suspect the hypothesis. van Andel (1994) glosses Merton’s account of serendipity along exactly these lines, as a surprising observation followed by a correct abduction. Surprise, in the schema, is a relational property: a fact is surprising with respect to a body of expectation, and the same fact meets a differently equipped observer without surprising anyone. Abduction thus provides a well-developed logic for the inferential step that follows generation, and it presupposes the configuration that the present account makes explicit.

§4 Contingency in Religious and Theological Thought

The religious traditions have thought about contingency longer than the philosophical and scientific literatures combined, and they contain both the sharpest opposition to the present account and several of its closest precursors. The section is organized by the position each tradition takes on a single question: whether the meaning that arrives in an unforeseen encounter was placed there in advance.

4.1 Providence and the Dissolution of Contingency

The strongest opposing position holds that apparent contingency is contingency only with respect to human ignorance. Calvin (1960) states it without softening: fortune and chance are terms whose meaning ought not to occupy pious minds, and there is no place left in human affairs for fortune and chance. The perspectival move follows immediately: however all things may be ordained by God’s plan according to a sure dispensation, for us they are fortuitous. The branch that falls and kills a passing traveller was foreseen and decreed. Applied to serendipity, this yields a complete and internally consistent account in which the encounter is arranged, the meaning is authored in advance, and the observer’s sagacity consists in recognition.

The Ash’arite occasionalism of al-Ghazālī (1997) reaches a structurally identical result by a different route. The connection between what is habitually taken for a cause and what is taken for an effect is not necessary; fire does not burn cotton; God is the direct agent of every event, and creation is continuously renewed. Where every event is a direct divine act, chance has no purchase and the question of where meaning arises is settled before it is asked. The interpretive literature divides on how thoroughgoing al-Ghazālī’s occasionalism is, with some readings preserving a non-necessitating secondary causality, and the division should be respected in any use made of him.

These positions cannot be met by evidence, since they are consistent with every observation. They can be met by a distinction. Causal determination and meaning-generation are separable operations, and a demonstration that an encounter was caused by a comprehensive agency leaves open where the meaning of that encounter arose for the observer who underwent it. The account developed here concerns the second question and is compatible with a range of answers to the first.

4.2 Contingency Preserved within Providence

A middle family preserves genuine contingency alongside comprehensive divine action, and its resources are more useful. Aquinas (1947) holds at Summa Theologiae I q.22 a.4 that divine providence imposes no necessity that would destroy contingency, having prepared necessary causes for some things and contingent causes for others; what happens by contingency is what the plan conceives to happen by contingency. The mechanism at q.116 and in Summa contra Gentiles III.74 is the concourse of causes: chance is real relative to particular causal orders, since independent chains meet and produce effects intended by neither.

That mechanism is worth extracting from its theological setting. Aquinas locates chance relationally, at the meeting of orders that do not include one another, which is structurally what the present account does with encounter. Boethius supplies the same structure in the register of consolation, with Fortuna as the appearance under which providence is misread. Maimonides (1904) contributes a claim of a different and more directly useful kind: providence reaches each individual in proportion to intellectual perfection. Whatever its theological standing, the form of the claim is the configuration thesis. What can arrive is graded by what the recipient has become able to receive.

4.3 Relational and Emergentist Theologies

Process theology supplies the strongest strictly theological ally. Whitehead (1978) composes reality of actual occasions that prehend their inherited world and reach determination through concrescence, with creativity holding the position of the ultimate. Cobb and Griffin (1976) draw the theological consequence: divine action is persuasive, offering an initial aim that each occasion freely actualizes, and the integration is the occasion’s own. Value arises in the self-creative synthesis of relational data. The metaphysical shape is close enough to Generative Relational Being that the affinity should be stated plainly, together with the divergence: the process account embeds generation in a panexperientialist cosmology of occasions, a commitment the present framework does not require.

Buber (1958) is the closest religious-philosophical precursor to a relational ontology of encounter, and the closeness is verbal as well as structural. In the beginning is the relation. All real living is meeting. Spirit resides between I and Thou. The passage that bears on sagacity is the one on how the Thou arrives: it meets me through grace, and is not found by seeking; every means is an obstacle, and only where means have collapsed does the meeting come about. Buber thus states the paradox this paper works on. The encounter cannot be produced by will, and readiness for it can be cultivated. His resolution, that readiness is a discipline of availability, is the resolution adopted in §7 in secular terms.

Marion (2002) supplies the phenomenological development. A saturated phenomenon gives more intuition than the concept can organize and than the intention can foresee; it arrives unforeseeably and reverses the direction of the gaze, constituting its recipient. Gschwandtner (2014) presses the correction that matters here: phenomena appear within a hermeneutic space already opened by a recipient’s active reception, so that what appears depends on givenness and on interpretation together. That correction is the present thesis arrived at from within religious phenomenology, and it is offered here as convergent support.

4.4 Preparation as a Discipline

Several traditions have developed technologies of preparation, and these bear on the practical side of the argument.

Weil (1951) gives the most exact Western description of maintained openness. Attention consists in holding thought empty, waiting, seeking nothing, and ready to receive in its naked truth the object that is to penetrate it. She distinguishes attention sharply from will, and treats the correction of faults as a work of attention that will cannot perform. The description matches the capacity defined in §7 closely enough that Weil should be regarded as its principal Western precursor. Ignatian discernment, with its examination and its reading of consolation and desolation, supplies the same capacity in the form of a trainable daily practice. Eckhart’s Gelassenheit and the apophatic literature supply its negative pole, the emptying that precedes reception.

Augustine (1961) furnishes the tradition’s paradigm case, and it repays reading as a case, with its doctrinal setting held aside. In a Milan garden in 386, in acute and prolonged crisis, Augustine hears a child’s voice next door chanting a phrase from a game, takes it for an instruction, opens Paul at random, and reads two verses that end the crisis. Every element of the structure is present. The stimulus is contingent, ambiguous, and trivial in itself. The configuration is a sustained and unresolved question held under pressure for years. The generation is immediate and total. A differently configured hearer in the same street hears children playing.

4.5 Non-Closure as a Practice

The tradition that comes nearest to naming the paper’s central claim about sagacity is Zen, and the proximity is close enough to require acknowledgement.

Kōan practice is the deliberate maintenance of an unresolved question. The tradition names the state 大疑 (daigi, great doubt), and Hakuin’s formula makes its function explicit: beneath great doubt lies great awakening; doubt fully and awaken fully; little doubt yields little awakening, and no doubt yields none. The resolution characteristically arrives through an ordinary contingent event. Xiangyan Zhixian, a scriptural scholar who had made no progress, burned his books and withdrew to sweep a path; a pebble thrown up by the broom struck a stalk of bamboo, and the sound resolved what years of study had not. Lingyun Zhiqin, after decades of search, saw peach blossoms across a valley and reported that from that moment he never doubted again.

The structure is the paper’s structure. A relation is held unresolved under sustained pressure; an ordinary contingent phenomenon arrives; generation follows immediately and is not reversible. What Zen supplies beyond the structure is the claim that the maintenance is trainable, that its difficulty is the point, and that premature resolution by the master would destroy the process. The differences deserve equal statement. The kōan is administered, so the tension is induced by a teacher and not carried by the practitioner’s own research question; and the tradition treats what is generated as the disclosure of something always present, which is a latency model and diverges from a generation model at that point.

The same latency qualification applies to two further resources. The Lurianic and Hasidic doctrine of sparks holds that every object contains holy sparks awaiting release by a prepared encounter with the ordinary, which is a powerful image of preparation and an account in which meaning pre-exists in the object. Tathāgatagarbha holds that awakening is intrinsic and uncovered. Both are allies on preparation and diverge on generation, and the distinction should be kept sharp, since a critic will otherwise collapse the present account into a latency model.

4.6 Relational Ontologies of the Encounter

The Buddhist and East Asian traditions supply the deepest ontological precursors.

Pratītyasamutpāda, 縁起 (engi, dependent arising), holds that phenomena arise in dependence on conditions and possess no independent self-nature. Nāgārjuna (1995) at Mūlamadhyamakakārikā 24:18 identifies dependent arising with emptiness and with dependent designation, yielding a position in which entities exist only relationally. This is the semantic thesis of the present paper stated as a general ontology, and it is the oldest and most rigorous version available. The Huayan development, with the mutual containment of Indra’s net and the non-obstruction of phenomenon by phenomenon, extends it to a totality in which each locus is constituted by its relations to all others.

The East Asian term 縁 (en in Japanese, yuan in Chinese, connection or affinity) lexicalizes the meaningful contingent encounter as a relational category. An encounter that would be described in European languages as chance is described here as a connection: one has 縁 (connection) with a person, a place, or a work. The category is neither necessity nor randomness, and it names precisely the phenomenon this paper analyses. That a major linguistic tradition has a common word for it, and that European languages must reach for a coinage from a Persian fairy tale, is itself worth recording.

The tea ceremony’s 一期一会 (ichigo ichie, one time, one meeting) supplies the practical doctrine. The formulation runs from Sen no Rikyū through Ii Naosuke’s Chanoyu Ichie Shū: however often host and guests may meet, one day’s gathering cannot be repeated, and both parties must therefore participate with complete sincerity and complete preparation. The ceremony is a technology of preparation for a singular unrepeatable encounter, and its emphasis falls on the shared occasion between people. Ibn ʿArabī’s principle that there is no repetition in divine self-disclosure gives the same singularity a metaphysical form, with each moment a distinct theophany and each being the disclosure of a configuration of names occurring once.

4.7 Contingency and Interpretation in Chinese Thought

Two further resources deserve separate statement.

The Huainanzi parable of the frontier man whose horse ran away is the classical statement of interpretive non-closure. The horse is lost, and the neighbours condole; it returns with fine horses, and they congratulate; the son is crippled riding one, and they condole; the conscription comes and the crippled son is spared. Each judgement is overturned by what follows, and the refrain asks how one could know that the present appearance is the case. The lesson bears directly on §5: to close at a settled evaluation is to fix a meaning that the relation had not finished generating.

Divination supplies the other. The Yijing produces a configuration by a chance procedure and yields meaning only through a prepared interpretive apparatus and a cultivated judgement. Zhu Xi’s account, that the text’s meaning emerges for each person through the process of divination and cannot be captured by a single commentator, is an explicitly emergentist hermeneutic. The associated concept 幾 (ji, the incipient) names the barely-perceptible first stirring of change and the capacity that detects it. Comparable systems appear across cultures, from the Yoruba Ifá corpus to the Latin sortes, and Augustine’s opening of Paul belongs to the same family. What the family demonstrates is that meaning-from-contingency has been engineered for millennia by combining a randomizing procedure with a prepared interpreter, which is the present account’s structure built as a practice.

4.8 Synchronicity and Its Limits

Jung (1973) proposed synchronicity as an acausal connecting principle, the meaningful coincidence of events where something other than the probability of chance is involved, developing the idea in conversation with Pauli and applying it in his foreword to the Wilhelm I Ching. The scarab episode is its best-known illustration.

The proposal must be addressed because it is the modern theory of meaningful coincidence and occupies adjacent ground. Two features separate it from the present account. Jung posits an acausal principle in the world that pairs the events, which is a metaphysical addition; and the criterion of a genuine synchronicity, in practice, is the felt meaningfulness of the pairing, which supplies no way of distinguishing the phenomenon from apophenia. The relational account requires no such principle and explains the same data by the structure of the encounter, which recommends it on grounds of economy. Where Jung locates meaningfulness in a correspondence between world and psyche, the present account locates it in what a configured cognition and a contingent phenomenon generate at their coupling.

4.9 The Position Inherited from the Traditions

Three results are carried forward. The providential family shows what a fully object-side account looks like and where it must be met, namely at the distinction between causation and meaning-generation. The disciplines of preparation, in Weil, in Ignatian practice, and above all in the Zen literature on great doubt, establish that maintained non-closure is a real, describable, and trainable capacity with a long practical history. And the relational ontologies of the encounter, in Madhyamaka, in Huayan, in 縁 (connection), and in Buber, establish that the priority of relation over relata is a position with substantial development behind it. The remainder of the paper works within that inheritance.

§5 The Configuration of the Encounter

The surveys establish the terrain. The constructive argument begins with the datum the whole literature agrees on and no account has fully exploited: two observers, one phenomenon, two outcomes.

5.1 The Two Observers

Return to the crystal. Two people, one specimen, one interval of attention. The first arrives at an appreciative judgement and departs. The second arrives at a question about how coherent particulars might compose a whole while retaining their difference, and departs with the beginning of an account of plurality in a shared political order.

The explanations available divide as the literatures do. The observer-side explanation says the second observer knew more. This is true and insufficient: the second observer’s prior knowledge contained crystallography and contained an interest in political plurality, and contained no connection between them, which is the thing that arrived. The object-side explanation says the crystal contains the structure that was read off it. This is true and insufficient in the same way: the grain-boundary structure is a fact about minerals and contains nothing about languages. The community-side explanation says that what makes the episode a discovery is a later judgement by competent others. This is true about validation and silent about the event.

What is required is an account in which the phenomenon’s structure and the observer’s configuration both participate and neither suffices. The vocabulary for such an account is available in the framework this paper works within, where generation is a property of relations and relata contribute the terms of a coupling without containing its product.

5.2 The Concept of Configuration

The observer’s contribution is described here by the term configuration: the determinate arrangement of questions, tools, commitments, and unresolved difficulties that a person carries into an encounter. Three features of the term are load-bearing.

Configuration is structured, and its structure matters. A configuration containing crystallography and political plurality without a connection between them differs from one containing either alone, and differs again from one in which the connection is already made. What can be generated depends on which relations are present and which are open.

Configuration operates differently from a stock. A quantity of knowledge, held in a resolved state, is a poor configuration for encounter, since resolved knowledge has no open valence to which a phenomenon can couple. This is the substance of the observation that expertise and receptivity can vary independently, and it is developed in §7.

Configuration is historical and slow. It is constituted by what a person has studied, worked on, failed at, and continued to worry about, over years. It cannot be assumed for an occasion, which is the sense in which serendipity resists planning.

5.3 The Aesthetic Terminus

The first observer’s response repays close attention, because it is where the standard accounts have least to say and where the present account earns its keep.

Nothing was defective in that response. The observer looked, attended, and was moved. The judgement was accurate: the crystal is beautiful. On any observer-side account the episode is simply a case of insufficient preparation, and on any object-side account it is a case of a signal that failed to find a receiver. Both descriptions miss what is distinctive. The response was complete. It arrived at a terminus and rested there, and the resting is the operative fact.

An appreciative judgement is a closure operation. It takes a phenomenon, assigns it to a category, and discharges the encounter. The category is a good one and the assignment is correct, and the discharge is what forecloses. Once the crystal has been classified as beautiful, the encounter has been completed, and a completed encounter generates nothing further. The phenomenon remains available in principle; the relation has been closed.

This is the sense in which the episode is a non-encounter. The contingency arrived, the observer was present and attentive, and no relation was sustained long enough for anything to be generated across it. Accident occurred without sagacity in the reconstructed sense, and what was missing was duration, not information.

Claim 1 (Differential generation and the aesthetic terminus). Two observers meeting one phenomenon generate differently in virtue of their configurations, and the differential is a fact about the relation each forms with the phenomenon. An encounter terminating in a settled judgement is a non-encounter: contingency arrives, closure is immediate, and generation does not follow. Closure, and not ignorance, is the general failure condition of serendipity.

The aesthetic case is the limiting instance of a wider family. Any settled response performs the same operation. The phenomenon is filed under an available category, and the filing discharges it. This is what makes the family diagnostically useful: the failure is visible in the speed and finality of the response, and is independent of how much the observer knows.

§6 The Generation of Meaning at the Relation

The account can be brought to a definition, and it is useful to set that definition beside the one the tradition has bequeathed. The two are given here in the order of their standing, the received formulation first.

Definition 1 (Received definition of serendipity). 有准备的心智在偶然性中辨认出了意义。 Serendipity is meaning discerned in contingency by a prepared mind.

This formulation is exact about the two factors and carries the whole weight of the account in one verb. 辨认 (biànrèn, to discern or make out) takes an object already present and brings it into view, so that the meaning waits in the contingency and preparation is what permits its retrieval. The definition offered here turns on that verb and on the locus it presupposes.

Definition 2 (Initial definition of serendipity in Generative Relational Being). Serendipity 是关系生成的偶然性被转化为延续系统生成过程的可能的过程。 The contingency generated by relations is transformed into the possibility of continuing the system’s generative process.

Three elements of the definition carry the argument, and each is developed in what follows. The contingency is generated by relations, which places it inside the field and removes the standing of a brute externality arriving from outside. The transformation is generative, which distinguishes it from discernment and from the retrieval of something waiting. And the product is a possibility of continuation, which locates the yield of a serendipitous event in what the system becomes able to generate thereafter, beyond the particular meaning that arrived.

The central claim can now be stated in its own terms and its consequences drawn.

6.1 The Structure of the Event

A serendipitous event has three moments and one product. A configured cognition carries a set of relations, some of which are open. A contingent phenomenon arrives, unscheduled with respect to those relations. A coupling occurs in which some structural feature of the phenomenon enters into relation with some open relation in the configuration. What is generated is a third term present in neither.

Each element does real work. The contingency of the arrival distinguishes serendipity from ordinary inquiry, in which the phenomenon is sought. The structure of the phenomenon distinguishes the account from projection, since the crystal’s grain boundaries participate in what was generated and a differently structured mineral would have generated differently or not at all. The openness of the relation distinguishes the account from disclosure, since a closed configuration meets the same phenomenon and generates nothing. And the thirdness of the product distinguishes the account from both latency models and retrieval models: the polycrystalline theory of plurality was not stored in the observer, and was not written in the mineral.

Claim 2 (The generated third term). The meaning generated in a serendipitous encounter arises at the coupling of a configured cognition with a contingent phenomenon and is held in advance by neither. The phenomenon supplies structure; the configuration supplies an open relation to which that structure can couple; the generated meaning is a third term whose content is determined by the pairing and by neither party alone.

6.2 Information and Meaning

The distinction that makes the claim precise is one the information sciences established for their own purposes and left undeveloped philosophically.

Shannon (1948) opens by setting semantics aside: the semantic aspects of communication are irrelevant to the engineering problem. Information in the resulting theory is a measure over a distribution, defined without reference to what anything is about, and the theory’s power derives from the exclusion. What follows is a clean statement of what a transmission model can and cannot deliver. A channel conveys a quantity from a sender to a receiver, and the quantity is conserved across the transfer.

Bateson (1972) reintroduces the receiver: information is a difference that makes a difference, which makes it relative to a system for which the difference registers. Luhmann (1995) develops the systems form, in which perturbations become information only where they make a difference for the meaning-processing of a system. Peirce’s triadic semiotics supplies the general statement, in which signification requires sign, object, and interpretant together, so that no dyad suffices.

Applied to the encounter, the distinction is exact. The crystal carries information in the engineering sense, and carries the same information for both observers, since the photons reaching two retinas do not differ in any relevant respect. Meaning is what one of the two relations generated. The transmission picture, in which something is sent from phenomenon to observer, describes the information and misdescribes the meaning: nothing about plurality in a political order was transmitted, because nothing about it was present at the source.

Claim 3 (Information conserved, meaning generated). Information is conserved across transmission and is a property of a signal relative to a distribution. Meaning is generated at a relation and is a property of neither relatum. A phenomenon may therefore carry identical information to two observers and participate in the generation of meaning with one, which is the general form of the two-observer datum.

6.3 Standing with Respect to the Neighbouring Ontologies

Three positions hold that relata do not precede their relations, and the account’s standing with respect to them should be fixed.

Barad (2007) holds that relata emerge through intra-action within a phenomenon and that there are no independent relata, only relata-within-relations. Simondon (2020) holds that relation has the same rank of reality as its terms and that the individual is a phase of being presupposing a preindividual metastable field, with transduction propagating structure from place to place. Deleuze (2000) holds that thought begins in a violent encounter with a sign that compels it, so that truth is sought under a constraint and not by good will.

The overlap is substantial and should be conceded without hedging: the priority of relation over relata, in these authors, is prior art for the ontological thesis. The account here specifies that ontology to a case they do not treat and adds two elements they do not contain. The case is discovery under contingency, with its Walpolean constraint that the finding was not sought. The additions are the temporal reconstruction of sagacity in §7 and the diagnosis of closure in §5. Deleuze’s encounter is a sudden imposition by the sign, with the observer’s contribution passive; the account here makes the observer’s sustained maintenance of an open relation a condition of the coupling, which is a different structure with different practical consequences.

One question these authors press deserves a direct answer. If relata do not precede relations, what is the standing of the configured cognition that §5 treats as an antecedent term? The answer adopted here is that a configuration is itself the sediment of prior encounters and carries no independence beyond that history, while remaining sufficiently stable across the interval of a given encounter to be described as a term of it. The two descriptions operate at different timescales and are compatible.

§7 Sagacity and the Maintenance of Unresolved Relations

The reconstruction of sagacity is the paper’s principal claim and the point at which the two-part folk formula is replaced.

7.1 The Reconstruction

Sagacity, on the received reading, is a quality of mind: acuity, breadth, alertness, a stocked memory, the capacity to notice. The reading has the merit of matching the exemplars, since the figures in the standard cases were in fact acute and well stocked. Its difficulty is that these qualities are common and serendipity is rare, and that the same person exhibits them continuously while generating from a contingency perhaps a handful of times in a career.

The reconstruction proposed here makes sagacity temporal and specific.

Claim 4 (Sagacity and maintained non-closure). Sagacity is the capacity to maintain a relation in an unresolved state for the interval required for an unforeseen phenomenon to couple to it. Its measure is duration under pressure to close, and its failure mode is early termination in a settled response. It is a property of how a question is held over time and admits of cultivation, with the encounter it prepares for remaining unschedulable.

Three consequences follow immediately.

The first is that the Walpolean constraint is satisfied. Walpole excluded discoveries of what one was seeking. A maintained unresolved relation falls outside the category of search: it specifies no target, and it is precisely the absence of a specified target that leaves the relation available to a phenomenon from an unrelated domain. A researcher seeking a solution to a stated problem will accept only candidates of the stated type. A researcher holding the difficulty open, with the form of a solution undetermined, can be met by a mineral.

The second is that the capacity is costly and its cost explains its rarity. An unresolved relation is uncomfortable. It occupies attention, resists summary, and produces nothing while it is held. Every professional incentive rewards closure: publication requires results, teaching requires answers, and institutional evaluation counts settled outputs. Maintained non-closure is therefore expensive under exactly the conditions in which research is conducted, and its scarcity is a structural fact about those conditions.

The third is that expertise and sagacity are independent. Expertise is organized, closed knowledge, and its value derives from the closure: an expert answers quickly and correctly because the relevant relations are resolved. A configuration of resolved relations offers few valences for an unforeseen phenomenon to couple to. This yields a testable expectation about where serendipity concentrates, examined in §10.

7.2 Failure Modes

Three ways of failing to maintain a relation can be distinguished, and they call for different remedies.

Premature resolution closes the relation by accepting an available answer. The answer may be adequate; adequacy is what makes the failure hard to see. Camus’s charge against the Kierkegaardian leap has this form, and so does the ordinary research pathology of settling on the first workable hypothesis.

Aesthetic termination closes the relation by discharging the phenomenon into a settled category. The crystal case is its type. The category is correct and the discharge is complete, and the response feels like engagement while performing closure.

Abandonment closes the relation by dropping it. The question is set aside as intractable or unprofitable, and the configuration loses the valence. This is the failure most encouraged by institutional pressure, since the abandoned question leaves no trace to be accounted for.

7.3 The Precedents for the Capacity

The capacity has a longer practical history than theoretical one, and three precedents establish that it is real and trainable.

Zen kōan practice, as §4 sets out, is the deliberate induction and maintenance of an unresolved question under sustained pressure, with the tradition holding explicitly that the depth of the eventual generation is proportional to the depth of the doubt maintained. The trigger is characteristically trivial and always contingent.

Weil’s attention describes the same capacity in the register of receptivity: thought held empty and waiting, seeking nothing, ready to receive the object that is to penetrate it, and distinguished from will, which cannot perform the operation.

Keats’s negative capability, formulated in a letter of December 1817, names the condition of remaining in uncertainties, mysteries, and doubts without irritable reaching after fact and reason. The formulation is aesthetic in origin and structurally identical in content, and it supplies the term’s clearest English statement.

That three traditions with no contact between them converged on the same capacity is evidence that the capacity is a real feature of cognition. What the present account adds is its function: the maintained relation is the valence by which a contingent phenomenon can couple, and the capacity is therefore a condition of generation, beyond its standing as a discipline of character.

7.4 The Second Condition

Maintenance is necessary and insufficient. A relation may be held open for years while the phenomenon that would couple to it is routinely encountered and routinely filed elsewhere. This is the condition treated in the next section, and the two together are what the central claim asserts to be jointly necessary.

§8 Relational Crystallization and the Foreclosure of Encounter

The account so far concerns an individual encounter. Its extension to the architecture of knowledge follows from a single observation: the categories that sort phenomena determine which encounters can occur.

8.1 Local Coherence

A discipline is a relational crystallization. Within it, methods, standards, vocabularies, and exemplars are mutually adjusted, and the adjustment is what allows work to proceed: a shared vocabulary permits argument, shared standards permit assessment, shared exemplars permit training. This local coherence is productive and is the condition of competence.

The metallurgical figure is apt in more than name. A polycrystalline solid derives its strength from its grain boundaries, which impede the propagation of dislocations; the Hall–Petch relation makes yield strength increase as grain size falls, so that a material of many small coherent domains outperforms one large uniform crystal. Local coherence with structured boundaries produces properties that homogeneity does not. Applied to knowledge, the figure recommends disciplines and recommends their multiplicity.

8.2 The Ontologization of a Boundary

The failure begins at a determinate point. A boundary that organizes work is taken for a boundary in the world, and local coherence is read as ontological independence. The discipline then holds that its objects are its own, that questions outside its remit concern other objects, and that the partition tracks a division among things.

The consequence for encounter is direct. A boundary of this kind sorts a phenomenon before an observer can meet it. The crystal is filed under crystallography, and filing is a closure operation of the kind §5 describes, performed by an institution and inherited by the individual. The observer who has internalized the partition meets the crystal already sorted, and the relation to a question about political plurality has been foreclosed before the encounter occurred. Foreclosure at the level of architecture and closure at the level of the individual response are the same operation at two scales.

Claim 5 (Local coherence and the ontologized boundary). Disciplinary boundaries are relational crystallizations whose local coherence is productive. Foreclosure begins where local coherence is taken for ontological independence, at which point the boundary sorts a phenomenon away from a question before the two can meet. The failure is the treatment of a working partition as a division among things.

8.3 The Existing Analysis and What Is Added

The sociology of science has established the constructed character of these boundaries. Gieryn (1983) analyses boundary-work as the rhetorical demarcation of science from non-science, undertaken for professional ends. Star and Griesemer (1989) identify boundary objects that are plastic enough to travel between social worlds and robust enough to maintain identity, permitting cooperation without consensus. Galison (1997) describes trading zones in which subcultures coordinate through local exchange languages while continuing to mean different things.

These accounts are descriptive and sociological, and they establish the premise. The extension offered here is a consequence about generation: a partition that is treated as ontological governs which encounters are available, so that the cost of disciplinary independence is paid in foregone couplings that no participant observes, since a foreclosed encounter leaves no record. This connects the sociological finding to the epistemological one and identifies what interdisciplinarity is for. Its value lies in the restoration of couplings that a partition had foreclosed, and this is a stronger and more specific rationale than the appeal to breadth that ordinarily supports it.

8.4 The Conjunction of the Individual and Structural Conditions

The two conditions can now be stated together. A configuration must carry live and unresolved relations, which is the individual condition of §7. And the architecture within which the observer works must leave the relevant boundaries permeable, which is the structural condition of this section. Either alone is insufficient. A scholar with maintained open questions, working within a partition that sorts every incoming phenomenon into a foreign compartment, generates nothing from contingency. A scholar in a permeable environment with no open questions files everything correctly and generates nothing either.

§9 The Dynamics of Absorption and Amplification

The terms of the account have an evident counterpart in the language of dynamical systems: an open relation, a perturbation, a threshold, and the conversion of a perturbation into a sustained state. This section develops that counterpart for a minimal model, with two aims. The first is to show that the two conditions of §8 can be carried by a single parameter. The second is to give the distinction between a wasted contingency and a converted one a determinate form, which in such a model is a threshold.

9.1 The Form of the Model

Let $x(t) \ge 0$ measure the generative activity sustained around an open relation within a relational system. Two tendencies act on it.

The first is closure. Left to itself an open relation resolves: the question receives an answer, the phenomenon is filed under an available category, the difficulty is set aside. A linear decay $-x$ represents this, returning the system to $x=0$, the state in which no relation is held open and every arriving contingency is absorbed without effect.

The second is the return of generation upon itself. What has been generated becomes available as a term for the next coupling, so that generation already underway makes further generation possible. This return saturates, since the capacity of a system to hold relations open is finite. A saturating autocatalytic term represents it, with $r>0$ collecting the strength of the return:

$$ \frac{dx}{dt} ;=; -x ;+; \frac{r,x^{2}}{1+x^{2}}. \tag{1} $$

The parameter $r$ carries the two conditions that §8 found jointly necessary. It rises with maintained non-closure on the side of the configuration and with permeability on the side of the architecture, and it falls as either declines. A system whose questions resolve quickly, and a system whose boundaries sort each arriving phenomenon into a foreign compartment, both have low $r$ whatever their stock of knowledge, which is the formal counterpart of the independence of expertise from receptivity claimed in §7.

9.2 Regimes and the Critical Value

The origin $x=0$ is a fixed point for every $r$, and it is stable throughout, since the linearization there gives $-1$. The remaining fixed points solve $x^{2}-rx+1=0$, so that

$$ x_{\pm} ;=; \frac{r \pm \sqrt{r^{2}-4}}{2}, \tag{2} $$

which is real for $r \ge 2$. The model therefore has a saddle-node bifurcation at $r_{c}=2$, where the two roots coincide at $x_{c}=1$. Figure 1 shows the resulting structure.

Figure 1. Fixed points of equation (1) against the coupling parameter. Solid branches are stable, the dashed branch unstable. Below $r_{c}=2$ the closed state is the sole attractor and every perturbation is absorbed. Above it a sustained state $x_{+}$ becomes available, reachable from perturbations exceeding the threshold $x_{-}$.

Three regimes follow, and each corresponds to a condition the earlier sections described in prose.

For $r<2$ the closed state is the only attractor. A contingency of any magnitude decays, and the system returns to the state in which nothing is held open. This is the regime of the aesthetic terminus of §5 and of the foreclosed architecture of §8, which the model renders as one condition seen twice.

At $r=2$ the sustained state appears at $x_{c}=1$, and the threshold appears with it.

For $r>2$ the system is bistable. A perturbation below $x_{-}$ decays and the contingency is wasted; a perturbation above $x_{-}$ is amplified and settles at $x_{+}$, where it persists without further input. The trajectory from a perturbation to $x_{+}$ is the process Definition 2 of §6 describes: a contingency generated within the field is transformed into the possibility of the system’s continued generation.

9.3 The Threshold of Sufficient Contingency

The threshold $x_{-}$ falls as $r$ rises, from $x_{-}=1$ at criticality toward zero for large $r$. A consequence follows that bears on the cases. The magnitude of contingency required to produce a conversion depends on the openness of the system receiving it, so that a system holding relations open under strong maintained non-closure can be moved by a contingency of very small magnitude, while the same contingency arriving at a system near criticality is absorbed and lost.

This yields a reading of a pattern the traditions record without explaining. In the accounts surveyed in §4, the trigger of a resolution reached after years of maintained doubt is characteristically trivial: a pebble against bamboo, blossoms across a valley, a phrase from a children’s game overheard through a wall. The triviality of the trigger and the depth of the maintained relation stand in the relation the model predicts.

Figure 2. Left: the response of equation (1) to a single perturbation of fixed amplitude $\varepsilon=0.70$ under four values of the coupling parameter. At $r=1.60$ no sustained state exists. At $r=2.05$ the sustained state exists and the threshold stands at $x_{-}=0.80$, so the same perturbation decays. At $r=2.20$ the threshold has fallen to $x_{-}\approx0.64$ and the perturbation is amplified, with the slow approach characteristic of a trajectory passing near a saddle-node. At $r=3.00$ the threshold stands at $x_{-}\approx0.38$ and the conversion is rapid. Right: the threshold amplitude against the coupling parameter, dividing perturbations that are converted from those that are wasted.

Figure 2 displays both features. In the left panel one perturbation of fixed amplitude meets four systems and has three fates, which is the two-observer datum of §5 generalized: the difference lies wholly in the receiving configuration. The case at $r=2.05$ deserves particular note, since there the sustained state exists and remains unreachable from a perturbation of this magnitude. A system may therefore possess the capacity for conversion and waste a given contingency for want of sufficient magnitude, which distinguishes the failure of §8, where no coupling is available at all, from a failure of degree.

The trajectory at $r=2.20$ shows the protracted approach characteristic of motion near a saddle-node. A conversion occurring close to the critical value takes long to consolidate and remains vulnerable throughout, since a further disturbance during the passage can return the system to the closed state. This offers a formal counterpart to the observation that an insight arriving in a barely-open configuration is easily lost.

9.4 The Standing of the Illustration

The model earns its place by the structure it exhibits, and its adequacy rests on three correspondences: between the decay term and closure, between the saturating autocatalytic term and the return of generation upon itself, and between the coupling parameter and the joint condition of maintained non-closure with permeability. Each is a claim about what the prose account describes, and each is available for objection independently of the others.

What would raise the illustration to a model in the working sense is stated here for the record. It requires an operational measure of $r$ in a research setting, which §12 identifies as the principal open problem; an independent identification of $x$ with something observable in a configuration, for which the count of maintained unresolved problems is the obvious first candidate; and a treatment of systems holding several open relations at once, where equation (1) becomes a coupled system and the couplings between open relations become the objects of interest. The reflexive case identified in §10, where the generated meaning alters the phenomenon, would enter such a treatment as feedback from $x$ to the perturbation itself.

§10 Case Constructions across Domains

Seven cases follow, drawn from six domains and constructed to bear on distinct elements of the account. Three are paired with a negative counterpart in the same domain, since the account’s diagnostic content lies in the failures as much as in the successes. All are drawn from the published record and are developed for illustration.

10.1 Materials Science and Political Plurality

The crystal case can now be given its structure. The configuration carries an unresolved question about whether a political order can hold a plurality of coherent linguistic worlds together without reducing them to a common medium, a question that resists resolution because the available answers appear to require either a shared language, which flattens, or an accepted fragmentation, which dissolves the order.

The phenomenon has a determinate structure. A polycrystalline solid consists of domains each internally ordered, differing in orientation, meeting at grain boundaries that neither dissolve the domains into one another nor separate them. The Hall–Petch relation establishes that the boundaries contribute to the strength of the whole. Nucleation and growth proceed by local rules, with no global template.

The coupling generates a third term: an order composed of internally coherent domains whose integrity is maintained by their boundaries, with the boundaries functioning as sites of relation, and with the strength of the whole arising from the structured heterogeneity. This is neither a fact about minerals nor a prior political position, and its transposition into the theory of multilingual plurality raises questions of its own about what corresponds to orientation and to dislocation. The case illustrates the thirdness of the product and the participation of the phenomenon’s structure.

10.2 Cosmology and the Interpretation of Noise

The case of the cosmic microwave background is the clearest instance in the modern record of one signal meeting two configurations.

In 1964 Penzias and Wilson, working with the Holmdel horn antenna at Bell Laboratories, measured an excess antenna temperature at 4080 Mc/s of approximately 3.5 K that they could not eliminate. Their configuration was that of radio engineers with an instrumental problem, and within it the signal was a residual to be accounted for. At Princeton, Dicke, Peebles, Roll, and Wilkinson carried an unresolved theoretical question about the thermal residue of an early hot universe, and were building an instrument to look for it. The two papers appeared together in Astrophysical Journal 142 in 1965, the measurement and its interpretation (Penzias and Wilson 1965; Dicke et al. 1965).

The case is instructive in three respects. The same information was available to both parties, and only one relation generated a cosmological meaning, which is the two-observer datum in its purest form. The Princeton configuration was open in the required sense: a question was being carried without a determined answer. And the generation occurred at a coupling across a boundary between radio engineering and theoretical cosmology, which illustrates §8 from the permeable side.

10.3 Intelligence Analysis, Positive and Negative

Two episodes in the same domain form a matched pair.

In October 1962, photographic imagery returned by a U-2 overflight of western Cuba was interpreted at the National Photographic Interpretation Center as showing a Soviet medium-range ballistic missile installation under construction. The imagery is a field with vehicles and cleared ground. Its interpretation required a configuration containing the signatures of Soviet missile-site layouts, held by analysts trained for exactly that recognition. The information in the photograph was available to anyone with the photograph; the meaning arose at a specific relation.

The negative counterpart is the finding of the 9/11 Commission that the relevant information was distributed across agencies and that the failure lay in the connection. The Commission’s characterization of a failure of imagination is precise on the present account. The information was present, the analysts were competent, and the architecture partitioned the material so that a phenomenon arriving in one compartment could not couple to a question held in another. This is foreclosure by architecture in its consequential form, and it illustrates why the cost of a partition treated as real is paid invisibly.

10.4 Decipherment

The Rosetta Stone was recovered in 1799 and remained substantially mute for two decades. The object’s information content did not change across that interval. What changed was the arrival of a configuration in which the Greek text, a knowledge of Coptic, and a hypothesis about the phonetic function of the cartouches were held together with the question unresolved, at which point the stone participated in the generation of a decipherment. The case isolates the temporal structure: the phenomenon waited, and the encounter occurred when a configuration capable of coupling to it existed.

10.5 Economic Interpretation

An inversion of the yield curve is a single quantity available simultaneously to every participant in a market. It is read by one party as a recession signal warranting a defensive reallocation, by another as a distortion produced by central-bank holdings and therefore uninformative, and by a third as a repricing opportunity. The three readings are generated at three relations to one signal, and the participants are equally informed in the transmission sense.

The economic case adds a feature the others lack. The generated meanings are acted upon, and the actions alter the phenomenon. This is a reflexive structure in which the relation feeds back into its own object, and it marks a limit of the account as presently stated, which treats the phenomenon as stable across the encounter.

10.6 Ordinary Relation

A remark made in passing over dinner is received by one hearer as small talk and by another, who has been carrying an unresolved difficulty about a decision, as the thing that resolves it. The speaker intended neither and often learns of the second reception later or never.

The domestic case is included because the account should hold outside organized inquiry, and because it displays the two conditions with unusual clarity. The hearer who generates was carrying a live question; the hearer who did not was not. Neither hearer was more intelligent, and the remark carried identical information to both. The case also displays the failure of the attribution model: what was generated cannot be credited to the speaker, who supplied a phenomenon and no meaning, and cannot be credited to the hearer alone, who supplied a question and no answer.

10.7 Cross-Domain Transfer

The final case concerns encounters between a configuration and a whole domain.

Eglash’s trajectory runs from a training in cybernetics and systems engineering into ethnomathematics, producing an analysis of recursive and fractal structure in African design and settlement patterns, and subsequently the concept of generative justice, an account of value that circulates in unalienated forms at its point of production. The pattern is the paper’s structure at the scale of a career. A configuration formed in one domain met the objects of another, and generated an account that neither domain contained: the mathematics did not contain the design tradition, and the design tradition had not been described in those terms. The prior training operated as the condition of the difference, and the encounter required a permeable boundary between a physical science and an ethnographic subject matter.

Comparable transfers are numerous. Schrödinger’s treatment of the aperiodic crystal carried a physicist’s configuration into the question of heredity and participated in the formation of molecular biology. Cybernetics entered the social sciences through the Macy conferences. Statistical mechanics entered finance. In each the generated account was in neither the exporting configuration nor the receiving domain.

The cases can be summarized by their common structure.

Setting	Configuration carried	Contingent phenomenon	Generated term
Materials and plurality	Unresolved question on coherence within plurality	Grain-boundary structure of a polycrystal	Order composed of bounded coherent domains
Cosmology	Thermal residue of an early hot universe	Irreducible excess antenna temperature	Observational confirmation of a cosmological model
Imagery analysis	Signatures of missile-site construction	Cleared ground and vehicle placement	Assessment of strategic deployment
Decipherment	Coptic, a Greek parallel, a phonetic hypothesis	A trilingual inscription	A working decipherment of a script
Market signal	Position, horizon, and model of the instrument	Inversion of a yield curve	Divergent readings acted upon
Ordinary relation	A carried and unresolved personal difficulty	A remark made in passing	A resolution credited to neither party
Cross-domain transfer	Cybernetic and recursive formalism	An unfamiliar design tradition	An account contained in neither domain

§11 Serendipity in the Conduct of Inquiry

Three consequences follow for how inquiry is conducted and organized.

11.1 The Standing of the Phenomenon

Serendipity has been treated in the literature on research policy as a marginal occurrence, valuable and unmanageable, to be accommodated at the edges of directed programmes. The account developed here places it differently. If meaning is generated relationally, and if a research programme consists in maintaining questions and encountering phenomena, then serendipity is the ordinary form of the arrival of new meaning and directed search is the special case in which the target has been specified in advance. The specification is efficient where the answer is of a known kind. Where it is not, the specification excludes in advance the couplings that would supply it.

11.2 Cultivation without Planning

The two conditions are both amenable to deliberate action, and neither amounts to planning an encounter.

On the individual side, the maintained open question is the unit to be protected. This has practical content. A researcher can keep a written record of unresolved difficulties and revisit it, decline to resolve a question by the first adequate answer, and treat the discomfort of an open problem as a working state. The cost identified in §7 indicates where the pressure will come from, and an institution that counts only settled outputs is applying that pressure continuously.

On the structural side, permeability is the property to be maintained. Its practical content includes exposure to material outside one’s partition without a requirement that the exposure be justified in advance by an expected yield, since a yield that could be specified in advance would fall under directed search. Galison’s trading zones and the boundary objects of Star and Griesemer describe arrangements in which such exposure occurs, and the account here supplies the reason to value them.

11.3 The Discipline of Non-Closure

The third consequence concerns intellectual conduct. The failure modes of §7 are all forms of closing early, and each has a respectable appearance. Premature resolution appears as decisiveness, aesthetic termination as appreciation, and abandonment as realism. A discipline of non-closure therefore requires the capacity to recognize a closure operation while performing it, which is what the traditions surveyed in §4 train and what the vocabulary offered here is intended to make available in secular terms.

§12 Limits and Further Work

12.1 The Standing of the Central Claim

The account rests on a claim about where meaning arises, and the claim admits of no direct observation. What can be observed is the differential: two configurations, one phenomenon, two outcomes. That differential is compatible with the account developed here and with a sufficiently elaborate observer-side account in which the generated meaning was latent in the configuration and released by any adequate trigger. The consideration that favours the relational reading is the participation of the phenomenon’s specific structure, since the polycrystalline account of plurality carries the grain boundary and the orientation with it and would not have been generated by an arbitrary trigger. This consideration is a matter of degree, and a latency theorist may hold that the structure supplied detail to a form already present. The dispute is real and is left open.

12.2 Points of Exposure

Four points are exposed.

The relation to Barad and Simondon requires more than the compatibility argument offered in §6. If relata are constituted within relations, the description of a configuration as an antecedent term needs a fuller account of the timescales at which each description holds.

The reflexive case identified in §10 lies outside the account as stated. Where the generated meaning is acted upon and alters the phenomenon, the encounter has a dynamics the present treatment does not supply.

The criterion of closure has been characterized and not operationalized. An account that can distinguish a maintained open relation from an abandoned one only after the fact is a description of cases and not yet an instrument for assessing them.

The Zen material raises a question the paper has acknowledged and not settled. If the kōan tradition holds that what arrives was always present, and if the account here holds that it is generated, then either the traditions describe different phenomena or one description is mistaken, and the cases do not decide between them.

12.3 Further Work

Three lines follow.

The first continues the formal treatment begun in §9. The illustration there carries a single open relation and a single scalar parameter, and the questions that matter lie beyond both: a configuration holding several open relations at once, the couplings among them, and the conditions under which activity at one relation raises or lowers the threshold at another. The reflexive case, in which the generated meaning alters the phenomenon, enters at the same point.

The second is empirical. The expectation stated in §7, that serendipity concentrates where configurations carry unresolved relations and where boundaries are permeable, is amenable to study in settings where research trajectories are documented. Careers that cross domains, and laboratories with recorded histories of abandoned and revived problems, are the tractable cases.

The third concerns the relation between this paper and the governance programme it belongs to. If foreclosure is a structural property of how knowledge is partitioned, then the design of institutions that maintain permeability is a governance question, and the criterion by which such designs would be assessed has not been supplied.

---

A note on the treatment of the traditions. The surveys in §2 through §4 range across literatures in which the present author holds no specialist standing, and they are offered at the level of structural comparison. Where a tradition has been characterized by a single doctrine, specialists will find the characterization thin, and in three places the internal disputes have been flagged in passing: the extent of al-Ghazālī’s occasionalism, whether Nāgārjuna advances a positive thesis, and the standing of the interpretation objection to Hanson. The comparisons are drawn to locate the account, and corrections that would relocate it are welcome.

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中文

摘要

机缘（serendipity）通常被分析为两个独立量的总和，一个偶然事件与一个有准备的心智，追随沃波尔对意外与睿识的配对。三个发达的传统精炼那个分析。第一个把那个决定性因素定位在观察者中，把准备当作某些个体在更高程度上拥有的一个认知性质。第二个把它定位在那个对象中或在把那个对象置于那里的那个秩序中，那是那个问题在天意诸学说之下并在强决定论之下所采取的形式。第三个，在近来的科学哲学中，把它定位在那个科学共同体中并在价值的回溯承认中。本文发展一个第四种说明。一次相遇是一个被配置的认知与一个偶然现象之间的关系，而在一个机缘事件中生起的意义在那个关系处被生成，两个关系项都不事先持有它。睿识相应地被重构为把一个关系持于未决、达一个不可预见现象耦合到它所要求之间隔的能力，一个持续非闭合的能力，其失败模式是在一个安定回应中的早期终止。终止于一个鉴赏判断的相遇作为那个极限情形被审查，在其中偶然到来而生成不随之而来。那个说明被延伸到探究的结构：诸学科被当作关系结晶，其局部相干是生产性的，而其对相遇的封锁始于局部相干被当作独立之处。诸案例在物理、宇宙学、情报分析、经济解释、国际实践与跨领域转移中被发展，连同对关于偶然性之存在主义、宗教与科学哲学诸文献的一次综述。

关键词： 机缘；偶然性；相遇；意义；关系本体论；准备；跨学科性；生成性关系存在。

关于本文站位的一则附记。 这是一个初步讨论。它占据一个本体论与一个治理纲领之间的位置：倘若存在是生成性与关系性的，那么随之而来的认识论必须说意义如何到来，而机缘是那个到来最可见的情形，因为那次相遇中没有任何东西被事先安排。阐述的次序追随那个论证的次序。既存诸说明被首先铺陈，跨三个鲜少被一起阅读的文献，而那个关系说明在它们共同承诺变得可见之点被引入。倘若那个现象被证明由观察者一侧的准备完全描述，那些中心诸节失去它们的地面。那些案例为例示被建构并从已发表的记录汲取；它们承载例示的分量。反对、改正与反证被欢迎至 huangwanhong@serendip.ngo。

§1 引论

两个人站在同一块晶体前。第一个看，发现它美，并走开。第二个看，而某样东西开启：局部的生长规则已产生一个通体有序而无处均匀的结构，其晶粒在把差异持在原处、而整体保有它完整之处的诸边界相遇。不到一小时这第二个观察者就在思考一个共享政治秩序中的诸语言，并思考一个诸相干世界的复数性能否被它们之间的诸关系持在一起。那块晶体是同一块晶体。它在同一个陈列柜中、同一道光下、达同一个间隔地坐着。无论发生了什么，都发生在那块矿物与看它的两人之一之间。

关于这个的寻常语汇是运气，而那个语汇的寻常精炼是运气偏爱有准备者。巴斯德 1854年里尔演说的那个公式已成为诸科学的安定智慧：在观察的场域中，机遇偏爱有准备的心智。霍勒斯·沃波尔一个世纪之前的那个杜撰有同样的两部分形态。1754年1月致 霍勒斯·曼恩 的信中，他以一个波斯故事的诸英雄命名一个凭意外与睿识作出发现、发现自己未在寻求之物的能力。那个配对已被证明持久，而它正确地命名那两个因素。那个配对留下开放的是它们之间的关系。意外与睿识被一个连词接合，而一个连词是那个可得的最弱连接词。它陈述两者都在场而就两者的在场如何产生了两者单独都不产生之物不说任何东西。

本文接手的问题关乎那个连接词。一次机缘相遇的意义在何处生起，而睿识必须是什么种类的东西才使那次相遇根本产出任何东西？

三个发达的立场回答那个问题，而它们按它们把那个意义置于何处而分开。

第一个把它置于那个观察者一侧。准备是一个心智的一个性质，跨诸个体不均地分布，而那个机缘发现是一个储备良好且警觉的认知遇到一个场合的产出。默顿的机缘模式在它经典读法中属于此处：一个未被预期的、反常的与策略性的材料成为延展一个理论的场合，而使它策略性之物是那个观察者所带来的理论装备。那个立场就它所及而言是健全的，而它奠基一个关于研究环境应如何被安排的大的实践文献。它的困难是它继承一个把对象当作惰性的图景。那个材料贡献它的反常而不贡献进一步之物；那个工作被在接收它的头脑内部完成。在这个图景上那块晶体是一个刺激，而那个复数性的多晶说明已在那第二个观察者中潜伏，等待任何充分的触发。

第二个把那个意义置于那个对象一侧，或置于安排了那个对象在那里之那个秩序一侧。这是那个问题在任何天意、命定，或全面判定的学说生效之处所采取的形式，而§4长篇处理它，因为宗教诸传统比诸科学更久且更艰苦地思考过偶然性。加尔文在《要义》中的处理是那个可得的最尖锐版本：命运与机遇是一旦天意被理解便在人类事务中不留位置的诸术语，而对我们显得偶然之物仅就我们对它原因的无知而言是偶然的。阿奎那保全更多，主张天意延伸到诸偶然物于它们的偶然性中，以致机遇相对于特定原因是真实的，即便它相对于神不是真实的。那个家族的强处是它以完全的严肃对待那次相遇的意义性。它的代价，就当下问题而言，是意义已完整地到达那次相遇。那个观察者所做之物是找到它。

第三个立场，被科普兰在近来的科学哲学中最谨慎地发展，把那个分析完全移出那个个体。机缘是一个分布跨一个共同体之发现过程的一个涌现性质，而它的承认是回溯的：一个有价值的结果必须被获得，对它意义的反思才能发生。格勒韦亚努，在同一个研究纲领中，进一步朝关系施加，提议那个什么躺在有准备心智之内的问题被一个关于什么在心智与世界之间发生的问题所替换。这个文献是最接近此处所发展说明的，而§3精确地陈述那些接触之点。那个剩余的距离关乎时间与所在。在那个社会认识论说明上那个意义被一个回顾的共同体所授予；那次相遇本身是一个其意义在别处且较晚被安定的事件。

跨三个不相互阅读的文献，一个单一承诺复现。意义被当作有一个所在。它坐落于那个观察者的装备中、或在那个对象与它背后的秩序中、或在那个共同体的回溯判断中，而那个分析任务是辨认哪一个。那些替代于是被安排为一场关于那个地址的争议。

当下这篇论文从一个不同的起点进行。生成发生在诸关系项之间并是两者之一的性质都不是。这是生成性关系存在的支配承诺，而机缘是以最少干扰显示它的情形，因为一次机缘相遇中没有任何东西被安排去产生它所产生的结果。在那个晶体情形中没有关于那块矿物、含有一个多语言民主理论的在先事实，而也没有关于那个观察者、含有它的在先状态。那第二个观察者携带一个关于诸相干殊相如何可能组成一个整体而不被压平为均匀的未决问题。那块晶体携带一个其中局部规则跨晶界产生有序异质的结构。两者都不是那个理论。那个理论在那两者进入关系时被生成，而那个关系产生一个在两者中都无的第三样东西。

从这个起点那两个寻常术语被重构。那个偶然现象有一个它自己的结构，参与被生成之物，那是为什么同一个有准备的观察者遇到一千个偶然而从少数几个生成。而睿识不再是一个智力的量或一个专长的储备。它成为一个时间性能力：把一个关系持于开放、未决与未闭合、达一个不可预见现象耦合到它所要求之间隔的能力。在这个读法上那第一个观察者对那块晶体的回应是那个诊断情形。注意或感受中什么也不缺。那个回应是鉴赏性且闭合的，而闭合是那个封锁生成之物。美作为一个终点到来。对那第二个观察者，美是那次相遇开启之处。

从这个起点所发展的说明产出四个贡献。

第一个是那个机缘事件的关系重构，它把那个涌现意义置于一个被配置认知与一个偶然现象的耦合处，并从那个安置推导机缘的被观察诸特征（§6）。

第二个是把睿识重构为被维持的非闭合，连同它的诸失败模式（§7）。这是本文的首要原创主张，而它把一个性情性术语转换为一个时间性术语。它也携带那个实践后果，即那个能力能被培养，尽管它所准备的那次相遇无法被计划。

第三个是把审美闭合当作那个非相遇的极限情形的处理（§5），它供出那个领域所缺的否定性诊断。既存诸说明解释机缘为何发生。它为何未能发生、在一个偶然事件与一个专注观察者两者在场的情况下的问题，不曾以这些术语被提出。

第四个把那个说明从那个个体相遇延伸到探究的架构（§8）。诸学科是关系结晶，而它们的局部相干是那个使它们生产性之物。对相遇的封锁始于局部相干被当作本体论独立之处，在那一点那个边界在一个现象与一个问题能相遇之前把它从那个问题分拣开来。

本文在一个更大的纲领中占据一个确定的位置。生成性关系存在供出一个其中关系优先于诸关系项的本体论。一个治理延伸为制度设计引出诸后果。在它们之间一个问题保持开放：倘若存在是生成性与关系性的，新意义凭什么路线进入，而一个认知者必须做什么才对它可得。机缘是那个答案最可辨识的情形，而此处所发展的说明作为那个纲领的认识论枢纽被供出。

这些在三个问题之下被追寻。

RQ1。 一次机缘相遇中所生成的意义驻留在何处，鉴于那个偶然现象与那个观察者的在先状态都不含有它？

RQ2。 观察者一侧的什么能力容许一个不可预见的现象耦合到那个观察者所携带的一个问题，而那个能力在什么条件下失效？

RQ3。 对探究的组织什么随之而来，鉴于那些使局部相干成为可能的边界也支配哪些相遇能发生？

第一个在§5到§6被处理。第二个是本文的中心并在§7被处理。第三个在§8被处理而它的诸后果在§11。

那个说明可被陈述为一个单一主张。

中心主张（在一次相遇处生成的两个条件）。 一次机缘相遇是一个被配置认知与一个偶然现象之间的关系，而从它生起的意义在那个关系处被生成，两个关系项都不事先持有它。睿识是把一个关系持于未决、达一个不可预见现象耦合到它所要求之间隔的能力。终止于一个安定回应的相遇是一个非相遇，在其中偶然到来而生成不随之而来。机缘的诸条件因而是两个且共同必要的：一个携带活的且未决之诸关系的配置，以及一个跨那些否则会在现象与问题相遇之前把现象从问题分拣开来之边界的开放。

其余部分如下进行。§2综述存在主义传统中对偶然性的处理，它比任何其他更彻底地思考过与粗野偶然性的相遇，并辨认它所遗留的投射模型。§3综述发现研究中的机缘，从沃波尔经 默顿到近来的社会认识论转向，连同直接关乎那个配置主张的理论负载文献。§4综述宗教与神学思想中的偶然性，在那里对那个说明的最强反对与它若干最接近的先驱两者都被定位。§5发展那次相遇的配置与审美闭合的情形。§6陈述那个生成性结构并把信息同意义区分开来。§7把睿识发展为被维持的非闭合。§8处理学科结晶与相遇的封锁。§10跨六个领域发展诸案例。§11为探究的进行引出诸后果，而§12陈述那个说明的界限与它留下开放的工作。

§2 存在主义传统中的偶然性

与粗野偶然性的相遇是整个一个哲学传统的奠基场景，而那个传统抵达了一个与此处所发展者相反的答案。谨慎地铺陈那个答案是第一项任务，因为它所遗留的投射模型是最可能被一个快速移动的读者归于本文的立场。

2.1 萨特中意义的撤离

罗冈丹，在公园里，看一棵栗树的根。词语已消失，而随词语事物的意义已消失；那根在那里，完全未经修饰，而存在把自己揭示为那个绝对、完美地无端。萨特（1964）使这成为与 contingence（偶然性）的范式相遇，而萨特（1956）的哲学装置形式化它：实际性是那个自为在不奠基的情况下同化的永久偶然性，而我存在是完全偶然的，因为我不是我存在的基础。

要标记的结构特征是那个运动的方向。在与原生偶然性的相遇处，意义流干。那个自在是稠密且无意义的；那个自为授予这样的意义如其所有；而与偶然性的对峙是那个授予作为授予被暴露的时刻。这是投射模型的最强形式，而它是此处所发展说明的精确反面。在萨特于与未被概念化者的相遇处发现恶心之处，当下的说明发现生成变得可能的场所。

那个场景内在的一个张力值得注意，因为它已被萨特的诸读者所观察并关乎那个论证。罗冈丹作为某样不同于一个未被配置的意识遇到一个赤裸对象之物到来。他是一个处于特定危机中的历史学家，已放弃一部传记，携带一组关于存在与辩护的特定未决问题，站在1930年代晚期一个法国外省公园里。那次相遇被彻底地配置。萨特所呈现为意识与纯然存在之对峙者本身是一个在观察者一侧带一个确定结构的关系事件，而那个恶心是那个特定配置所生成之物。在当下的说明上这不令人惊讶。一个被不同地配置的观察者，被呈现同一个根，生成得不同。

2.2 海德格尔中的揭示与在先视域

海德格尔（1962）主张诸存在者仅在一个已到位的指引总体之内作为某物显现。那个世界是一个实体能作为上手被遭遇于其中的关系整体，而现成在手是那个整体被悬置时所获得的派生模式。被抛，Geworfenheit，命名我们的存在总是已被交付于这样一个处境；后来 Ereignis（本有）的语汇重做同一个结构，希恩把它渲染为被抛的开放。

这是存在主义传统中最接近那个配置主张的东西，而它应作为它的一个祖先被主张。准备，在海德格尔的措辞中，是那个先在的揭示性视域，没有它没有任何东西作为任何东西显现。那个分歧之点关乎那个视域做什么。海德格尔的视域支配揭示：一个实体作为它在一个世界之内已经所是之物显现。§6中所发展的主张关乎生成：在那次相遇处生起之物在那个视域与那个实体中都无，而那个视域的贡献是使耦合成为可能，带那个耦合产生一个第三项。揭示与生成是不同的操作，而那个差异是本文就现象学而言的首要债务与背离。

2.3 梅洛-庞蒂中的交错

梅洛-庞蒂（1968）发展那个传统所含的最近乎关系的立场。意义在肉、la chair 中生起，一个原初的可逆组织，其中看者与被看、触者与被触，是一个织物的诸模态；那个交织抵抗被分解为两个分离项之间的一个关系，而一个 écart，一个厚度或分歧，把那些项在它们的可逆性之内持开。

与当下说明的交叠是实质的：意义真正地在之间、在两者单独中都无。那个分歧是精确且有后果的。梅洛-庞蒂把那个两项结构消解进一个单一的可逆肉，以致那些项是一个组织的诸模态。此处的说明保留两个被不同地结构化且可独立描述的关系项，一个带一个确定配置的认知与一个带一个确定结构的现象，并把生成定位在它们的耦合处。那个区分对那些案例要紧。那个多晶的晶界结构是否参与被生成之物，还是仅仅为一个在观察者一侧的展开提供机缘，是一个在那两个本体论之下有不同答案的问题，而§10中的诸案例被建构以关乎它。

2.4 加缪中作为一个关系的荒谬

加缪（1955）供出那个传统中对本文所论证之逻辑形式的最清楚陈述。那个荒谬本质上是一个离异；它躺在被比较诸元素中的任一个都不；它诞生于它们的对峙。那个荒谬不在人类存在中而不在世界中，而在它们一起的在场中，而目前它是接合它们的唯一纽带。它诞生于人类对清晰的要求与世界不合理的沉默之间的对峙。

那个形式恰恰是那个中心主张的形式。一个质仅驻留在两个关系项中的任一个都不而从它们之间的关系生起。两个差异把当下说明的位置对着它固定。加缪理论化一个否定的关系，一个离异与一个张力，其产物是一个永久的不谐；此处的说明理论化一个生产性的关系，其产物是新意义。而加缪的两个关系项是固定且通用的，一个人类要求与一个沉默世界，以致那个荒谬跨诸观察者不变。当下的说明使那个观察者的配置可变，那是那个容许两人站在一块晶体前而生成得不同之物。

加缪对 克尔凯郭尔之跳跃的拒绝在闭合问题上是有教益的。那个跳跃，在加缪的读法上，是哲学自杀：一个凭一个意志行为终止那个张力的被迫解决。§7的语汇恢复这个：过早的闭合解决一个开放的关系并放弃那个关系可能已生成之物。加缪与本文在保持开放的纪律上一致，而在保持开放是否生产性上不一致。

2.5 九鬼中作为第一哲学的偶然性

九鬼（1935）构成现代非西方文献中对偶然性（gūzensei，偶然性）最持续的处理，而它在欧洲语言的讨论中大体缺席。九鬼凭必然性的否定界定偶然性，打破必然性所要求的那个同一，并给它一个首要的形而上学位置。在此要紧的举动是他把那个范畴奠基于那个偶然相遇：一个现在所面对、无需被面对，而其必然性无法被恢复的在场。

两个特征为当下论证推荐九鬼的处理。他取那次相遇、而非那个孤立的偶然事实，为那个原始项，那是§6中所作的同一个选择。而他把那个分析延伸进诗学，把偶然押韵的美当作诸声音的偶然相遇，那开始把偶然者的美学连到它的形而上学。九鬼的说明与当下这个之间的关系配得上一个比此处所能给更长的处理；从它所取之物是把那次相遇本身当作分析单位的许可。

2.6 从那个传统所继承的立场

存在主义传统把与偶然性的相遇确立为一个头等的哲学问题，供出被抛、配置与视域的语汇，而在加缪中供出一个驻留在一个关系中之质的逻辑形式。它所遗留之物，在它主导的萨特一线中，是一个投射模型，其中意义从意识流向一个没有意义的世界。本文的其余部分发展那个传统自己的诸资源所使可得、而那个传统不曾采取的替代。

§3 发现研究中的机缘

以机缘为它明确对象的文献更年轻且更经验，而它在七十年间已收敛于一个相当接近此处所论证者的立场。铺陈那个收敛确立当下说明所继承之物与它所添加之物。

3.1 那个原初配对

沃波尔 1754年1月28日致 Mann 的信供出那个术语与它的两部分结构。锡兰的诸王子凭意外与睿识作出发现、发现他们未在寻求之物，而沃波尔添加一个被引用多于被尊重的约束：对一个人正在寻找之物的发现不落于那个描述之下。那个约束做真正的工作。它排除一个有准备的观察者找到那个准备所瞄准之物的情形，那是寻常的胜任，并分离出一个准备产出那个准备未瞄准之物的情形。任何睿识的说明因而必须解释一个配置如何能就一个它未被配置去应对的现象是生产性的。§7中的说明被建来迎击这个约束。

3.2 那个有准备的心智与那个机缘模式

巴斯德 1854年的里尔表述为诸科学固定了那个观察者一侧的读法，而默顿与巴伯（2004），写于1950年代晚期并数十年后被出版，给了它它的社会学发展。那个机缘模式是观察一个未被预期的、反常的与策略性的材料的经验，那个材料成为发展一个新理论或延展一个现存理论的场合。默顿的三个形容词值得注意。未被预期定位那个偶然；反常定位那个材料就一个期待之体而言的一个性质，那是一个关系性质；策略性定位它对理论的关涉，那以同样的方式是关系性的。默顿自己的分析因而已把三个条件中的两个置于那个关系处，而那个解释性分量继续停靠于那个受纪律的观察者。

雅各布（2018），从默顿的档案工作，供出那个领域最有用的分类法，凭搜索与发现之间的关系区分四种类型，而凭那个发现到来所经由的路线区分四种机制，其中有一个网络涌现机制，其中那个连接被跨诸方作出。那个分类法是描述性的并与那次相遇的若干本体论相容；此处的说明可被读为供出一个。

3.3 那个关系转向

科普兰（2019）把那个分析决定性地移离那个个体。科学中的机缘最好被在那个科学共同体的语境之内理解，而那个个体的洞见是不足的，因为发现过程取决于环境因素并取决于那个共同体的结构。科普兰的肯定表述把机缘当作那个发现过程的一个涌现性质，描述一个过程的结果与驱动它之诸意图之间的一个斜向关系。

格勒韦亚努（2022）以非常接近当下论题的诸术语把同一个纲领朝关系施加：那个什么在有准备心智之内的问题让位于一个关于在创造性机缘的诸时刻中什么在心智与世界之间发生的问题，带惊奇、好奇与惊叹把那个有准备的心智扩展为一个自我与他者、心智与文化、人与世界之间开放且动态之诸关系的系统。

这个文献与此处所发展说明之间的距离可被以两点陈述。第一个关乎何时。科普兰的机缘被回溯地范畴化：一个有价值的结果必须被获得，对它意义的反思才能发生，以致那个意义被一个较晚的共同体判断所授予。此处的说明把那个生成定位在那次相遇处，带承认与验证作为不同的操作随之而来。第二个关乎什么被维持。格勒韦亚努的诸关系系统是共时的，一个关于一个心智如何在一个时刻被关系地构成的描述。§7中的主张是历时的：做那个工作之物是一个关系在一个未决状态中跨时间的维持，以及那个被维持关系被一次无法被排定的相遇所激活。

3.4 配置与那个观察文献

科学哲学中的一条线如此直接地关乎那个配置主张，以致它必须在那个主张被作出之前被陈述。汉森（1958）论证观察是理论负载的，而看比遇到眼球者更多。那个规范例示有第谷与 开普勒在黎明的一座山上带相同的视网膜像：那个地心观察者看见一个固定地平线之上的一个移动太阳；那个日心观察者看见一个固定太阳与一个下沉地平线。库恩（1962）在一个气泡室中供出同一个结构，其中那个学生看见混乱且破碎的线而那个物理学家看见一个熟悉亚核事件的记录。

与那个配置主张的交叠接近到足以要求明确的处理。汉森的论题是一个理论之下感知的认识论：一个观察者所看见之物被那个观察者所持的理论所条件化。此处所发展的主张是一个生成的本体论：在那次相遇处生起之物被任一方都不事先持有，而那个配置的角色是使耦合成为可能。对汉森的标准反对，即那两个天文学家看见同一个东西而不同地解释它，是一场关于那个感知层次的争议，当下的说明能把它留下开放，因为相关意义上的生成发生在无论那个感知裁断结果为何之下游。汉森所确立之物、并从他所取之物，是两个观察者对一个现象的差异性回应是一个带一段长分析在它背后的严肃哲学材料。

3.5 溯因与那个令人惊讶的事实

皮尔士的溯因图式供出被分析事件的推理对应物：一个令人惊讶的事实被观察；倘若某个假说为真，那个事实会理所当然地随之而来；因此有理由怀疑那个假说。范安德尔（1994）恰恰沿这些线注解默顿对机缘的说明，作为一个令人惊讶的观察后随一个正确的溯因。惊讶，在那个图式中，是一个关系性质：一个事实就一个期待之体而言令人惊讶，而同一个事实遇到一个被不同地装备的观察者而不惊讶任何人。溯因因而为那个随生成而来的推理步骤供出一个发达的逻辑，而它预设当下说明所使明确的那个配置。

§4 宗教与神学思想中的偶然性

宗教诸传统比哲学与科学诸文献合起来更久地思考过偶然性，而它们含有对当下说明的最尖锐反对与它若干最接近的先驱两者。本节按每一个传统就一个单一问题所取的立场被组织：那个在一次不可预见相遇中到来的意义是否被事先置于那里。

4.1 天意与偶然性的消解

那个最强的反对立场主张表面的偶然性仅就人类无知而言是偶然性。加尔文（1960）不加软化地陈述它：命运与机遇是其意义不应占据虔诚心智的诸术语，而在人类事务中没有位置留给命运与机遇。那个视角性举动立即随之而来：无论一切事物如何可能按神的计划依一个确定的处置被规定，对我们它们是偶然的。那根落下并杀死一个路过旅人的树枝被预见并被命定。被应用于机缘，这产出一个完整且内部一致的说明，其中那次相遇被安排、那个意义被事先撰写，而那个观察者的睿识在于承认。

加扎利（1997）的艾什尔里派机会论经一条不同的路线抵达一个结构上同一的结果。习惯地被当作一个原因之物与被当作一个结果之物之间的连接不是必然的；火不烧棉花；神是每一个事件的直接施动者，而创造被持续地更新。在每一个事件是一个直接神圣行为之处，机遇没有抓力而那个意义在何处生起的问题在它被问之前被安定。那个解释文献在加扎利的机会论多彻底上分歧，带某些读法保全一个非必然化的次级因果性，而那个分歧应在对他所作的任何使用中被尊重。

这些立场无法被证据迎击，因为它们与每一个观察一致。它们能被一个区分迎击。因果判定与意义生成是可分开的操作，而一个一次相遇被一个全面施动所导致的证明留下开放那次相遇的意义为承受它的观察者在何处生起。此处所发展的说明关乎那第二个问题并与对那第一个的一系列答案相容。

4.2 在天意之内被保全的偶然性

一个中间家族在全面的神圣行动旁边保全真正的偶然性，而它的诸资源更有用。阿奎那（1947）在《神学大全》I 卷 q.22 a.4 主张神圣天意不强加会摧毁偶然性的必然性，已为某些事物准备必然原因而为其他事物偶然原因；凭偶然发生之物是那个计划设想为凭偶然发生之物。在 q.116 与在《反异教大全》III.74 的那个机制是诸原因的汇合：机遇相对于特定因果秩序是真实的，因为独立的诸链相遇并产生任一者都不意图的诸结果。

那个机制值得从它的神学设定中被抽出。阿奎那关系地定位机遇，在不相互包含之诸秩序的相遇处，那在结构上是当下说明对相遇所做之物。波爱修斯在慰藉的语域中供出同一个结构，带 Fortuna 作为天意被误读所处的表象。迈蒙尼德（1904）贡献一个不同种类且更直接有用的主张：天意按智性完美的比例抵达每一个个体。无论它的神学地位，那个主张的形式是那个配置论题。能到来之物被那个接收者已变得能够接收之物所分级。

4.3 关系与涌现主义的神学

过程神学供出那个最强的严格神学盟友。怀特海（1978）以摄入它们被继承世界并通过合生达到判定的现实机缘组成实在，带创造性持有那个终极的位置。科布与格里芬（1976）引出那个神学后果：神圣行动是劝说性的，供出一个每一个机缘自由地现实化的初始目标，而那个整合是那个机缘自己的。价值在关系材料的自我创造综合中生起。那个形而上学形态接近生成性关系存在到足以使那个亲缘应被直白地陈述，连同那个分歧：那个过程说明把生成嵌入一个诸机缘的泛经验主义宇宙学，一个当下框架不要求的承诺。

布伯（1958）是对一个相遇之关系本体论最接近的宗教哲学先驱，而那个接近是言辞的一如结构的。太初有关系。一切真实的生活是相遇。精神驻留在我与你之间。关乎睿识的那个段落是关于那个你如何到来的一个：它通过恩典遇到我，而不被寻求所找到；每一个手段是一个障碍，而唯有在诸手段已崩溃之处那个相遇才发生。布伯因而陈述本文所工作的那个悖论。那次相遇无法被意志所产生，而对它的准备能被培养。他的解决，即准备是一个可得性的纪律，是§7中以世俗术语被采纳的那个解决。

马里翁（2002）供出那个现象学的发展。一个饱和现象给出多于那个概念能组织且多于那个意向能预见的直观；它不可预见地到来并反转那个凝视的方向，构成它的接收者。格施万德特纳（2014）施加在此要紧的那个改正：诸现象在一个已被一个接收者的能动接收所开启的诠释空间之内显现，以致所显现之物取决于给予性与解释两者。那个改正是从宗教现象学之内被抵达的当下论题，而它在此作为汇聚的支持被供出。

4.4 作为一门纪律的准备

若干传统已发展诸准备的技术，而这些关乎那个论证的实践一侧。

薇依（1951）给出对被维持之开放的最精确西方描述。注意在于把思想持空、等待、什么也不寻求，而准备好以它的赤裸真理接收那个要穿透它的对象。她把注意同意志尖锐地区分开来，并把诸过失的改正当作一个意志无法履行的注意之工作。那个描述同§7中所界定的能力匹配到足以使薇依应被视为它的首要西方先驱。依纳爵式的辨别，带它的省察与它对慰藉与荒凉的解读，以一个可训练日常实践的形式供出同一个能力。埃克哈特的 Gelassenheit（泰然任之）与否定神学文献供出它的否定极，那个先于接收的清空。

奥古斯丁（1961）供给那个传统的范式情形，而它值得作为一个案例被阅读，带它的教义设定被搁置一旁。386年在一个米兰花园里，处于急性且延长的危机中，奥古斯丁听见隔壁一个孩子的声音吟诵一个游戏中的短语，把它当作一个指示，随机翻开保罗书信，并读到两节结束那个危机的经文。那个结构的每一个元素都在场。那个刺激是偶然的、含混的，而本身微不足道。那个配置是一个在压力之下被持有多年的持续且未决的问题。那个生成是即时且全部的。同一条街上一个被不同地配置的听者听见孩子们在玩。

4.5 作为一种实践的非闭合

最接近命名本文关于睿识之中心主张的传统是禅，而那个接近近到足以要求承认。

公案实践是对一个未决问题的刻意维持。那个传统把那个状态命名为大疑（daigi，大疑），而白隐的公式使它的功能明确：大疑之下有大悟；疑得彻底而悟得彻底；小疑产出小悟，而无疑产出无。那个解决特征性地通过一个寻常的偶然事件到来。香严智闲，一个不曾取得进展的经典学者，烧了他的书并退隐去扫一条路；一颗被扫帚扬起的石子击中一根竹子，而那个声音解决了多年的学习所未解决之物。灵云志勤，在数十年的寻求之后，看见一道山谷对面的桃花，并报告说从那一刻起他再未怀疑。

那个结构是本文的结构。一个关系在持续压力之下被持于未决；一个寻常的偶然现象到来；生成立即随之而来而不可逆。禅在那个结构之外所供出之物是那个维持是可训练的、它的困难是那个要点，而由那个师父的过早解决会摧毁那个过程的主张。那些差异配得上同等的陈述。那个公案是被给予的，故那个张力被一个教师所诱导而不被那个实践者自己的研究问题所携带；而那个传统把被生成之物当作某样总是在场之物的揭示，那是一个潜伏模型并在那一点从一个生成模型分歧。

同样的潜伏限定适用于两个进一步的资源。卢里亚派与哈西德派的火花学说主张每一个对象含有等待被一个与寻常者的有准备相遇释放的神圣火花，那是一个准备的有力意象与一个其中意义在那个对象中预先存在的说明。如来藏主张觉悟是内在的并被揭开。两者都是准备上的盟友并在生成上分歧，而那个区分应被保持尖锐，因为一个批评者否则会把当下说明坍缩进一个潜伏模型。

4.6 相遇的关系本体论

佛教与东亚诸传统供出最深的本体论先驱。

Pratītyasamutpāda，缘起（engi，缘起），主张诸现象在对诸条件的依赖中生起并不拥有独立的自性。龙树（1995）在《中论》24:18 把缘起同空性并同依赖性施设等同，产出一个其中诸实体仅关系地存在的立场。这是当下这篇论文的语义论题作为一个一般本体论被陈述，而它是那个可得的最古老且最严格的版本。华严的发展，带因陀罗网的相互含摄与事事无碍，把它延伸到一个其中每一个所在被它对一切其他的诸关系所构成的总体。

东亚术语縁（日语中的 en，中文中的 yuan，连接或缘分）把那个有意义的偶然相遇词汇化为一个关系范畴。一个在欧洲语言中会被描述为机遇的相遇在此被描述为一个连接：一个人与一个人、一个地方，或一个作品有縁（缘）。那个范畴既非必然也非随机，而它恰恰命名本文所分析的现象。一个主要语言传统有一个为它的共同词，而欧洲语言必须伸手够到一个来自一个波斯童话的杜撰，本身值得记录。

茶道的一期一会（ichigo ichie，一期一会）供出那个实践学说。那个表述从千利休经井伊直弼的《茶汤一会集》流传：无论主客多常相遇，一日的聚会无法被重复，而两方因而必须以完全的真诚与完全的准备参与。那个仪式是一个为一次单一不可重复相遇之准备的技术，而它的强调落在诸人之间的那个共享场合上。伊本·阿拉比那个在神圣自我披露中没有重复的原则给那个单一性一个形而上学形式，带每一个时刻是一个独特的神显而每一个存在是一个发生一次之诸名配置的披露。

4.7 中国思想中的偶然性与解释

两个进一步的资源配得上分开的陈述。

《淮南子》那个边塞人其马跑掉的寓言是解释性非闭合的经典陈述。那匹马丢了，而诸邻居吊唁；它带着好马回来，而他们道贺；那儿子骑一匹时致残，而他们吊唁；那征兵到来而那个致残的儿子被免。每一个判断被随之而来者推翻，而那个叠句问一个人如何能知道那个当下的表象是那个情形。那个教训直接关乎§5：在一个安定的评价处闭合是固定一个那个关系尚未完成生成的意义。

占卜供出另一个。《易经》凭一个偶然程序产生一个配置，而唯有通过一个有准备的解释装置与一个被培养的判断产出意义。朱熹的说明，即那个文本的意义为每一个人通过那个占卜的过程涌现而无法被一个单一注释者所捕捉，是一个明确的涌现主义诠释学。那个相关联的概念幾（ji，几微）命名变化那勉强可感知的第一次萌动与探测它的那个能力。可比的诸系统跨诸文化出现，从约鲁巴的 Ifá 语料到拉丁的 sortes，而奥古斯丁对保罗书信的翻开属于同一个家族。那个家族所示范之物是从偶然而来的意义已被工程化了数千年，凭把一个随机化程序与一个有准备的解释者相结合，那是当下说明的结构作为一门实践被建造。

4.8 共时性及其界限

荣格（1973）提议共时性作为一个非因果的连接原则，诸事件的有意义巧合，在那里某样不同于机遇之概率之物被涉及，在与泡利的对话中发展那个想法并在他为 卫礼贤《易经》的前言中应用它。那个圣甲虫插曲是它最知名的例示。

那个提议必须被处理，因为它是有意义巧合的现代理论并占据相邻的地面。两个特征把它同当下说明分开。荣格在那个世界中假定一个配对那些事件的非因果原则，那是一个形而上学的添加；而一个真正共时性的判据，在实践中，是那个配对被感到的意义性，那供出没有把那个现象同幻觉性联想区分开来的方式。那个关系说明要求没有这样一个原则并凭那次相遇的结构解释同样的数据，那在经济性的根据上推荐它。在荣格把意义性定位在世界与心灵之间的一个对应中之处，当下的说明把它定位在一个被配置认知与一个偶然现象在它们耦合处所生成之物中。

4.9 从诸传统所继承的立场

三个结果被向前承载。那个天意家族显示一个完全对象一侧的说明看起来像什么以及它必须在何处被迎击，即在因果与意义生成之间的区分处。诸准备的纪律，在薇依中、在依纳爵式实践中，而首先在关于大疑的禅文献中，确立被维持的非闭合是一个真实的、可描述的与可训练的能力，带一段长的实践历史。而相遇的诸关系本体论，在中观中、在华严中、在縁（缘）中，而在布伯中，确立关系优先于诸关系项是一个带实质发展在它背后的立场。本文的其余部分在那个继承之内工作。

§5 那次相遇的配置

那些综述确立那个地形。那个建构性论证从整个文献都同意而没有说明完全利用的那个材料开始：两个观察者、一个现象、两个结果。

5.1 那两个观察者

回到那块晶体。两个人、一个标本、一个注意的间隔。第一个抵达一个鉴赏判断并离去。第二个抵达一个关于诸相干殊相如何可能组成一个整体、同时保留它们差异的问题，并带一个共享政治秩序中之复数性说明的开端离去。

那些可得的解释如那些文献一般分开。那个观察者一侧的解释说那第二个观察者知道更多。这是真的且不足的：那第二个观察者的在先知识含有晶体学并含有一个对政治复数性的旨趣，而含有它们之间没有连接，那正是到来之物。那个对象一侧的解释说那块晶体含有从它被读出的那个结构。这以同样的方式是真的且不足的：那个晶界结构是一个关于诸矿物的事实而含有关于诸语言的无物。那个共同体一侧的解释说使那个插曲成为一个发现之物是一个由胜任的其他人所作的较晚判断。这关于验证是真的而关于那个事件沉默。

所要求之物是一个其中那个现象的结构与那个观察者的配置两者都参与而任一者都不充分的说明。为这样一个说明的语汇在本文所工作于其内的框架中可得，在那里生成是诸关系的一个性质而诸关系项贡献一个耦合的诸项而不含有它的产物。

5.2 配置的概念

那个观察者的贡献在此被术语配置所描述：一个人带入一次相遇的诸问题、诸工具、诸承诺与诸未决困难的确定安排。那个术语的三个特征是承载分量的。

配置是被结构化的，而它的结构要紧。一个含有晶体学与政治复数性而它们之间没有连接的配置不同于一个含有任一者单独的，而又不同于一个其中那个连接已被作出的。什么能被生成取决于哪些关系在场而哪些开放。

配置的运作不同于一个储备。一个知识的量，被持于一个已解决状态，是一个为相遇的差配置，因为已解决的知识没有一个现象能耦合到的开放化合价。这是专长与接受性能独立地变化那个观察的实质，而它在§7中被发展。

配置是历史的且缓慢的。它被一个人已研究、已工作于、已在其上失败，而已继续担忧之物、经年地所构成。它无法为一个场合被假定，那是机缘抵抗计划的那个意义。

5.3 那个审美终点

那第一个观察者的回应值得近的注意，因为它是那些标准说明有最少可说、而当下说明挣得它报酬之处。

那个回应中什么也不有缺陷。那个观察者看、专注，而被打动。那个判断是准确的：那块晶体是美的。在任何观察者一侧的说明上那个插曲仅仅是一个不足准备的情形，而在任何对象一侧的说明上它是一个未能找到一个接收者之信号的情形。两个描述都错过那个独特之物。那个回应是完整的。它抵达一个终点并在那里安歇，而那个安歇是那个起作用的事实。

一个鉴赏判断是一个闭合操作。它取一个现象、把它指派给一个范畴，并解除那次相遇。那个范畴是一个好的而那个指派是正确的，而那个解除是那个封锁之物。一旦那块晶体已被分类为美的，那次相遇已被完成，而一个已完成的相遇不生成任何进一步之物。那个现象原则上保持可得；那个关系已被闭合。

这是那个插曲是一个非相遇的意义。那个偶然到来、那个观察者在场且专注，而没有关系被维持得够久以致任何东西能跨它被生成。意外在被重构意义上的睿识缺席下发生，而所缺之物是持续时间、不是信息。

主张1（差异性生成与那个审美终点）。 两个观察者遇到一个现象凭它们的诸配置生成得不同，而那个差异是一个关于每一个与那个现象所形成之关系的事实。一个终止于一个安定判断的相遇是一个非相遇：偶然到来、闭合是即时的，而生成不随之而来。闭合、而不是无知，是机缘的一般失败条件。

那个审美情形是一个更宽家族的极限实例。任何安定的回应都履行同一个操作。那个现象被归档于一个可得范畴之下，而那个归档解除它。这是那个使那个家族在诊断上有用之物：那个失败在那个回应的速度与终局性中可见，而独立于那个观察者知道多少。

§6 意义在关系处的生成

那个说明能被带到一个定义，而把那个定义安置在那个传统所遗留者旁边是有用的。那两个在此按它们地位的次序被给出，那个既有表述在先。

定义1（机缘的既有定义）。 有准备的心智在偶然性中辨认出了意义。 Serendipity is meaning discerned in contingency by a prepared mind.

这个表述关于那两个因素是精确的并以一个动词承载那个说明的整个分量。辨认（biànrèn，辨别或看出）取一个已在场的对象并把它带入视野，以致那个意义在那个偶然性中等待而准备是那个许可它检索之物。此处所供出的定义转在那个动词上并转在它所预设的那个所在上。

定义2（机缘在生成性关系存在中的初始定义）。 Serendipity 是关系生成的偶然性被转化为延续系统生成过程的可能的过程。 The contingency generated by relations is transformed into the possibility of continuing the system’s generative process.

那个定义的三个元素承载那个论证，而每一个在随之而来之物中被发展。那个偶然性被诸关系所生成，那把它置于那个场域之内并移除一个从外部到来之粗野外在性的站位。那个转化是生成性的，那把它同辨认并同某样等待之物的检索区分开来。而那个产物是一个延续的可能，那把一个机缘事件的产出定位在那个系统此后变得能够生成之物中，超出那个到来的特定意义。

那个中心主张现在能被以它自己的术语陈述而它的诸后果被引出。

6.1 那个事件的结构

一个机缘事件有三个环节与一个产物。一个被配置的认知携带一组关系，其中某些是开放的。一个偶然现象到来，就那些关系而言未被排定。一个耦合发生，其中那个现象的某个结构特征进入与那个配置中某个开放关系的关系。被生成之物是一个在两者中都无的第三项。

每一个元素做真正的工作。那个到来的偶然把机缘同寻常探究区分开来，在寻常探究中那个现象被寻求。那个现象的结构把那个说明同投射区分开来，因为那块晶体的晶界参与被生成之物而一块被不同地结构化的矿物会生成得不同或根本不生成。那个关系的开放把那个说明同揭示区分开来，因为一个闭合的配置遇到同一个现象而不生成任何东西。而那个产物的第三性把那个说明同潜伏模型与检索模型两者区分开来：那个复数性的多晶理论不曾被贮存在那个观察者中，而不曾被写在那块矿物中。

主张2（那个被生成的第三项）。 一次机缘相遇中所生成的意义在一个被配置认知与一个偶然现象的耦合处生起并被任一者都不事先持有。那个现象供出结构；那个配置供出一个那个结构能耦合到的开放关系；那个被生成的意义是一个第三项，其内容被那个配对所判定而被任一方单独都不判定。

6.2 信息与意义

那个使那个主张精确的区分是一个信息诸科学为它们自己的目的所确立并在哲学上留下未发展的。

香农（1948）以把语义搁置一旁开篇：沟通的语义方面同那个工程问题不相关。那个由此产生理论中的信息是一个在一个分布之上的度量，被界定而不参照任何东西关于什么，而那个理论的力量从那个排除派生。随之而来之物是一个关于一个传输模型能与不能交付什么的清晰陈述。一个信道从一个发送者向一个接收者输送一个量，而那个量跨那个转移被守恒。

贝特森（1972）重新引入那个接收者：信息是一个作出一个差异的差异，那使它相对于一个那个差异为之登记的系统。卢曼（1995）发展那个系统形式，其中诸扰动仅在它们为一个系统的意义处理作出一个差异之处成为信息。皮尔士的三元符号学供出那个一般陈述，其中意指要求符号、对象与解释项一起，以致没有二元组充分。

被应用于那次相遇，那个区分是精确的。那块晶体在工程意义上携带信息，而为两个观察者携带同样的信息，因为抵达两个视网膜的光子在任何相关方面都不不同。意义是那两个关系之一所生成之物。那个传输图景，其中某样东西被从现象发送到观察者，描述那个信息而误描那个意义：没有关于一个政治秩序中之复数性之物被传输，因为没有关于它之物在那个源头在场。

主张3（信息被守恒，意义被生成）。 信息跨传输被守恒并是一个信号相对于一个分布的一个性质。意义在一个关系处被生成并是两个关系项之一的性质都不是。一个现象因而可为两个观察者携带相同的信息而与一个观察者参与意义的生成，那是那个两观察者材料的一般形式。

6.3 就诸相邻本体论而言的站位

三个立场主张诸关系项不先于它们的诸关系，而那个说明就它们而言的站位应被固定。

巴拉德（2007）主张诸关系项通过一个现象之内的内行动涌现而没有独立的诸关系项，只有关系之内的诸关系项。西蒙东（2020）主张关系有同它诸项一样的实在等级而那个个体是存在的一个相，预设一个前个体的亚稳场，带转导从地方到地方传播结构。德勒兹（2000）主张思想在与一个强迫它之符号的一次暴力相遇中开始，以致真理在一个约束之下被寻求而不凭善良意志。

那个交叠是实质的并应被无回避地让步：关系优先于诸关系项，在这些作者中，是那个本体论论题的先有技艺。此处的说明把那个本体论规定到一个它们不处理的情形并添加两个它们不含有的元素。那个情形是偶然性之下的发现，带它那个发现未被寻求的沃波尔式约束。那些添加是§7中睿识的时间性重构与§5中对闭合的诊断。德勒兹的相遇是那个符号的一个突然强加，带那个观察者的贡献被动；此处的说明使那个观察者对一个开放关系的持续维持成为那个耦合的一个条件，那是一个带不同实践后果的不同结构。

这些作者所施加的一个问题配得上一个直接的回答。倘若诸关系项不先于诸关系，§5当作一个先在项处理的那个被配置认知的站位是什么？此处所采纳的回答是一个配置本身是诸在先相遇的沉积物并携带没有超出那个历史的独立，而同时保持跨一个给定相遇的间隔足够稳定以被描述为它的一个项。那两个描述在不同的时间尺度上运作并是相容的。

§7 睿识与未决关系的维持

睿识的重构是本文的首要主张与那个两部分民俗公式被替换之点。

7.1 那个重构

睿识，在那个既有读法上，是一个心智的一个品质：敏锐、宽广、警觉、一个被储备的记忆、注意到的能力。那个读法有匹配那些范例的优点，因为那些标准情形中的诸人物事实上敏锐且储备良好。它的困难是这些品质是常见的而机缘是稀罕的，而同一个人持续地展示它们而在一段生涯中从一个偶然生成也许屈指可数的几次。

此处所提议的重构使睿识时间性且具体。

主张4（睿识与被维持的非闭合）。 睿识是把一个关系维持在一个未决状态、达一个不可预见现象耦合到它所要求之间隔的能力。它的量度是在闭合压力之下的持续时间，而它的失败模式是在一个安定回应中的早期终止。它是一个关于一个问题如何被跨时间持有的性质并容许培养，带它所准备的那次相遇保持不可排定。

三个后果立即随之而来。

第一个是那个沃波尔式约束被满足。沃波尔排除对一个人正在寻求之物的发现。一个被维持的未决关系落于搜索的范畴之外：它规定没有目标，而正是一个被规定目标的缺席把那个关系留得对一个来自一个不相关领域的现象可得。一个寻求对一个陈述问题之解的研究者将只接受那个陈述类型的候选者。一个把那个困难持开、带一个解之形式未被判定的研究者，能被一块矿物遇到。

第二个是那个能力是昂贵的而它的代价解释它的稀罕。一个未决的关系是不舒服的。它占据注意、抵抗概括，而在它被持有时产生无物。每一个专业激励奖励闭合：出版要求结果、教学要求答案，而制度评价计数安定的产出。被维持的非闭合因而恰恰在研究被进行所处的诸条件之下是昂贵的，而它的稀缺是一个关于那些条件的结构事实。

第三个是专长与睿识是独立的。专长是被组织的、闭合的知识，而它的价值从那个闭合派生：一个专家快速且正确地回答，因为那些相关关系被解决了。一个被解决关系的配置为一个不可预见现象供出很少能耦合到的化合价。这产出一个关于机缘在何处集中的可检验期待，在§10中被审查。

7.2 诸失败模式

三种未能维持一个关系的方式能被区分，而它们要求不同的补救。

过早解决凭接受一个可得答案闭合那个关系。那个答案可能是恰当的；恰当是那个使那个失败难以看见之物。加缪对 克尔凯郭尔式跳跃的指控有这个形式，而那个安定于第一个可行假说的寻常研究病理也如此。

审美终止凭把那个现象解除进一个安定范畴闭合那个关系。那个晶体情形是它的典型。那个范畴是正确的而那个解除是完整的，而那个回应感觉像投入而同时履行闭合。

放弃凭抛下那个关系闭合它。那个问题作为棘手或无利可图被搁置一旁，而那个配置失去那个化合价。这是最被制度压力所鼓励的失败，因为那个被放弃的问题不留下痕迹被交代。

7.3 那个能力的诸先例

那个能力有一段比理论更长的实践历史，而三个先例确立它是真实且可训练的。

禅公案实践，如§4所铺陈，是在持续压力之下对一个未决问题的刻意诱导与维持，带那个传统明确地主张那个最终生成的深度正比于被维持之疑的深度。那个触发特征性地是微不足道的且总是偶然的。

薇依的注意以接受性的语域描述同一个能力：思想被持空且等待、什么也不寻求，准备好接收那个要穿透它的对象，而同意志区分开来，意志无法履行那个操作。

济慈的消极能力，在1817年12月的一封信中被表述，命名那个安住于诸不确定、诸神秘与诸疑而不烦躁地够向事实与理性的状况。那个表述在起源上是审美的而在内容上结构地同一，而它供出那个术语最清楚的英语陈述。

三个之间没有接触的传统收敛于同一个能力是那个能力是认知一个真实特征的证据。当下说明所添加之物是它的功能：那个被维持的关系是一个偶然现象能借之耦合的化合价，而那个能力因而是生成的一个条件，超出它作为一门品格纪律的站位。

7.4 那第二个条件

维持是必要且不足的。一个关系可被持开多年，而那个会耦合到它的现象被例行地遇到并被例行地归档于别处。这是下一节所处理的条件，而那两者一起是那个中心主张断言为共同必要之物。

§8 关系结晶与相遇的封锁

到此为止的说明关乎一个个体相遇。它向知识架构的延伸从一个单一观察随之而来：那些分拣诸现象的范畴判定哪些相遇能发生。

8.1 局部相干

一个学科是一个关系结晶。在它之内，诸方法、诸标准、诸词汇与诸范例被相互调整，而那个调整是那个容许工作进行之物：一个共享词汇许可论证、诸共享标准许可评估、诸共享范例许可训练。这个局部相干是生产性的并是胜任的条件。

那个冶金学的比喻在多于名义上贴切。一个多晶固体从它的晶界派生它的强度，晶界阻碍位错的传播；霍尔–佩奇关系使屈服强度随晶粒尺寸下落而增加，以致一个许多小相干域的材料胜过一个大的均匀晶体。带被结构化边界的局部相干产生均质性所不产生的诸性质。被应用于知识，那个比喻推荐诸学科并推荐它们的多重性。

8.2 一个边界的本体论化

那个失败在一个确定的点开始。一个组织工作的边界被当作世界中的一个边界，而局部相干被读为本体论独立。那个学科于是主张它的诸对象是它自己的、它职责之外的诸问题关乎其他诸对象，而那个划分追踪诸事物之间的一个分割。

那个对相遇的后果是直接的。这一种类的一个边界在一个观察者能遇到它之前分拣一个现象。那块晶体被归档于晶体学之下，而归档是§5所描述那一种类的一个闭合操作，被一个制度所履行并被那个个体所继承。那个已内化那个划分的观察者遇到那块已被分拣的晶体，而对一个关于政治复数性之问题的关系在那次相遇发生之前已被封锁。在架构层次的封锁与在个体回应层次的闭合是在两个尺度上的同一个操作。

主张5（局部相干与那个被本体论化的边界）。 学科诸边界是关系结晶，其局部相干是生产性的。封锁始于局部相干被当作本体论独立之处，在那一点那个边界在一个现象与一个问题能相遇之前把它从那个问题分拣开来。那个失败是把一个工作的划分当作诸事物之间的一个分割。

8.3 那个既存分析与所添加之物

科学社会学已确立这些边界的被建构性质。吉尔因（1983）把边界工作分析为科学与非科学的修辞划界，为专业目的被承担。斯塔与格里泽默（1989）辨认可塑到足以在诸社会世界之间行进且稳健到足以维持身份、许可没有共识之合作的诸边界对象。加利森（1997）描述诸交易区，在其中诸亚文化通过局部交换语言协调而同时继续意指不同的东西。

这些说明是描述性与社会学的，而它们确立那个前提。此处所供出的延伸是一个关于生成的后果：一个被当作本体论的划分支配哪些相遇可得，以致学科独立的代价被以没有参与者观察到的被放弃诸耦合支付，因为一个被封锁的相遇不留下记录。这把那个社会学发现连到那个认识论发现并辨认跨学科性是为了什么。它的价值在于对一个划分曾封锁之诸耦合的恢复，而这是一个比通常支持它的对宽度之诉求更强且更具体的理据。

8.4 那个个体条件与结构条件的合取

那两个条件现在能被一起陈述。一个配置必须携带活的且未决之诸关系，那是§7的那个个体条件。而那个观察者工作于其内的架构必须把那些相关边界留得可渗透，那是本节的那个结构条件。任一者单独是不足的。一个带被维持之开放问题的学者，在一个把每一个进入现象分拣进一个外来隔间的划分之内工作，从偶然生成无物。一个在一个可渗透环境中而没有开放问题的学者正确地归档一切而也生成无物。

§9 吸收与放大的动态

那个说明的诸术语在动态系统的语言中有一个明显的对应物：一个开放关系、一个扰动、一个门槛，以及一个扰动向一个持续状态的转换。本节为一个最小模型发展那个对应物，带两个目的。第一个是显示§8的两个条件能被一个单一参数所承载。第二个是给一个被浪费偶然与一个被转换偶然之间的区分一个确定的形式，在这样一个模型中那是一个门槛。

9.1 那个模型的形式

设 $x(t) \ge 0$ 测量围绕一个关系系统之内一个开放关系被维持的生成活动。两个倾向作用于它。

第一个是闭合。留给它自己，一个开放关系解决：那个问题接收一个答案、那个现象被归档于一个可得范畴之下、那个困难被搁置一旁。一个线性衰减 $-x$ 表示这个，把那个系统返回到 $x=0$，那个其中没有关系被持开而每一个到来的偶然被吸收而无效果的状态。

第二个是生成对它自己的返回。已被生成之物变得作为下一个耦合的一个项可得，以致已在进行的生成使进一步生成成为可能。这个返回饱和，因为一个系统持关系开放的能力是有限的。一个饱和的自催化项表示它，带 $r>0$ 汇集那个返回的强度：

$$ \frac{dx}{dt} ;=; -x ;+; \frac{r,x^{2}}{1+x^{2}}. \tag{1} $$

那个参数 $r$ 承载§8所发现为共同必要的那两个条件。它随那个配置一侧的被维持非闭合并随那个架构一侧的可渗透性上升，而它随任一者下降而下落。一个其诸问题快速解决的系统，与一个其诸边界把每一个到来现象分拣进一个外来隔间的系统，无论它们的知识储备都有低 $r$，那是§7中所主张之专长同接受性之独立的形式对应物。

9.2 诸区制与那个临界值

那个原点 $x=0$ 对每一个 $r$ 是一个不动点，而它自始至终稳定，因为那里的线性化给出 $-1$。那些剩余的不动点解 $x^{2}-rx+1=0$，以致

$$ x_{\pm} ;=; \frac{r \pm \sqrt{r^{2}-4}}{2}, \tag{2} $$

它对 $r \ge 2$ 是实的。那个模型因而在 $r_{c}=2$ 处有一个鞍结点分岔，在那里那两个根在 $x_{c}=1$ 重合。图1显示那个由此产生的结构。

图1。 方程（1）对着那个耦合参数的诸不动点。实线诸分支是稳定的，虚线分支不稳定。在 $r_{c}=2$ 之下那个闭合状态是唯一的吸引子而每一个扰动被吸收。在它之上一个持续状态 $x_{+}$ 变得可得，从超过那个门槛 $x_{-}$ 的诸扰动可达。

三个区制随之而来，而每一个对应于一个较早诸节以散文描述的条件。

对 $r<2$ 那个闭合状态是唯一的吸引子。任何量级的一个偶然衰减，而那个系统返回到那个其中无物被持开的状态。这是§5那个审美终点与§8那个被封锁架构的区制，那个模型把它渲染为一个被看两次的条件。

在 $r=2$ 那个持续状态在 $x_{c}=1$ 出现，而那个门槛与它一起出现。

对 $r>2$ 那个系统是双稳的。一个在 $x_{-}$ 之下的扰动衰减而那个偶然被浪费；一个在 $x_{-}$ 之上的扰动被放大并安定于 $x_{+}$，在那里它无进一步输入地持续。从一个扰动到 $x_{+}$ 的轨迹是§6的定义2所描述的过程：一个在那个场域之内被生成的偶然被转化为那个系统继续生成的可能。

9.3 那个充分偶然的门槛

那个门槛 $x_{-}$ 随 $r$ 上升而下落，从临界处的 $x_{-}=1$ 朝大 $r$ 的零。一个关乎那些案例的后果随之而来。产生一个转换所要求的偶然量级取决于接收它之系统的开放，以致一个在强被维持非闭合之下持关系开放的系统能被一个极小量级的偶然所移动，而同一个偶然到达一个近临界的系统被吸收并失去。

这产出对一个诸传统记录而不解释之模式的一个读法。在§4所综述的诸说明中，一个在数年被维持之疑之后所抵达之解决的触发特征性地是微不足道的：一颗石子对着竹子、一道山谷对面的花、一个透过一堵墙听到的孩子游戏中的短语。那个触发的微不足道与那个被维持关系的深度立于那个模型所预测的关系。

图2。 左：方程（1）对一个固定振幅 $\varepsilon=0.70$ 之单一扰动在四个耦合参数值之下的回应。在 $r=1.60$ 没有持续状态存在。在 $r=2.05$ 那个持续状态存在而那个门槛立于 $x_{-}=0.80$，故同一个扰动衰减。在 $r=2.20$ 那个门槛已下落到 $x_{-}\approx0.64$ 而那个扰动被放大，带一个通过一个鞍结点附近之轨迹所特征的缓慢趋近。在 $r=3.00$ 那个门槛立于 $x_{-}\approx0.38$ 而那个转换是快速的。右：那个门槛振幅对着那个耦合参数，把被转换的诸扰动同被浪费的诸扰动分开。

图2显示两个特征。在左面板中一个固定振幅的扰动遇到四个系统并有三个命运，那是§5那个两观察者材料被一般化：那个差异完全躺在那个接收配置中。在 $r=2.05$ 的情形配得上特别注意，因为在那里那个持续状态存在而从这个量级的一个扰动保持不可达。一个系统因而可拥有转换的能力而为缺乏充分量级浪费一个给定的偶然，那把§8的失败、在那里根本没有耦合可得，同一个程度的失败区分开来。

在 $r=2.20$ 的轨迹显示鞍结点附近运动所特征的拖长趋近。一个在接近那个临界值处发生的转换需长时间巩固并在整个过程中保持脆弱，因为一个在那个通过期间的进一步扰动能把那个系统返回到那个闭合状态。这为一个洞见在一个勉强开放的配置中到来是易被失去的那个观察供出一个形式对应物。

9.4 那个例示的站位

那个模型凭它所展示的结构挣得它的位置，而它的恰当性停靠于三个对应：在那个衰减项与闭合之间、在那个饱和自催化项与生成对它自己的返回之间，以及在那个耦合参数与被维持非闭合连同可渗透性的联合条件之间。每一个是一个关于那个散文说明所描述之物的主张，而每一个可独立于其他被反对。

什么会把那个例示提升到一个工作意义上的模型在此为记录被陈述。它要求一个 $r$ 在一个研究设定中的操作量度，§12把它辨认为那个首要开放问题；一个 $x$ 同一个配置中某样可观察之物的独立辨认，为它被维持之未决问题的计数是那个明显的第一候选；以及一个对一次持有若干开放关系之诸系统的处理，在那里方程（1）成为一个耦合系统而诸开放关系之间的诸耦合成为有旨趣的对象。§10中所辨认的那个反身情形，在其中那个被生成意义改变那个现象，会作为从 $x$ 到那个扰动本身的反馈进入这样一个处理。

§10 跨诸领域的案例建构

七个案例随之而来，从六个领域汲取并被建构以关乎那个说明的不同元素。三个与同一领域中的一个否定对应物配对，因为那个说明的诊断内容一如在诸成功中那般躺在诸失败中。全部从已发表的记录汲取并为例示被发展。

10.1 材料科学与政治复数性

那个晶体情形现在能被给它的结构。那个配置携带一个关于一个政治秩序能否把诸相干语言世界的一个复数性持在一起而不把它们还原为一个共同媒介的未决问题，一个抵抗解决的问题，因为那些可得答案显得要求要么一个共享语言，它压平，要么一个被接受的碎片化，它消解那个秩序。

那个现象有一个确定的结构。一个多晶固体由诸域组成，每一个内部有序、在取向上不同，在既不把诸域彼此消解也不把它们分离的晶界相遇。霍尔–佩奇关系确立那些边界对整体的强度作出贡献。成核与生长凭局部规则进行，没有全局模板。

那个耦合生成一个第三项：一个由内部相干诸域组成的秩序，其完整由它们的诸边界所维持，带那些边界作为关系的诸场所起作用，而带整体的强度从那个被结构化的异质生起。这既非一个关于诸矿物的事实也非一个在先的政治立场，而它进入多语言复数性理论的转置提起它自己的关于什么对应于取向与位错的诸问题。那个案例例示那个产物的第三性与那个现象结构的参与。

10.2 宇宙学与噪声的解释

宇宙微波背景的案例是现代记录中一个信号遇到两个配置的最清楚实例。

1964年彭齐亚斯与威尔逊，用贝尔实验室的霍姆德尔号角天线工作，测量到一个在4080兆周/秒约3.5 K的过剩天线温度，他们无法消除它。他们的配置是带一个仪器问题之无线电工程师的配置，而在它之内那个信号是一个待被交代的残余。在普林斯顿，迪克、皮布尔斯、罗尔与威尔金森 携带一个关于一个早期热宇宙之热残余的未决理论问题，并正建造一个仪器去寻找它。那两篇论文一起出现在1965年《天体物理学杂志》142，那个测量与它的解释（彭齐亚斯与威尔逊 1965；迪克等 1965）。

那个案例在三个方面有教益。同样的信息对两方都可得，而只有一个关系生成一个宇宙学意义，那是那个两观察者材料在它最纯的形式。那个普林斯顿配置在所要求意义上开放：一个问题正被携带而没有一个被判定的答案。而那个生成发生在一个跨无线电工程与理论宇宙学之边界的耦合处，那从可渗透一侧例示§8。

10.3 情报分析，肯定与否定

同一领域中的两个插曲形成一个匹配对。

1962年10月，一次 U-2 对古巴西部飞越所返回的摄影影像在国家摄影解译中心被解释为显示一个建造中的苏联中程弹道导弹设施。那个影像是一个带车辆与被清理地面的场域。它的解释要求一个含有苏联导弹阵地布局之签名的配置，被恰恰为那个识别受训的诸分析员所持有。那张照片中的信息对任何有那张照片者可得；那个意义在一个特定关系处生起。

那个否定对应物是9/11委员会那个相关信息被分布跨诸机构、而那个失败躺在那个连接中的认定。那个委员会对一个想象力失败的刻画在当下说明上是精确的。那个信息在场、那些分析员胜任，而那个架构划分那个材料以致一个到达一个隔间的现象无法耦合到一个持于另一个隔间的问题。这是架构封锁在它有后果的形式中，而它例示为什么一个被当作真实之划分的代价被不可见地支付。

10.4 解读

罗塞塔石碑1799年被寻回并保持实质哑默达二十年。那个对象的信息内容跨那个间隔不变化。所变化之物是一个配置的到来，在其中那个希腊文本、一个对科普特语的知识，以及一个关于那些王名圈之语音功能的假说被连同那个未决问题一起持有，在那一点那块石碑参与一个解读的生成。那个案例分离出那个时间性结构：那个现象等待，而那次相遇在一个能够耦合到它的配置存在时发生。

10.5 经济解释

一次收益率曲线的倒挂是一个对一个市场中每一个参与者同时可得的单一量。它被一方读为一个保证一个防御性再配置的衰退信号、被另一方读为一个被央行持有所产生因而无信息的扭曲，而被一个第三方读为一个重新定价的机会。那三个读法在对一个信号的三个关系处被生成，而那些参与者在传输意义上被同等地告知。

那个经济案例添加一个其他所缺的特征。那些被生成意义被行动于其上，而那些行动改变那个现象。这是一个反身结构，其中那个关系反馈进它自己的对象，而它标记那个如当下所陈述之说明的一个界限，那个说明把那个现象当作跨那次相遇稳定。

10.6 寻常关系

一个晚餐时顺带作出的评论被一个听者接收为闲谈而被另一个、一直携带一个关于一个决定之未决困难者，接收为那个解决它之物。那个说者两者都不意图并常较晚或从不得知那第二个接收。

那个家常案例被包括，因为那个说明应在有组织探究之外成立，而因为它以不寻常的清晰显示那两个条件。那个生成的听者正携带一个活的问题；那个不生成的听者不。两个听者都不更聪明，而那个评论为两者携带相同的信息。那个案例也显示那个归属模型的失败：被生成之物无法被归功于那个说者，说者供出一个现象而没有意义，而无法被归功于那个听者单独，听者供出一个问题而没有答案。

10.7 跨领域转移

那最后一个案例关乎一个配置与一整个领域之间的诸相遇。

埃格拉什的轨迹从一个控制论与系统工程的训练跑进民族数学，产生一个对非洲设计与聚落模式中之递归与分形结构的分析，而随后是生成性正义的概念，一个价值在它生产之点以未被异化形式流通的说明。那个模式是本文的结构在一段生涯的尺度上。一个在一个领域中形成的配置遇到另一个领域的诸对象，并生成一个两个领域都不含有的说明：那个数学不含有那个设计传统，而那个设计传统不曾以那些术语被描述。那个在先训练作为那个差异的条件运作，而那次相遇要求一个物理科学与一个民族志主题之间的可渗透边界。

可比的诸转移是众多的。薛定谔对那个非周期晶体的处理把一个物理学家的配置带入遗传的问题并参与分子生物学的形成。控制论通过梅西会议进入社会科学。统计力学进入金融。在每一个中那个被生成说明在那个出口配置与那个接收领域中都无。

那些案例能被它们的共同结构概括。

设定	所携带的配置	偶然现象	被生成的项
材料与复数性	关于复数性之内相干的未决问题	一个多晶的晶界结构	由有界相干诸域组成的秩序
宇宙学	一个早期热宇宙的热残余	不可还原的过剩天线温度	一个宇宙学模型的观测确认
影像分析	导弹阵地建造的诸签名	被清理的地面与车辆放置	对战略部署的评估
解读	科普特语、一个希腊平行文、一个语音假说	一块三语铭文	一个脚本的可行解读
市场信号	那个工具的头寸、期限与模型	一次收益率曲线的倒挂	被行动于其上的分歧读法
寻常关系	一个被携带且未决的个人困难	一个顺带作出的评论	一个被归功于任一方都不的解决
跨领域转移	控制论与递归的形式体系	一个不熟悉的设计传统	一个在任一领域中都不含有的说明

§11 探究进行中的机缘

三个后果为探究如何被进行与被组织随之而来。

11.1 那个现象的站位

机缘在研究政策的文献中已被当作一个边缘的发生，有价值且不可管理，待被在受指导纲领的边缘被容纳。此处所发展的说明把它不同地安置。倘若意义被关系地生成，而倘若一个研究纲领在于维持诸问题并遭遇诸现象，那么机缘是新意义之到来的寻常形式而受指导搜索是那个目标已被事先规定的特殊情形。那个规定在那个答案是一个已知种类之处是有效的。在它不是之处，那个规定事先排除那些会供出它的诸耦合。

11.2 无计划的培养

那两个条件都对刻意的行动可服从，而任一者都不等于计划一次相遇。

在那个个体一侧，那个被维持的开放问题是待被保护的单位。这有实践内容。一个研究者能保持一个未决困难的书面记录并重访它、谢绝凭第一个恰当答案解决一个问题，并把一个开放问题的不适当作一个工作状态对待。§7中所辨认的那个代价指示那个压力将从何处来，而一个只计数安定产出的制度正持续地施加那个压力。

在那个结构一侧，可渗透性是待被维持的性质。它的实践内容包括对一个人划分之外材料的暴露而不要求那个暴露被一个被期待的产出事先辩护，因为一个能被事先规定的产出会落于受指导搜索之下。加利森的诸交易区与斯塔与格里泽默的诸边界对象描述这样的暴露发生于其中的诸安排，而此处的说明供出重视它们的理由。

11.3 非闭合的纪律

那第三个后果关乎智识的进行。§7的诸失败模式都是早闭合的诸形式，而每一个有一个可敬的外表。过早解决表现为果决、审美终止表现为鉴赏，而放弃表现为现实主义。一门非闭合的纪律因而要求在履行一个闭合操作的同时认出它的能力，那是§4所综述诸传统所训练之物与此处所供出语汇意在以世俗术语使可得之物。

§12 界限与进一步的工作

12.1 那个中心主张的站位

那个说明停靠于一个关于意义在何处生起的主张，而那个主张容许没有直接观察。可被观察之物是那个差异：两个配置、一个现象、两个结果。那个差异与此处所发展的说明相容，也与一个足够精致的观察者一侧说明相容，在其中那个被生成意义在那个配置中潜伏并被任何恰当触发所释放。那个偏爱关系读法的考量是那个现象特定结构的参与，因为那个复数性的多晶说明把那个晶界与那个取向随它一起携带，而不会被一个任意触发所生成。这个考量是一个程度的事，而一个潜伏理论家可主张那个结构为一个已在场的形式供出细节。那个争议是真实的并被留下开放。

12.2 诸暴露之点

四个点被暴露。

对巴拉德与 西蒙东的关系要求多于§6中所供出的相容性论证。倘若诸关系项在诸关系之内被构成，那么把一个配置描述为一个先在项需要一个更充分的关于每一个描述在哪些时间尺度上成立的说明。

§10中所辨认的那个反身情形躺在如所陈述之说明之外。在那个被生成意义被行动于其上并改变那个现象之处，那次相遇有一个当下处理不供出的动态。

那个闭合的判据已被刻画而未被操作化。一个只能在事后把一个被维持开放关系同一个被放弃的区分开来的说明是一个诸案例的描述而尚不是一个评估它们的工具。

那个禅材料提起一个本文已承认而未安定的问题。倘若那个公案传统主张所到来之物总是在场，而倘若此处的说明主张它被生成，那么要么那些传统描述不同的诸现象要么一个描述是错的，而那些案例不在它们之间裁定。

12.3 进一步的工作

三条线随之而来。

第一条继续§9中所开始的形式处理。那里的例示携带一个单一开放关系与一个单一标量参数，而那些要紧的问题躺在两者之外：一个一次持有若干开放关系的配置、它们之间的诸耦合，以及在一个关系处的活动抬高或降低另一个处之门槛所处的诸条件。那个反身情形，其中那个被生成意义改变那个现象，在同一点进入。

第二条是经验的。§7中所陈述的期待，即机缘集中于配置携带未决关系且边界可渗透之处，在研究轨迹被记录的诸设定中对研究可服从。跨诸领域的诸生涯，以及带被放弃与被复活问题之被记录历史的诸实验室，是那些可处理的情形。

第三条关乎本文与它所属之治理纲领之间的关系。倘若封锁是一个关于知识如何被划分的结构性质，那么维持可渗透性之诸制度的设计是一个治理问题，而这样的诸设计会被评估所凭的判据不曾被供出。

---

一则关于诸传统之处理的附记。 §2到§4中的诸综述跨越诸文献，当下作者在其中不持有专家站位，而它们在结构比较的层次上被供出。在一个传统已被一个单一学说所刻画之处，专家将发现那个刻画单薄，而在三处那些内部争议被顺带标记：加扎利机会论的范围、龙树是否推进一个肯定论题，以及对汉森之解释反对的站位。那些比较被划出以定位那个说明，而会重新定位它的诸改正被欢迎。

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