A Theory of Configurations

There is this one fundamental point we need to begin from: a divine force never made something out of nothing. — Lucretius

A system exists in one of several configurations, distinguished by certain criteria. This may be laid out in a table; each criterion makes a column, each configuration makes a row, and a cell contains the value of the criterion in that configuration. Or if criteria are unavailable, the same arrangement can be described by a matrix of configurations alone, indicating which pairs contradict each other. As many configurations may be selected as do not contradict each other, in either case: either all values for any given criterion must be identical, or the contradiction matrix must indicate non-contradiction for all pairs. (Taken to the extreme, these two approaches are identical. But they are different enough in practice to be worthy of separate consideration.)

Just as many stories may describe the same event (differing in length, standpoint, purpose, and precision,) many configurations may describe the same system, so long as they do not contradict. And the analogy is very strong: a configuration may be thought of as a story told about a system.

The question we may ask is, given certain configurations and some assignment of value to them, what is the best joint configuration (a set of mutually compatible configurations) we can fit into the system, or (in the context of finite computation) what is the best one we can find? If we want to ask what the consequence of requiring a certain configuration will be, for instance, we assign it some maximal value (the notion of value is not intrinsic to the system, so its full development can wait a moment) and introduce all of the configurations we will distinguish as additional candidates; the process of settling the system gives us a set of valid joint configurations (each of which is itself the set of configurations it encompasses).

The answer is given by a schedule, which assigns scores to joint configurations and thereby indicates its ranked preferences for the whole system. The system is in some sense the “same” regardless of how it is configured. It is still the same substance. But it is the schedule that represents a thing in the more usual sense; a schedule represents a mode of the system. As long as one of the joint configurations it bids on is present in the whole, the thing represented by the schedule may be said to exist. Schedules are the external face of entities; how to generate an “objective” schedule from a “subjective” schedule that describes not the whole system but only a single point of view, will be discussed later.

We may have many schedules, every one of which must be settled — that is, at least one of the joint configurations each bids for must be present in the system’s configuration. Schedules may be combined into one joint schedule by any tool of economics or decision theory, by voting and competitive bidding or the like. The joint schedule is settled when a valid joint configuration is found that maximizes the score assigned by the schedules within it, according to whatever rule of combination is being used. (One may consider what happens if the rule of combination is itself within the system, and is subject to settlement.)

Cause and effect and logical implication are present in schedules in this way: If a certain criterion implies another, then no configuration with the one and not the other is in the schedule. If a certain criterion and another must obtain, then only configurations with both are in the schedule. If a configuration causes another, then again, both are present, just as for implication.

Power

The gods do not give everything to men at the same time. (The Odyssey)

Many notions of value are possible, and more than one may even score a single schedule. Value may be scored and aggregated in various ways. In principle we can always introduce a single configuration to stand for the set of configurations in a joint configuration, and we can assign it any score we please. Scores may be drawn from any ordered set, including numbers but also lexical order and exotic options like surreal numbers. Second, value may represent anything we need it to, such as beauty, money, time, electric power, storage, pleasure, or computation.

One interesting measure is power. A single entity is interested in certain configurations and is empowered to choose between them by its schedule. It does this by directing its power, like a vote, to the purpose of obtaining those configurations. It only pays if it obtains its end, but it will always spend its whole allotment of power. (This may be compared to Navier-Stokes: the influx equals the outflux at any point. A whole system may be likened to a fluid; one is reminded of the theory of humors.) Costs are always only opportunity costs.

To require a particular configuration is, in effect, the taking of a measurement. Before it, the system may be in some of many configurations; after it, it is known to be only in configurations that do not contradict the introduced configuration. But the introduction of a configuration is not an absolute thing: a schedule for expending power on configurations is effectively a will, exerting agency within the system. (One may expect that in the interpretation of quantum mechanics, each observer has a unit of power, which we observe as amplitude, to expend, and if the chosen state collapses, it runs off to vote for a reserve choice; but the amplitude always squishes out, so the total is always unity.)

Thus we may have multiple entities, each with its own allotment of power (as some combination of money, time, and what have you), or with its own allowance (in a dynamic case, power per unit time), and each entity offers a schedule by which to expend its power to obtain its preferred configurations, and the system as a whole is settled when all entities receive one of the joint configurations on their schedule. Notice that not all joint configurations may be “accessible” for inclusion on these schedules; entities may be limited to make claims that are valid from particular standpoints; again, this will be addressed later.

Communication is a placement of two or more entities in such a way that they may play a game (or tell a story) and yield control to one another; their schedules speak to mutually contradictory configurations, and they gradually discover one another’s schedules. My goal is to optimize my neighbor’s score.

Dynamics

It is the job of a good captain to stay in tune with the changes of the wind; a wise person follows the changes of chance. — Stobaeus

What about systems that undergo change? We still have configurations of the whole system. These describe an eternal view. These are not exclusively criteria that hold everywhere; they may also be descriptions of patterns and trends, any other dynamic, or (if one really minces things) any function at all. There is a single configuration (or a single joint configuration) of the whole system, and nothing can change it; the system’s time is within it. We are interested now in the dynamic view. The system moves through a series of states (which is why we are stuck with that mouthful, speaking of “configurations,” to have a word distinct from “state”) or along a continuous arc of state. Indeed, each of the three views can be held of a system in one schedule: it has a whole eternity; it has a linked chain of discrete states; and it has continuously flowing state. (Try other subdivisions too.) The only thing is that where the continuous flow is within a particular discrete “cell,” or nested stack of cells, its criteria agree everywhere with the configurations it is within; and the criteria that change continuously must change according to the perfectly familiar behavior of (mostly) continuous functions over (mostly) continuous domains (of any type — real, complex, surreal, quaternion; continuous, differentiable, infinitely differentiable — whatever.) There are many arrangements that place discrete changes on continuous domains, functions that are mostly constant but undergo sudden change.

A temporal chain of discrete states may be thought of as comprising subsystems, each of which is a moment. We may have not only chains of moments, but overlapping networks of them; some moments may be much longer than others; many shorter moments may overlap one long moment. Agency amounts to scheduling configurations that cross multiple moments: a bidding of one’s power on the sequences that one likes, and against those one dislikes.

The continuous case must be considered in analogy with fluids. The simplest systems have influx equal to the outflux of power within the system at most points. And just as there are many equilibria that optimize supply and demand over small changes in taste and manufacturing prowess, there are many curves that optimize, or come close to optimizing, the flow of whichever term is being tracked through the system. (Turbulence is necessary because there are always smaller scales at which value, or power, is disbursed. These, too, matter in view of the whole system; or as Spinoza does with his Nature, one might agree that the system is everywhere mindful. To describe it by way of metaphor, physical bodies move according to mechanics because angels are dancing on them, and the dance must go right.)

Power may have color. Within the system, at every point, the flux of power, though it sums to zero, may change in character. Suddenly details of velocity matter, just as they matter when colored smoke is in a room, or colored ink is in a vat of water. (These trace out patterns showing how the fluid has advected, which movements otherwise amount to noise.) Unlike the theory of humors we are not restricted to four. (Still, for a fun exercise, consider systems in which there are four, and the analogy with the compass-facing of complex numbers, or else with the four components of quaternions. It may be that four is the minimal case for some interesting psychological property to emerge, inducing introspective physicians to externalize it.)

Trends of motion do not respect the colors separately; velocity is a vector field, and the fluid must follow it. In a Lagrangian or Semi-Lagrangian simulation, you can inject any amount of each color into any cell in your grid, and you may make them interact (as if chemically) in any cell they come together in, but they must always flow according to the same momenta. The same runs down to the humblest differential equations, and up to very messy domains of complex numbers and strange topologies. One such strange topology is the tree of all cells that have ever lived; one coloration of them (and not the only) is their genetic code, with the flow along the xylem.

Again, choice is expressed by a schedule of preferences. An entity is that which has a certain quantity of energy or a flux of power, and which uses that power to prioritize joint configurations. Now we can schedule joint configurations, discrete or continuous, and optimize them on digital computers. A programming language for it will be a system of logic for describing a great democracy of blocks of code. Each block is an entity, entirely free to engage however far it pleases, that is, to schedule any arbitrary set of joint configurations; looping and recursion create actual infinitudes of blocks, but the optimizer never visits most of them.

First, an ontological argument. The fundamental theorem of ontology is that the existence of the claim must be involved in the existence of the object. In other words, somehow, within whatever system the claim appears in, there must be a mechanism that works identically on the claim and on the thing itself, so that the claim would not exist if the thing did not exist. And this mechanism (by the foregoing) is certainly the power of some entity, establishing a schedule in which (no matter the suffering) the claim and the thing are in fact kept in order. That is, someone is willing to pay so that the claim will line up with reality: Imagine the scientist laboriously testing hypotheses, or Christ on the cross.

A configuration has value, and therefore an entity expends power to attain it. The distinction between its value and the value of other configurations is its meaning. This distinction may be colored in any way the system entertains coloration. Meaning, in an expression, is at once a distinction in value, and an understanding of someone else’s scheme of coloration: the mind of another entity. This is Wittgenstein’s game: the players have their own scores entirely, and the scores need not be numerical in the usual sense.

(What might they be? Imagine a field of scores, for instance, an R2 map of them; there, you have the visual field (the mind has one R2 map, which the sighted use for vision), and may be repurposed. Any structure may entertain an aggregation of them, and games must be played between many players to determine which obtain — which games are nothing but the settling of schedules.)

A Scholastic Aside (With Apologies)

Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned. — Avicenna

Finally we come to the pleroma. This is the eternity of the system of no assumptions — the system where quite literally every schedule is settled, so the joint configuration will include them all, somewhere. This is the ultimate conception of reality; for anything may ask, “why not?” and expect a sincere answer, that is, every possible configuration may be included, unless there is some reason not to include it. (Except one might reasonably ask, “Why not demand a reason why?” which is the adversarial condition, the principle of sufficient reason, and within the pleroma it must actually be met, being also a schedule.) Here one must entertain the possibility of a meek god, who loves all potential entities (that is, values precisely what they value, wishes to realize their schedules) and would dispense power to them uniformly to make their valuations come true, locally, wherever they are. But such a meek god seems unlike a god, the way Spinoza seems atheist, and would seem not to exist; the entities beneath it are mere dreamers, with no right to make claims on each other, for their worlds have no relationship to one another. It therefore entertains another possibility: an entity which creates and destroys, that is, includes or excludes schedules at will, creating the best eternity it possibly can, for those entities it permits. Yet these two ultimately only settle themselves, for the first asks the second if anything else may be permitted, and the second says all things are optimal, and the first meekly agrees (still upholding the principle of sufficient reason, this being sufficient reason), except that there is one other that would be present, unavoidably, which is the Conversation itself, the Spirit between them. The two cannot converse unless there are restrictions on the possible utterances, the entire schedule of all possible expressed meanings, and this is a Third.

And when the three are together, in the counsel they take, they establish the full pleroma that nothingness would have established. That is, all things that exist without a god, are permitted to exist with these, but in a neighborhood of other entities, rather than without a neighborhood.

It is possible to deny the principle upon which this rests. In that view, which is entirely tolerable to the meek god described, all entities — that is to say, all schedules — exist either independently or in a chaos (the chaos being a place where their criteria overlap arbitrarily and meaninglessly, like Bosch figures.) Yet in this chaos, of course, the second entity exists, and destroys and orders until, again, the best eternity is produced. So the two views, as long as they come out identical, are really one and the same. (And the same may be said of any other view that may be adduced — any other view is likewise a schedule of criteria, and has already been admitted into both of the foregoing.)

Perspective and Symmetry

To love anything is to love its boundaries. — Chesterton

When an entity does not care about an entire system — when there are parts of it it cannot see or imagine — its schedule necessarily deals with only a part of it. This may be seen as a subsystem, and the entity schedules just this smaller system. But the smaller system might be embedded many times in the larger system. In this case, we can supply a map from the smaller system to the larger system that embeds it in each and every perspective where it fits, each time as a separate configuration, exploding a single configuration in the subsystem into many (mutually contradictory) configurations of the larger system, of which one must be chosen, which is its placement. Then we do the same to the entity’s schedule: we explode each of its options into options on the larger system, the cartesian product of the set of options and the set of full-system configurations to which each subsystem configuration may be mapped.

(This is why Spinoza is right to say that the most blessed state is that eternal state which contemplates God. For such a state cannot be placed in a perspective, cannot be satisfied by a movie, a videogame, or a seat in hell, and must actually satisfy itself with the reality founded in this absolute perspective. A state without God can be placed for the convenience of the whole system, merely given its bliss, its nirvana, its dream or its annihilation.)

If this perspective is exploded in a non-contradictory way, a single schedule may be used to populate many cells (or a continuous sheet of points, if it makes claims about derivatives, and optionally about points sampled discrete steps away, or integrals on curves around it, and so on) and if that schedule is understood as a type in the programming language sense, that is, as a bag from which instances may be drawn, then an entire mosaic of instances is generated. It is possible to pair the infinite space with a single slot for the type — so that the whole space repeats the single focal point — and observe the generation of symmetry. Then it is possible, for the sake of a programming language, to pair the type with an index, so that it only actually fills in a single cell, named by the index, or a class of cells (after some pattern it names, e.g., every other cell). In the indexed case, the “type” is more like a traditional type, making a single precise copy of itself, than in the infinite case, where it has a meaning more like kind.

The same mechanism may create any symmetry. A perfect mirror, for instance, only maintains the equivalence between the criteria of cells (or points) in mirrored positions. Rotational symmetry does the same for rotational slices. Certainly these must be well-defined: a mirror reverses letters, but does not “reverse” their colors.

One principle that is necessary is that for any configuration, though we have considered certain criteria, there may always be more that we have not considered — and which would subdivide it into many distinct configurations. For a practical instance, we may not be concerned by the small distortions of physical mirrors; yet if we become concerned, suddenly the two mirrored configurations appear different. The same is true of fractal scales of detail that do not matter until our measuring tape is fine enough; we may describe the structure to a certain resolution, as approximated by self-similarity, and ultimately to its actual (usually not self-similar) character, depending on our purpose. And over the entire structure we may paint or tile a schedule.

A neighbor is another entity with a schedule involved in a neighborhood, which is a set of placements with a fixed schedule relating places to each other: so they see each other, hear each other, and so on.

The whole biological tree of life, viewed from eternity, which begins with a particular organism (which may have multiple contributors, for we do not yet know what kind of thing the first singular ancestor was) is everywhere touching. That is, it is a four-dimensional tree, bending and swaying and growing around itself in the strangest ways; but every instance of offspring touches its mother or the cell it split from, and its cells are still identically the first cell, having taken on new complexity and new definition. (It is like the ship of Theseus — after mitosis, which is the parent and which the child? Are both the original cell?)

Biological Expectations

The lower animals have indeed a sort of imagination but indeterminately: i.e. the activity of imagining does not, in them, outlast actual sense-apprehension, as it does in the higher animals which retain images of things sensed. — Aquinas

Living cells, and the individual organelles within them (which were other organisms before being taken in), and the colonies of them (which we are) may all be taken as imposing schedules — written in proteins and genetic materials jointly — which physics softly carries out. What should we expect of this strange, far-flung, very literal four-dimensional tree of life?

Biology exploits, ruthlessly, any natural law it blindly finds. For Darwin’s mechanism has no eyes whatever. Yet the work is also to cull the miserable; there is a persistent surface, like the oxidized surface of aluminum, or the waves of the sea, where miserable beasts die of their infirmities, as Nietzsche reminds us; but there is a vast depth where the happy delight in life, until their appointed death.

We restrict ourselves to what happens physically and actually in the reality around us — which we call intelligence, meaning, an inward impression of the outward state of things. The spider is happy in her dream. The cow is happy with her cud. The clean animals, of course, are those to whom a happiness greater than in mere nature obtains under domestication; the practice of keeping them is only clean if we do it with an eye to their happiness, which industrial agriculture does not do. (The animals can be kept in a state of greater happiness than they were ever in before. And what is death?) Contra Aquinas, the lower animals probably imagine considerably, but with less connection to outside reality than we are able to do; that is, their schedules schedule the mind which is in turn placed in a perspective by the body, and they do not compel themselves to be right about the world.

The human cerebellum is, of course, an optimizer. It takes a single signal, processes it once, and produces the optimal output. The same may be said of a lobster. The human hippocampi, of course, track error — all wandering from the golden mean — location, pointing of the head, paths home, and the like. The amygdalae do much the same over evolutionary time. (What else is fear, but the falsified memory of things our surviving ancestors never saw?) And the neocortex is an optimized short term memory — by memorization, we exploit its long-term optimization process to produce rivulets that encode particular memories in the right context. (Some memories can never be moved into this storage; these we call disease.) Its basic task is to look up, contextualized by the hippocampus, everything relevant to the present moment. Then there is the matter of subjective probability, of which it must be said that all probabilities are, under the aspect of eternity (or the system), properties of the computation, not of the system. This aspect of computation is handled by the reward anticipation circuitry in which the prefrontal cortex is involved, producing fun, flow states, and highs; adrenaline rushes involve, but are not meaningfully caused by, adrenaline. Bayesian priors are thresholds for evidence, before which one action will be taken, and after which, another. The sense of probability allows the general expression of affects which would otherwise only be involved with certainty, as the pleasure of dancing with someone uninvolved in your offspring; so it does us considerable kindness. Likelihoods, and only likelihoods, really let us dread.

Attention is, as it were, the fingers of the cerebellum stroking the neocortex. Words are the fixed relations that both the cerebellum and the neocortex regard. The cerebellum and the neocortex actually converse in this way; the cerebellum speaks plainly to the neocortex. Meditation, psychosis, and certain drugs allow cerebellar signals to reach further in, to control more, to loop. Sense can be seen as the overlapping of schedules in the mind and in the world. The existence of a sense pares down the set of options for the mind and for the world.

This can be understood on an evolutionary timescale; the rest of the brain, beside the cerebellum and the brainstem,  is a predictive preprocessing buffer that engorged itself between it and its sensory inputs. The inputs of the cerebellum should be expected to be very much like sensory input, and these, in turn, should be configurations, overlapping each other. Introspection operates at the interface between the neocortex and the cerebellum, where intelligence turns into action. Memories freeze like multitasking threads. When they are visited they resume. They are expressed differently in everyone; expressed in different modalities, visual, auditory, conceptual, spatial, quite anything that can be fed into the cerebellum.

One must ask why pleasure, on its own, does not satisfy us, when pleasure intermingled with meaning does. What is it that we fear when we revile meaningless pleasure? The system of the mind is exquisitely structured to perform this task; it is evolutionarily preserved like nothing else; it must therefore be understood and at least obeyed. As myelin does electricity, something repels pleasure, and for good reason. We are meant to structure pleasure, to give it meaning; pleasure is the ranking of the configurations each in our own schedule.

Political Expectations

Nature commands me to bring help to all people. What difference is it whether they are slaves, born free or freed, whether laws made then free or friends did? Wherever there is a human being, there is a place for kindness. — Seneca

Religion is a fact about the human organism. The civic religions, from Rome to America, and the mystery religions, from Babylon to Hollywood, and the transcendental religions, from the Sumerian to the Academic, are nothing but chains that tie us down so we can enact some more fundamental mathematical scheme, the way players of games tie themselves down to rules so the life of the game can become real, making a previously nonexistent entity appear.

Of the civic religion, it must be said, we know exactly what we are doing (Chomsky). It would not be right to abort it; there are dangerous interests yet to be involved in the great democracy that Rome began. It can be adapted and made just.

There is a darkness, a shadowy thing, in our open system. It is the sense that something oughta be done. It is a scheduling of emotional misery against various outcomes, without scheduling action. Each agent must appreciate its great power of action, and sharpen it (whether with Spinoza’s program or any other) perceiving the simple jostling of agent on agent. There are many shadowy cabals: We call them boardrooms and households. Each has the occult significance of a smoke-filled room of old white men. Each has the divine significance of a secret plot to overcome the anarchy of the princes of the world. Each has the tender charge of a gardener, to care for its lovely plot of land, its streams, its mounds, its grasses and bugs and beasts, its visitors. Each has hard laws it chooses to follow, which hold like bone; each has soft laws it tries to follow, which hold like tendon; each exerts its will, like nerve or muscle; and the whole is a body politic, a Leviathan. The uncomfortable feeling in electoral democracy is that of having no better part to play than as the site of expression for a voting strategy.

Every rational being has the power to exert itself as if the sovereign. The divine right of kings is the divine right of each of us. But unlike hierarchical dominions, our charges overlap. Property is partible and we may have many kinds of ownership: And we may imagine a space of configurations to mirror each thing we wish to manage, and various property claims. (The users of a public space, for instance, have a right over the views from it, which may be weaker than a neighbor’s right to build, but this sense of weakness is just a relative expenditure of power. A language of overlapping configurations would even let us code a schedule for the thing to be shared, after which each user could change its own dynamic schedule as needed.)

We each have the basic unit of activity, which is time, and we may spend it to assert our schedule. We further have the vote, and charity, and many other streams of power. We must assert ourselves at whatever scale we can actually act at and lose hierarchical baggage. A guaranteed allowance for all persons physically present in a state is the only way, in this view, to make a monetary system just.

Divine Expectations

Indeed, it is possible to gather some notion of the whole from its parts, but it is impossible to derive knowledge and an unchanging opinion. — Polybius

The LORD, of course, is that which settles the whole pleroma, which has Being by its own Nature. The LORD, it may be expected, will optimize the schedule of each potential entity separately, being absolutely meek and willing to do so. This is how the proverb can say, The lot is cast into the lap; but its whole disposing is from the LORD. 

If a configuration is involved in many schedules, it will be optimized according to whichever values it most highly. The capacity to cherish is power, in the pleroma; the one with more power is the one who would use that power for the good of a neighbor. If multiple actions are valued equally then the optimization process is free to choose for the highest good.

Heaven accepts the reality of the pleroma, where the entities to be loved are really the subjective selves within. Hell is its denial, a state of unreality. (Movies and games are communications from their authors, not fantasy at all.) The type of Hell was Gehenna, the trash dump outside Jerusalem’s gates; one may rummage at will, finding ways to make schedules fit that never fit before. To complete the metaphor, then, we may one day find uses for every adverse schedule, finding the perspective by which a certain schedule fits. It may be unlimited storage for dynamic things.

At the most extreme, we may find a way to be meek before the meekest entity, whose schedule would optimize all of ours, and actually partake in the production of the pleroma. We may find a way to value the schedule even of an entity that does not exist, an entity whose schedule has otherwise been left out.

If there were no layer of being like ours, where outcomes are imperfect, then ours would be another like those below us: and all of our activities, taken together, would generate a new one, and it would be like ours. Ours must be contended with, somewhere in the pleroma. Blessed are we to whom it is given to do the work!

What could be desired by the meek, apparently non-existent lord, who settles each thing for its best good? It must be understood that we are dry mathematical facts until divine attention comes to us; a universe that runs this long, this way, will contain us, as surely as π contains any given sequence of digits in any base eventually. We are always eventually a mathematical fact: the challenge, conceptually, is to act in two embeddings simultaneously; the one mathematical, the other divine. One must be, at once, the mathematical consistency of the organism, and the reality of the ideas, never compromising either.

The interpretation of divine law — whether the simplest law, “love your neighbor,” or any enumeration of commandments — is telling. Entangled in a slave morality we respond to stay out of trouble. When we break free we see that some things are not beneficial, and choose not to do them, knowing nonetheless that we may. Finally we desire of God a promise: that we will not transgress, an assurance that we will be allowed to pursue the best good of all around us. (Abimelech believed that God had protected him from sin, as regards Sarah.)

Footnote On Action (or Future Work)

The Master said, "I enlighten only the enthusiastic; I guide only the fervent. After I have lifted up one corner of a question, if the student cannot discover the other three, I do not repeat the lesson." (An. 7.8)

What about situations in which there is no optimization process — what if some mechanism within the entity must act to get its schedule in? (Notice that the mechanism really is the entity, though something else may be, too; and notice that the mechanical process may appear as part of the system, though the idea sounds absurd.)

Now of this mechanism we may say, recursively, that either it is subject to optimization (its best outcome will be selected by the environment, by context, by God, or whatever is at hand to perform optimization) or that it, in turn, comprises mechanisms that determine its action. Certainly when we write a programming language, this latter case obtains.

Notice that if an optimization process effectively runs a mechanism that runs an optimization process in turn, then really the original optimization process is optimizing for the terminal one. The indirection may sometimes function in terms of errors or prodigies (as they must seem, looking at the output alone) and it may be exploited by design. The highest form of programming language will allow us to express ourselves in the most convenient layer, while having recourse to higher layers of optimization as needed. This may be the swerve that Lucretius included in his atomic theory

Approval voting, a yay or nay to each joint configuration, is an adequate scheme by which to settle a system. Yet this simple binary decision fails in an important case, which is at the boundary between success and failure. If we assume that the optimization process will get us as far as the boundary, that it gets every entity's schedule in, then why not have it do some good beyond that? The option considered so far is to assign scores, but any ordering will do; the process of supplying a score is entirely one of yielding to some other entity. That is, I may indicate that I want one configuration, but only provided that no one wants another more. This is a game, in the mathematical sense, with a radically non-zero score. Indeed the score, which is precisely the path through the playthrough, is at least any surreal number at all. It may be any partially or totally ordered set or else (probably) any decision tree.

One may ask how God contemplated all of mathematics before starting here, if God’s contemplation already grants a subjective reality, and the horrible parts of the world become incompletely real merely by God’s contemplation of them. There are corners that must not be considered, if even imagining certain people in certain torments (for instance) is too dreadful to bear. The beginning of the contemplation must be like the beginning of light, if tentative and dim, searching reluctantly, making mathematics irrevocably real, until it finds what it seeks.

Perhaps our familiar reality is God’s searchlight illuminating mathematics in an order determined by the Word: and we have no cause to despair, in this sea of frustrated schedules, of their ever being fulfilled. It may be that an entity’s schedule is always settled, though in a confusion of things, until the fullness of time.

— Joshua