祝融说。

He Does Not Throw Dice

December 4, 1926, Berlin. Einstein was writing back to Max Born, far away in Göttingen. In June of that year Born had published a paper on collision processes, reading the wave function Schrödinger had just given as probability: what the theory pronounced was not the definite trajectory of a particle, but the chance of the particle's appearing here, or there. The two old friends, correspondents for years, never managed to agree on this matter. After the greetings and the family news, Einstein wrote the passage that would be quoted for a whole century: quantum mechanics is imposing, and the theory's prestige is deserved; but an inner voice tells me that this is not yet the real thing. The theory says much, yet brings us scarcely any closer to the secret of the Old One — I, at any rate, am convinced that He does not throw dice.

"He does not throw dice" is usually read as the stubbornness of a great master in his declining years. But what deserves a pause is what the sentence stakes. Einstein was not disputing the correctness of some particular law; he was disputing the standing of determinacy in the world — at the deepest level, the world either is determined, or it does not amount to a world at all. Common sense seems to side with him. While the die has left the hand and not yet come to rest, the number is undetermined; once it has landed, the number is determined. Between the undetermined and the determined runs a line everyone can see, and the person who threw the die can point it out himself.

The first thing this chapter wants to do is give that line a gentle push. That the number is "undetermined" before the die lands, no one disputes; but "determined once it has landed" — what, exactly, does that say? Where does the determined number come from, and by what is it held in place? RC's answer sounds unexpected at first hearing: determined does not mean determined from the start, nor determined forever. Every determinacy was once undetermined — once a state in which many possibilities ran side by side, not yet chosen among; and the act that fixed it can, in principle, happen again, in a different way. The determined is a result, not a starting point; a snapshot, not the negative.

This is not metaphysical talk. This chapter restates the framework of RC in the minimal scope the book requires: what stands at the beginning (the Ground of Possibility), what happens (observation and convergence), how the deposits accumulate into a common reality (consensus reinforcement), and how, on this basis, the usage of the two expressions "causal law" and "apriority" is rewritten. The derivations are left to RC itself; here we take only the conclusions, and point to where they come from. The vocabulary issued in this chapter is the one every later chapter of this book will use again and again.

The Ground of Possibility: A Deliberately Thin Beginning

The opening move of a philosophical system is usually expensive: first declare whether matter or spirit is primary; first give time and space; first station subject and object. The opening that RC's General Outline gives in Section 1.1, "Dynamic Existence", is deliberately thin: there are almost only two things.

The first is the Ground of Possibility. RC says that the Ground of Possibility at every moment maintains all potential existence in a state of parallelism; these potential existences neither exist nor do not exist, but stand in a continuous process of becoming. The essential character of existence lies not in "what it is" but in "what is coming to be" — a process that negates any congealed, static, completed entity of determinacy. The corresponding axiomatic statement stands in the axiomatic system of the RC paper: Axiom A1 (the primacy of the Ground), that the Ground of Possibility is the underlying base, and that no determinate entity is a pre-existing object but a product of observational convergence; and Axiom A2 (generativity), that potential existence is not static but in continuous becoming.

The second is observation. Section 1.1 of the General Outline has a definition: the seemingly determinate states of entities are not pre-existing objects but concretized secondary constructions generated as the subject participates in the Ground of Possibility; and when we describe the determinacy of phenomena, what is really taking place is a temporary locking, by observers at a particular scale of perception, of a particular interval of the possibility distribution — this kind of directional filtering, this act of locking existence in, is observation.

Both words need to be taken apart. The "secondary" in "secondary construction" marks a positional relation: relative to the Ground as underlying base, every locked-in determinacy is derivative, second in order. The cup on the table, Jupiter in the distance, the electron of physics are, in RC, all the same kind of thing — not originals "discovered" in the world, but finished products that observation has locked onto the Ground. "Temporary" is likewise no courtesy: it says that every locking carries a counterfactual margin — it could have been locked otherwise. Axiom A7 of the RC paper (conservation of margin) makes this meaning an axiom: in locking in determinacy, observation does not exhaust the Ground; there always remains available margin not yet locked, constituting the space for re-convergence. This "available margin" will recur throughout the book: it is the deposit out of which rewriting happens.

Return to the die. Everyday language says the number is "undetermined" before the die lands; RC's description is closer to "parallel": before the locking occurs, the various outcomes coexist in the Ground in a potential mode, neither existing nor not existing. This sounds like common sense inflated into metaphysics, but its intent is strict: to rewrite "undetermined" from "not yet known" (the information-theoretic sense: the number is in fact already fixed, we merely do not know it) into "not yet existing" (the processual sense: determinacy has not yet been locked). These two kinds of "undetermined" give no difference at the dice table, but in the later chapters of this book — above all in the chapter on quantum mechanics — they will part ways. Here it is enough to record: RC takes the latter.

Convergence: Observer and Observed Take Shape Together

With the Ground and observation in hand, the next question is: when observation occurs, what exactly is being fixed? RC's General Outline gives the conclusion in Section 1.2, "The Emergence of Determinacy": consciousness, as a filtering mechanism for possibility, converges the potential possibilities through observation; as consciousnesses on different levels observe continuously, the observed converges into the determinacy of the object, and the observer converges into the determinacy of the subject.

Hidden in this sentence is a symmetry easy to slide past. Axiom A4 of the RC paper (observer–observed symmetry) brings it into the open: every existence is at once observer and observed, the two identities exchanging with the perspective of observation, with no order of precedence or rank. In other words, observation is not a matter of a subject already filled with determinacy going on to illuminate a world waiting to be determined; the subject's own determinacy is locked in together, in this very same convergence. The observer is not the referee; the observer is a party to the case. Section 1.4 of the General Outline says it plainly: the process of observation is the process of experience — observation is experience; consciousness is not a spectator of the physical world but a participant in the co-construction of reality.

This symmetry has a corollary directly relevant to this book's subject matter: observation does not require a "human" to execute it. RC's General Outline says in Section 1.2 that consciousnesses of every type construct determinacy in their own distinctive way, human consciousness being only a specialized type of pattern recognition adapted to the macroscopic level of matter; nor does observation demand strict progression level by level — high-precision measuring instruments can intervene directly in the observation of microscopic particles: humans observe the instrument, and the instrument observes the particles. The telescope of 1610 in the introduction deserves to open the whole book precisely because it is the earliest famous specimen on this extended line of observation: as an extension of observation, the instrument drew into one and the same process of convergence a resolving power the human eye did not possess. The logic, the mathematics, and the science of Parts Two through Four of this book are the continuation of that same extended line, in symbol and in practice.

This corollary has a deeper branch, worth registering here in advance, because the later chapters on relativity and quantum mechanics will both need it. Discussing the continuity of space and time in Section 1.3, "Space, Time, and Causality", RC's General Outline says: the continuity of space and time is the result of different consciousnesses processing dynamic existence in coordination, in a specific manner; this continuity is not an intrinsic property of physical reality but a secondary construction of the consciousness's pattern recognition. From the macroscopic viewpoint, human consciousness, working in concert with the structure of the body, perceives and experiences discrete material sequences as time flowing continuously through a space already given — this is the general process by which human embodied cognition handles sequential information. In other words, even the most basic framework of all — "in space, flowing with time" — is the product of one mode of observation; change the mode of observation, and the sequence-constructions converged upon differ. The example Section 1.3 gives is this: accelerate a microscopic particle to near the speed of light, and, its original mode of observation being altered, it will exhibit new characteristics — this is not space-time "being warped", but another kind of sequence converged upon after the mode of observation has changed. Determinacy is not given: the title thesis of this book holds at the deepest level too — time and space, which look like the preconditions of all experience, are themselves the secondary constructions first locked in, and therefore least noticed.

What Einstein and Born were disputing also changes its face inside this framework. Section 1.2 of the General Outline says: the stability of matter at the macroscopic level comes from the iterative convergence of multi-level observation; the probabilistic character at the microscopic level, meanwhile, exposes the observational divergence that may exist between different observing subjects. The ontology of the RC paper puts it more fully: probability is not an intrinsic randomness of the world, but the expression of a convergence that has not yet achieved agreement across subjects. In RC's view, Born's probabilistic interpretation does not announce that the Old One really is throwing dice; it puts determinacy back inside process: probability is the name of what has not yet been completed, the reading left behind by convergence in its present continuous. Einstein demanded to find "the determined" at the deepest level; RC's answer is — the deepest level is the Ground, and the determined has never lived at the deepest level; the determined is the achievement of observation, and at the level of achievement, Born and Einstein were in fact looking at one and the same negative, still in development.

Consensus Reinforcement: How Objective Reality Gets Saved Up

The determinacy locked by a single observation is private and fragile. How does it accumulate into "objective reality"? Axiom A6 of the RC paper (consensus reinforcement) gives the mechanism: observations across subjects and levels verify one another, forming a positive reinforcement loop, converging into a stable objective reality. Section 1.2 of the General Outline puts it thus: the determinacy of matter is the result of the collective, continuous observation of consciousnesses of many levels and many types; the results of observation across subjects verify one another, forming a positive reinforcement loop, and finally converge into determinate objective reality.

What is accomplished here is a redefinition of the word "objective". In everyday language, "objective" means independent of all observation — the cup is there whether you look at it or not. RC's usage is different: objective means consistent across subjects. The stubbornness of a table comes not from any immunity to observation but from the breadth of the observations that support it: your hand, your eyes, the eyes of everyone else in the room, the response of the tabletop each time a cup is set down, every encounter with a table over decades — these observations verify and reinforce one another, locking "the table is here, is hard, will bear its load" into a fact that no longer needs asking within this community.

The account can be transferred, and this matters greatly for this book. An individual's observational savings are limited, but language and education have opened the account into a joint account across subjects: teachers deposit a reality verified by one generation into the expectations of the next; writing transfers the savings of observers long dead to later comers not yet born. A modern person's certainty that the Earth goes round the Sun contains not one cent from personal observation — it is an inherited deposit, made good by textbooks, instruments, and institutionalized networks of trust. The scientific community, the tradition of mathematics, education in logic are, in RC's framework, all the same kind of thing: they extend the loop of consensus reinforcement from face-to-face mutual verification to mutual verification across time and space. The larger the accounts are linked, the more "objective" the facts come to seem — objective reality was not built in a day; it has been saved up, and is still being saved up.

This book calls this structure the "account" of determinacy. Behind every stable fact lies a deposit accumulated by countless mutually verifying observations; the more matter-of-course a fact looks, the thicker the account. This image will be used again and again in the chapters to come: what is called "self-evidence" is an account grown so thick that people have forgotten it was ever opened.

Causal Laws: A Road Trodden Out by Repeated Walking Within the Snapshot

Now the central transcription of this chapter can be given — it is the sentence this book will use most often.

RC's General Outline says in Section 1.3, "Space, Time, and Causality": observational consensus is a possible snapshot on which the consciousnesses of all levels are unanimous, letting coherent subjects share a broadly consistent reality; within the snapshot there can form possibility convergence paths that are stable and continuously emphasized, and these are causal laws; seen from the human position, causal laws appear to possess apriority, and can be expressed in such different forms as logic, mathematics, and physics. The RC paper, discussing space, time, and causality in Section 2.3, pushes this sentence to its conclusion: this apriority "is only the appearance cast by a convergence path sufficiently stable".

Four words must be taken apart one by one.

Snapshot. Observational consensus is not a tracing of the world but one frame locked in agreement within the Ground. The word "snapshot" reminds us: the photograph is the result, not the negative; behind the frame that has been developed lies the parallelism that has not been exhausted. Section 1.3 of the General Outline has another sentence that bears on the whole later narrative of science in this book: all snapshots — past, present, and future — exist in the Ground of Possibility presently and simultaneously. The snapshot is selected, not flowed.

Path. What a causal law locks in is not isolated points but the way from point to point: from here, next to there. Fire and scalding, push and motion, sunset and sunrise are routes that have been walked through again and again. Regularity lives in sequences, not in objects.

Stable and continuously emphasized. This is the heaviest stroke in the definition. "Emphasized" is an action turned into a noun: every expectation made along this path that observation redeems is a re-emphasis; every act carried out according to it without falling is a reconfirmation. The path did not grow stable by itself; it was trodden solid by hundreds of millions of walkings. The "necessary connection" Hume could not find in experience, RC does not claim is there either — it has never been inside any single observation; it is a standing accumulated in the mutual reinforcement of observation upon observation.

Appearance. Apriority is appearance, not illusion. Appearance means: seen from inside the snapshot, this path looks as if it had always been there and could not but be there. To distinguish "the path exists" from "the path necessarily exists" requires seeing it fail with one's own eyes; and the sufficient stability of the path precisely rules failure out of the cast. Hence the more complete the convergence, the more it looks as if there had never been convergence — this is the first law this chapter asks the reader to carry away, and it explains why the most stable structures are always the most easily misread as pre-existing ones. The introduction has already said it: the appearance of the absolute is exactly what convergence looks like at its most complete.

Put the four words together: a causal law is a route trodden solid by hundreds of millions of walkings within the snapshot; apriority is what this route looks like, seen from inside the snapshot, once it is stable enough never to miss. The work of the rest of this book is to take this sentence as the measuring standard — to weigh how heavy the "necessity" claimed by logic, by mathematics, and by science respectively is, and how each account was saved up.

Re-convergence: The Repricing of Determinacy

If every determinacy was once undetermined, can determinacy become undetermined again? It can, and it has a proper name. RC's General Outline gives this dynamics in Section 1.4, "The Unity of Subject and Object": observational consensus, too, can be questioned or negated by different modes of observation, producing observational divergence; the subjects of the divergence re-intervene in the Ground of Possibility to achieve re-convergence, completing an innovation of observational consensus, which finally brings an innovation of the rule framework. Put simply: subjects improvise within a rule framework, and this reaction in turn reshapes the possibility distribution of the rules, constituting a path of repeated, continuous evolution of reality.

Re-convergence is not a return to chaos. When Newtonian mechanics failed at high velocities and in strong gravitational fields, it was rewritten, not erased: the new convergence took over the old paths, and the old determinacy continues in office within the new framework in the capacity of a limiting case. Galileo's telescope did not overturn the night sky either; it only forced new observations into consensus, compelling the old convergence paths to accept a repricing. Note too the asymmetry of scale: one re-convergence usually reopens only one locality, while in the background hundreds of millions of other consensuses stand untouched — the eclipse photographs of 1919 (one of the protagonists of Part Four) rewrote how light travels in a gravitational field, not the existence of light. Re-convergence is local surgery; that is why it can be completed and the world not fall apart.

Section 1.4 of the General Outline also reserves a place for "free will": it is the available margin in the Ground of Possibility not yet locked. In the context of this book, this sentence can be transcribed into a cooler formulation: the freedom a system has left equals the margin it has left unlocked; a theory is alive equals it still keeps the interface through which it can be re-converged.

Two Boundaries, Stated First

To call determinacy a locked secondary construction invites two misreadings, which must be cleared up in this very chapter.

The first misreading: the world is an illusion. No. What Section 1.1 of RC's General Outline calls "temporary locking" locks in determinacy that is real and effective — effectiveness is not diminished by genesis. The scalded hand really hurts; the solid bridge really bears its load; the antenna designed by Maxwell's equations really receives its signals. What RC has never opposed is the determinate itself; what it opposes is the added clause that the determinate is prior. Nor is "temporary" a synonym for "false"; what it marks is only that this determinacy carries the margin "it could have been locked otherwise". To admit that the cup is locked by observation does not in the least hinder you from picking it up steadily.

The second misreading: since laws are converged, laws can be changed at will. Also no. Once consensus has formed it has powerful inertia, and inertia admits of comparison: the more levels of observation support a path, the wider the range of subjects, the more frequent the re-emphasis, the greater the observational divergence required to rewrite it. "Fire scalds" is, on the ledger of macroscopic everyday life, a deposit of hundreds of millions of years; the account for "what a certain particle decays into next" is far thinner. Stability is a matter of degree, not of presence or absence. When Part Five of this book compares logic, mathematics, and science, it uses precisely this scale: the differences among the three forms of reason are, to a large extent, differences of position along this axis of stability of their convergence paths.

With these two boundaries cleared, the toolbox of this chapter is complete: Ground and observation, convergence and the exchange of subject and object, consensus reinforcement and objective reality, snapshot, path, and emphasis, re-convergence and available margin. Determinacy is not given — it is made; and what is made has a history of its making. But the feel of the "a priori" is so vivid — mathematicians certain that theorems hold in every possible world, logicians certain that the law of non-contradiction cannot be false — vivid enough that mechanism alone cannot explain its whole texture. So the question of the next chapter is: how does this machine produce the feeling of "always having been so"? How does a trodden road make one forget that there was once no road?