祝融说。

A Plank with a Groove Cut in It

In 1638, in Leiden, the Elzevir press printed a new book: Discourses and Mathematical Demonstrations Relating to Two New Sciences. The author was not present. Galileo Galilei was at that time under house arrest in Arcetri on the outskirts of Florence, seventy-four years old and completely blind; the manuscript had been smuggled out of Italy by friends, and this was the first book of his whole life to be published without examination by the Church. The two interlocutors of the book discuss two new sciences, one the strength of materials, the other motion. On the Third "Day", the interlocutor Salviati describes an apparatus plain to the point of austerity.

Take a wooden beam about twelve cubits long and about three fingers thick, and cut into its side a straight groove a little wider than one finger; line the walls of the groove with parchment and polish them as smooth as possible. Then take a hard, smooth, and very round ball of bronze. For timekeeping, no pulse and no song: take a pail of water — a thin tube soldered into its bottom lets the water drip evenly — catch the outflow for the whole time the ball spends rolling down the groove, and then weigh the water on a precise balance. Each fall corresponds to a puddle of water, and the weight of the water is the time.

We call it today the inclined plane experiment. It is worth pausing over every detail of the apparatus to ask: why this, of all things. The beam has a groove — the ball can travel only along one straight line; the groove is lined with parchment — friction is pressed to a minimum; the ball is of bronze, dense and round — irregularities of rolling are pressed to a minimum; the plane itself is inclined — the fall is slowed to a pace the naked eye and the water clock can keep up with; water and balance — time is no longer the private sensation of "a little while" but a weight that can be written down, checked, and weighed out again on another person's balance. Not one item is for looks. Every item is taking the same thing apart: peeling a single observation out of the world's noisy background.

At the close of Part Three it was said that Galileo's telescope still stands in the night of the introduction. Part Four begins with another instrument of the same pair of hands. The telescope extends the range of observation — the resolving power the human eye cannot supply is handed over to the lenses; the inclined plane transforms the structure of observation — the clean conditions the world will not offer of its own accord are built by human hands. The former forcibly introduces new observations into consensus (so the introduction told it); the latter is this chapter's protagonist: a deliberately constructed artificial scene, which does not wait for nature to display itself but compels nature to answer a question designed in advance. The thesis of this chapter can accordingly be stated first: experiment is controlled observation. These words are Part Four's first theoretical component; the prediction, the revolution, and the probability to come all stand upon it.

Bacon's Program: Making Observation into Questioning

A dozen years and more before the groove was cut, the program had already been written. In 1620 Francis Bacon published the Novum Organum, its title aimed squarely at Aristotle's Organon: the old logic was for winning disputations; the new method was to be for conquering nature. Bacon's scheme was induction: shake off preconceptions (he called them the idols of the tribe, the cave, the marketplace, and the theater), compile "tables of presence", "tables of absence", and "tables of degree" — set side by side all instances in which a phenomenon appears, is absent, or waxes and wanes, and let the law rise out of the tables by itself. He also left the simile of the ant, the spider, and the bee: the empiricists are like ants, which only collect and never use; the dogmatists are like spiders, which spin only from their own bellies; the true road belongs to the bee, which both gathers and transforms.

The weightiest thing in Bacon's program is one insight into the nature of experiment. The secrets of nature, he said, disclose themselves faster under the vexations of art than in the natural course of things. This sentence deserves to be weighed word for word: it concedes that nature's everyday display is not enough — the world runs before our eyes day after day, yet never spreads its laws open to the naked eye; to make it speak, it must be put into non-everyday situations — heated, compressed, twisted, driven to extremes. Part Three told how mathematicians question and answer themselves on purely internal ground; Bacon is saying another thing: the questioning of nature, too, can be designed.

The distance between program and fulfillment must be recorded at the same time. Bacon slighted mathematics and gave scarcely any response to the work of his contemporaries Galileo and Kepler; his "three tables" never in fact produced a single law. The program goes ahead, the fulfillment comes after — this is the norm of intellectual history. But the program made one unprecedented thing into a public self-awareness: observation is not waited for, it is questioned out; and a question can be manufactured.

RC's General Outline says, discussing dynamic existence in Section 1.1, that observation is the "directional filtering" by observers at a particular scale of perception of a particular interval of the possibility distribution. Bacon's program, in this book's reading, is the making-conscious of the word "directional": since observation is always and only a directional filtering, it is better that the direction be decided explicitly by human beings than left to accident, custom, or authority. The experimental apparatus is a question made into wood, bronze, and water. The question the inclined plane asks is: what is the relation between distance and time? Once this question has been manufactured cleanly enough, the world has nothing else to say and can only hand over the answer — distance is proportional to the square of the time; in successive equal intervals the distances run through by the ball increase as one, three, five, seven. Salviati says in the book that they repeated this experiment a full hundred times, and the results never showed a discernible discrepancy.

Isolation: Cutting a Frame from the Stream of Observation

Now the thesis can be formally established. Experiment is controlled observation — isolating a fragment of nature from the mixed stream of observation so as to minimize the noise of cross-subject re-verification. For every component of this sentence, the inclined plane can supply the evidence.

Take mixture first. Observation in daily life is never single-variable: when you see an apple fall you are at the same time seeing the wind, seeing the spring of the branch, seeing the apple's shape and ripeness; any single "seeing" is the joint output of hundreds of millions of variables. On such a stream of observation two people can hardly reconcile accounts — you say the apple fell fast because it was heavy, he says because it was ripe, and each one's "heavy" and "ripe" have never once been let out separately. The vocabulary Part Three used again and again comes into its own here: the stream of observation is a thick cable of many convergence paths tangled together, and experiment is the drawing out of one strand alone.

The means of drawing it out is control. Every item of the inclined plane's design shuts a door: the groove shuts out drift in two dimensions, the parchment shuts out gross friction, the homogeneous ball shuts out noise of material, the angle of incline shuts out too rapid a fall, the water clock shuts out the privateness of the felt time. When the last door is shut, only two variables remain — distance and time — and their relation is exactly what is being asked. Axiom A6 of the RC paper (consensus reinforcement) says that when observations across subjects and levels verify one another, they form a positive reinforcement loop, converging into stable objective reality. The meaning of control is now clear: noise is the natural enemy of consensus reinforcement — every deviation that cannot be attributed makes two re-verifiers draw two different conclusions; to press noise to a minimum is to clear the ground for mutual verification. The invitation to re-verify therefore changes from "come and have a look yourself" (a look cannot tell right from wrong) into "with this apparatus, put the same question yourself" — only when the question is reproducible can the answers be compared.

Here lies the achievement of controlled observation most easily overlooked: it makes observation weighable. The water clock turns time into weight, weight into number, and number into something that can be posted in a letter to another city. Part Three told of mathematics' origins — counting, surveying, the calendar: symbolic practices that differentiated out of observational activities; what the inclined plane does is lay the gangway for mathematics' return: once observation has been cleansed into a sequence of numbers (one, three, five, seven), the machine of Part Three, that "self-enclosure and expansion", can take over and press it into a law. Galileo himself said in The Assayer that the great book of nature is written in the language of mathematics; this book's reading must add the genetic second half of the sentence: this book could be read at all because a batch of people had first trimmed its pages to one and the same width.

One further entry in the ledger of idealization must be made. The inclined plane did not eliminate air resistance, the parchment did not eliminate all friction, and the times come out astonishingly "round" — historians have argued ever since over how many runs Galileo actually made and how accurately he measured. But this does not disturb the thesis; it rather completes it: idealization is not concealment but the explicit setting down of the factors not yet being asked — they are a clearly marked "supplementary register" in the ledger, to be asked about when conditions allow. Controlled observation thereby turns the available margin of which Chapter One spoke from a muddled account into an open one.

The Public Machine: Boyle's Air Pump

The inclined plane was one man's room; for observation to become science, one further link was needed, outside the room. Around 1659 Robert Boyle, with the assistance of his assistant Robert Hooke, built England's first air pump: a glass receiver joined to an exhausting cylinder, which could pump the air within down to an unprecedented thinness. In 1660 he published New Experiments Physico-Mechanical, Touching the Spring of the Air, recording upwards of forty experiments in vacuo: a candle in the receiver went out, a bell fell silent, a little bird died while heated balance weights took no harm — the "spring" of the air, and the ingredient on which sound, combustion, and life depend, were for the first time brought to confront one another inside one and the same glass vessel.

Boyle did something more important than the experiments themselves: he made them public events. The experiments were demonstrated before gatherings of the Royal Society, and apparatus, procedure, and readings were all written into open reports; he even recorded the failures — which pump leaked, which step could not be carried out, all set down. The machine was then sent round to be repeated, and the history of the repeating is instructive: most of the pumps copied elsewhere worked poorly, and even the one Huygens built could not reach Boyle's degree of vacuum; the philosopher Hobbes attacked on precisely this ground, charging that the whole experimental program rested upon private craftsmanship that no one could audit. Historians later wrote the quarrel into a famous book, and its conclusion strikes to the heart of this book's matter: the earliest "public experiments" stood half on the machine and half on the writing — describing the apparatus and the procedure finely enough that those not present could also become witnesses.

In 1662, in a volume of replies to objections, Boyle added the quantitative stroke: the pressure of a confined quantity of air is inversely proportional to its volume. This rule, later called Boyle's law, was one of the first quantitative deposits in the account of controlled observation — no longer a list of phenomena of the kind "pump out the air and the candle goes out", but a path carrying numbers, which anyone with another pump and another barometer ought to be able to walk through.

This history should be entered in RC's ledger under two heads. First: failed repetition is not a scandal but the foundation of the institution. Had the air pump succeeded at the first build and worked at the first repetition, "the method is reproducible" would be a mere description of fact and not a norm that had to be written into the charter. It is precisely because repetition is hard that the community had to make "every result must be reduplicable by those who took no part in it" a condition of entry into the account. Second: the experimental report thereby acquired a constitutional standing — it is the instrument drawn on the joint account. Chapter One said that accounts can be transferred: language and education deposit a reality verified by one generation into the expectations of the next; the experimental report is the standard format of this transfer within science: what it claims is not "I saw", but "anyone following these steps ought to see".

Chapter Three said that logic and mathematics take their community as unlimited by default, and that science alone fits its community with sluice gates and ledgers. This chapter can now supply the first page of the ledger: the two meta-norms of the scientific community — results public, method reproducible — are Axiom A6 institutionalized: "the results of observation across subjects verify one another" no longer depends on the accident of neighborhood and disciples, but has been made into the procedure of review, assessment, and repetition. Controlled observation solves the minimization of noise; publicity solves the maximization of verification; taken together, they turn observation from private conviction into public deposit.

Newton's Synthesis: Heaven and Earth Share One Account

In August 1684 Edmond Halley came to Cambridge to call on Newton and asked the famous question: if the planets are drawn toward the sun by a force varying inversely as the square of the distance, what curve should the orbit be? Newton answered at once: an ellipse — and he had already calculated it. From this came Halley's promotion of (and his own financing of) the writing and publication of the Mathematical Principles of Natural Philosophy. In 1687 the book appeared, and the synthesis with which nothing else in the history of science can be ranked was complete.

The raw material of the synthesis was three deposits gathered separately over the preceding eighty years. Kepler, in the Astronomia Nova of 1609, gave the first two laws of planetary motion (the planets run in ellipses; the areas swept out are proportional to the times), and in the Harmonices Mundi of 1619 added the third (the squares of the periods are proportional to the cubes of the semi-major axes) — but Kepler's laws were purely observational summaries, three paths grown out of Tycho's ledger, and no one knew why they held. The Galilean line supplied the mechanics of the earth: inertia, free fall, projectile motion — but these governed only the world below the Moon. And behind the two traditions still lay the iron rule that ran from Aristotle: the heavenly bodies are made of a stuff different from everything on earth, and heaven and earth are two worlds. The introduction told how the first crack in this iron rule was the moons of Jupiter and the face of the Moon in the telescope.

What Newton did was merge the two worlds into one account. It is worth glancing first at the format of the book: definitions, axioms or laws of motion, propositions derived therefrom — a Euclidean structure. Chapter Eight told how the axiomatic method is the technique of explicitly publishing the starting point of a convergence path; until then it had written the territory of geometry, and now for the first time it was used to write the system of the universe itself. Universal gravitation — the attractive force between any two bodies proportional to the product of their masses and inversely proportional to the square of the distance — one rule governing apple and moon alike: the planets' ellipses are no longer Kepler's mystic geometry but theorems of this rule; Galileo's law of falling bodies is its approximation near the ground; the tides are the moon's and the sun's gravitation pulling at the sea; the precession of the equinoxes, the orbits of comets, all entered into the account. The title of Book Three of the Principia speaks the content of a revolution with perfect plainness: The System of the World. From two worlds to one system — in Chapter One's vocabulary: the observations of heaven and of earth thenceforward verify one another in one and the same loop of consensus reinforcement — experiments on earth make deposits to the laws of the heavens, observations of the heavens make deposits to the mechanics of the earth, and the account rolls ever thicker.

The re-verification crossed continents. From 1735 the French Academy of Sciences sent out two surveying parties, one to Peru near the equator and one to Lapland inside the Arctic Circle, to adjudicate by geodetic measurement the shape of the Earth: the Newtonian framework predicted that the Earth, by its rotation, is flattened at the poles, while the French tradition of the Cassinis held that it is lengthened toward them. The Lapland party returned in 1737, and the data stood with Newton — the flattening prevailed. A prediction calculated on paper indoors was checked by two parties that had spent years frozen in the polar regions and the Andes — for the first time in human history. Thereafter came the punctual return of Halley's comet (the protagonist of the next chapter), the refinement of lunar theory, the string of victories of celestial mechanics at the end of the eighteenth century — into the nineteenth century, the predictions of the Newtonian framework met not one true failure. "Classical reality" was thereby locked in as the most solid snapshot of all: so thick that Kant could crown it with confidence, proclaiming Newton's laws the a priori forms of reason (Chapter Two told of that operation). The law of Chapter One here reaches its maximum in the history of science — the account so thick that people forgot it had ever been opened, the convergence so complete that, seen from inside the snapshot, it looks like the skeleton the world was born with.

Controlled Observation: The Core Transcription

Now the components of this chapter can be put together for Part Four's transcription number one.

Experiment is controlled observation. It isolates a fragment of nature from the mixed stream of observation, shuts the irrelevant variables out one by one, and cleanses the relation under interrogation into a weighable series of numbers, so that anyone, anywhere, walking the same path by the published steps — thereby turning the loop of consensus reinforcement (A6) from an accident into an institution. Bacon supplied the self-awareness of the program: nature's secrets disclose themselves faster in designed situations; Galileo supplied the exemplar of the craft: groove, ball, and water clock, every item a noise-reducing device; Boyle supplied the charter of publicity: results public, method reproducible; Newton supplied the exemplar of synthesis: one framework converging heaven and earth at once, cross-continental re-verification without a single miss, locking "classical reality" into the most solid of snapshots.

Two boundaries must be nailed fast. First, controlled does not mean coercive. Bacon's followers loved the rhetoric of the rack, but experiment holds no power of torture over nature: the apparatus can determine the question, not the answer. The inclined plane asks after the relation of distance and time; the world's answer arrives in the form of readings, and readings may always fail expectation — which is the whole plot of the next chapter and the one after. What control empties out is noise, not surprise. Second, controlled observation itself stands inside the triple boundary that RC's General Outline points out in Section 2.3, discussing theoretical dimensional reduction: the level of observation determines the limits of representation — the precision of the instrument fixes the precision of the questions that can be asked; the co-construction of subject and environment engraves the designer's imprint on the apparatus; explanatory power decays with time — today's clean experiment is tomorrow's old evidence under a new framework. Controlled observation is the keel of the ship of science, but the ship is still at sea.

This chapter lacks only a last step. Controlled observation fixes the asking of questions and turns the reconciling of accounts into procedure; but up to this point, theory and world are still an extemporaneous dialogue of question and answer. After Newton's synthesis, the rhythm of the dialogue changed: theory walks ahead of observation, writing the answer out first, sealing it, and handing it over to the world to judge in the future. For the first time, humanity possessed a machine able to advance determinacy on credit. The first instrument it was to print was the date of return of a comet — and the man who made the prediction had been dead for sixteen years.