George E. Smith Tufts University

TURNING DATA INTO EVIDENCEThree Lectures on the Role of Theory in Science1. CLOSING THE LOOPTesting Newtonian Gravity, Then and Now2. GETTING STARTEDBuilding Theories from Working Hypotheses3. GAINING ACCESSUsing Seismology to Probe the Earth’s Insides George E. Smith Tufts University

AT THE BEGINNING: THE CHALLENGE • As matter of historical fact, the more theory available to a science, the greater its capacity to turn data into evidence • Implication: In the initial stages of theory construction a science has limited means for developing evidence • Consequently, many of the most fundamental principles in a science became accepted on the basis of very weak evidence • Implication: The foundations of many sciences must involve elements that were (and still are?) epistemically arbitrary • Challenge: How then can the sciences claim to have so much greater epistemic authority than other disciplines?

A DIFFERENT VIEW • In the early stages of theory construction in any area of science some fundamental claims have to be “accepted” even though the evidence that they are true is very weak, or worse • This does not entail that these fundamental claims ever were epistemically arbitrary, for evidence to justify predicating further research on them can still have been compelling • Rather than threatening the epistemic authority of the sciences this process of getting started can make an indispensable contribution toward achieving such authority

OUTLINE • Introduction: the issue • The concept of a working hypothesis: J.J. Thomson • The fundamental assumptions of Newtonian science A. Newton’s laws of motion as working hypotheses B. Still more fundamental Newtonian assumptions • Concluding remarks

Heinrich Hertz: 1883 Cathode rays do not consist of charged particles: e.g. they are not deflected by an electric field across a pair of parallel plates Arthur Schuster: 1884, 1890 Deflection by a magnetic field yields an equation in two unknowns, the velocity of the charged particles and their mass-to-charge ratio CATHODE RAYS : 1880s

A second equation from a variation of an experiment by Jean Perrin, 1895 The two equations together give: J. J. THOMSON: April 1897

A different second equation from figuring out how to get electrostatic deflection: J. J. THOMSON: October 1897

ASSUMPTIONS IN THE EXPERIMENTS • Magnetic field is uniform with no end effects • All kinetic energy of the particles is converted to Temp • No electric charge is lost at the collector • Electric field is uniform with no end effects • No residual ionization reducing the electric field • Cathode ray velocity remains constant in the tube • Cathode rays consist of negatively charged particles, all with the same definite mass-to-charge ratio The last assumption is a working hypothesis common to both experiments; without it they are not measuring the same thing

The prediction: Each experiment will yield a stable value of m/e as the dimensions, voltage, etc. are varied The two experiments will yield converging values for m/e (The experimental design can be refined to produce increasingly precisem/e) The questions: What is the value of m/e for the cathode ray particles? How does this m/e vary from one residual gas to another and from one cathode metal to another? There was no way to predict the answer to these questions; the empirical world had to give us the answer TESTING A PREDICTION vs.PUTTING A QUESTION TO THE WORLD

THOMSON’S DATA: October 1897

JJT’S EXPANDED WORKING HYPOTHESIS Entering into the 1897 experiments: Cathode rays consist of negatively charged particles, all with the same definite mass-to-charge ratio Coming out of the 1897 experiments: All cathode rays consist of negatively charged particles “of one and the same kind” with a character-istic mass-to-charge ratio three orders of magnitude smaller than that of the hydrogen ion – “matter in a new state” To accept H = To predicate further research on H

Wiechart, Kaufmann, Lenard, etc. in 1897, 1898 JJT’s Continuing Research: Dec. 1898: the order of magnitude of the charge e of ions Dec. 1899: thermionic and photo-electric discharges consist of negatively charged particles with the same order of magnitude m/e and the same order of magnitude e SAFEGUARDS AGAINST A GARDEN PATH

JJT’s WORKING HYPOTHESIS, Dec. 1899 All negative electricity is carried by particles of the same kind with a characteristic m/e three orders of magnitude smaller than the smallest m/e for carriers of positive electricity. “From what we have seen, this negative ion must be a quantity of fundamental impor-tance in any theory of electrical action; indeed, it seems not improbable that it is the fundamental quantity in terms of which all electrical processes can be expressed. For, as we have seen, its mass and its charge are invariable, independent both of the proces-ses by which the electrification is produced and of the gas from which the ions are set free. It thus possesses the characteristics of being a fundamental conception of electri-city; and it seems desirable to adopt some view of electrical action which brings this conception into prominence. These considerations have led me to take as a working hypothesis the following method of regarding the electrification of a gas or, indeed matter in any state.” (Phil. Mag., Dec. 1899) Conduction of Electricity Through Gases(1903, 1906, 1928&1933)

JJT’s 1897 working hypothesis: The constituents of cathode rays are particles, not waves The constitutive w. hypothesis: The constituents of cathode rays exhibit particle-like behavior to the extent of obeying certain laws for charged particles CONSTITUTIVE vs. HEURISTIC

WORKING HYPOTHESES: THE CONCEPT • Substitute for established theory when getting started • To accept one is to presuppose it in ongoing research • Grounds for acceptance: promise it offers in this research • Promise of evidence allowing research to get off the ground • … plus safeguards against an extended garden path • Everything coming out in the wash more important than final truth • Continuing evidence from the success of that research • Especially when empirical world gives unequivocal answers • Over time, gratuitous heuristic elements eliminated • Sustained success leads to increasing entrenchment

NEWTON’S FIRST TWO LAWS OF MOTION Law 1: Every body perseveres in its state of being at rest or of moving uniformly straight forward except insofar as it is compelled to change its state by forces impressed Law 2: A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed “By means of the first two laws and the first two corollaries Galileo found that the descent of heavy bodies is in the squared ratio of the time and that the motion of projectiles occurs in a parabola, except insofar as these motions are somewhat retarded by the resistance of air. What has been demonstrated concerning the times of oscillating pendulums depends on the first two laws and first two corol-laries, and this is supported by daily experience with clocks.”

If a body deviates from uniform motion in a straight line, then there must be an unbalanced impressed force that is compelling it to do so. The magnitude of this force varies as the displacement in a given time from where the given body would have been forcemass (limQR/t2) WHAT NEWTON MEANT BY THESE LAWS

How great the force of this striving is We see, too, that the stone which is in a sling makes the rope more taut as the speed at which it is rotated increases; and, since what makes the rope taut is nothing other than the force by which the stone strives to recede from the center of its movement, we can judge the quan-tity of this force by the tension. Descartes, Principia, III, 59 ORIGINS OF THE FIRST LAW

The tension in the string that retains a body in uniform circular motion varies as EG v2/r times the weight of the body HUYGENS ON “CENTRIFUGAL FORCE”

If centrifugal tension  wv2/r then the acceleration of gravity is uniform if and only if distance dg of fall in 1st second is a constant equal to dg = 15 P. ft., 1 in., 2 lines HUYGENS’S CONICAL PENDULUM MEASUREMENT OF GRAVITY (1659)

If speeds acquired in vertical fall are independent of path taken then the acceleration of gravity is uniform if and only if distance dgof fall in 1st second is a constant equal to dg= 15 P. ft., 1 in., 2 lines HUYGENS’S CYCLOIDAL PENDULUM MEASUREMENT OF GRAVITY (1659)

If centrifugal tension  wv2/r then the acceleration of gravity is uniform if and only if period of a paraboloidal conical pendulum clock is a constant = dg= 15 P. ft., 1 in., 2 lines HUYGENS’S PARABOLOIDAL CONICAL PENDULUM CLOCK (1660s)

THE EVIDENCE FOR NEWTON’S FIRST TWO LAWS OF MOTION (1687) • Huygens had devised four different theory-mediated ways of measuring the strength of surface gravity, all yielding the same four-significant figure value of 15 Paris ft., 1 in., 2 lines • Two of these ways – the constant height conical pendulum and the paraboloidal conical pendulum clock – presuppose direct forerunners to Newton’s first two laws of motion • The other two ways – the cycloidal pendulum (including clocks), the small-arc circular pendulum – presuppose only weaker Galilean assumptions about velocity acquired in fall • The two laws of motion were therefore in effect allowing the empirical world to give an independently confirmed precise answer to the question, what is the strength of surface gravity?

To derive “if … , then …” inference-tickets that allow the magnitude, proportions, and species of the centripetal forces retaining planets and their satellites in their curvi-linear orbits to be inferred from phenomena of motion That is, to have the empirical world answer some questions forcemass (limQR/t2)  mass (limQR/(QTSP)2)  mass (lim v2/(ρsin SPR)) where 1/ρ is the curvature at P NEWTON’S PRIMARY USE OF HIS FIRST TWO LAWS OF MOTION

THE STATUS OF THE FIRST TWO LAWS IN 1687 • Sweeping universal claims for which there was very little evidence that they are true for forces of all different kinds • Strong evidence for their promisein allowing theory-mediated measurements of the magnitudes and proportions of forces • Safeguards against an extended garden path • Independent confirmation of their use in measurement by Huygens • Demand comparable precision in their extended use in measurement • Limit inferences to magnitude, proportions, and species of forces • Impose the third law of motion as a constraint on forces • Best to regard them as working hypotheses at the time • Subsequently became entrenched through the success of the research the Newtonian tradition predicated on them

ASSUMPTIONS IMPLICIT IN NEWTON’S USE OF HIS THREE LAWS OF MOTION • Sidereal time (23 hrs. 56 min. 4 sec. per day) provides at least a good first approximation to true time. • The fixed stars provide at least a good first approximation to what we now call an inertial reference frame. • The geometric structure of space is Euclidean (at least to high approximation). • With suitable corrections for systematic errors, all questions about duration of time and simultaneity have unequivocal answers. • One can always, at least in principle, distinguish between inertial motion and free fall under uniform gravity.

NEWTON ON “TRUE” TIME “In astronomy, absolute time is distinguished from relative time by the equation of common time. For natural days, which are commonly considered equal for the purpose of measuring time, are actually unequal. Astronomers correct this inequality in order to measure celestial motions on the basis of a truer time. It is possible that there is no uniform motion by which time may have an exact measure. All motions can be accelerated or retarded, but the flow of absolute time cannot be changed. … Accordingly, duration is rightly distinguished from its sensible measures and is gathered from them by means of an astrono-mical equation. Moreover, the need for using this equation in determining when phenomena occur is proved by experience with a pendulum clock and also by eclipses of the satellites of Jupiter.”

IMPLICATIONS OF NEWTON ON TIME 1. Quantities in physics are separate – abstracted by physical theory – from their measures • Physics must contain its own theory of measurement • All measurement is provisional, and hence so too are lawlike relationships among quantities • Stability, convergence, and precision of measurement cannot help but be a primary form of evidence 5. Assumptions underlying measures are unavoidable when getting started, whether recognized or not

What serves for promise when getting started? Often, almost an any-port-in-a-storm mentality What provides safeguards against an extended garden path? A demand for stability, convergence, and increasing precision in measurement as theory grows A commitment to continuing critical review of measures as theory grows A strong preference for having the empirical world supply answers to our questions “Mathematics requires an investigation of those quantities of forces and their proportions that follow from any conditions that may be supposed. Then, coming down to physics, these proportions must be compared with the phenomena, so that it may be found out which conditions of forces apply to each kind of attracting body. And then, finally, it will be pos-sible to argue more securely about the physical species, physical causes, and physical proportions of these forces.”

Why I call them “working” hypotheses: Because they have to enter constitutively into the process of research at a stage when they cannot be tested in any customary sense; for they are needed to allow other claims to be tested and, more generally, to allow data to be turned into evidence at all.

PRIMARY CONCLUSIONS • Constitutive working hypotheses substitute for theory in the role of turning data into evidence when an area of research is just getting started • Newton’s laws of motion and the fundamental assumptions he made in the way he used the laws are best regarded as in this category • The issue to raise about a working hypothesis is not whether it is true, but (1) the promise it shows in enabling data to be turned into evidence and (2) safeguards against a garden path

THE QUESTION OF EPISTEMIC AUTHORITY • Fundamental principles of sciences have been accepted at a stage in which the evidence that they are true was very weak • That does not imply that these principles were or are arbitrary • Nor does it automatically jeopardize the claim to epistemic authority • A two-stage picture of acceptance of fundamental principles • Initially, as working hypotheses, predicating research on them • Continuing entrenchment as this research proves successful • The key issue: How has evidence been brought to bear on such principles during the course of the research predicated on them?

ON ANSWERING THIS QUESTION • My quarrel with much philosophy of science: even when attention is paid to history, it is paid to the history of “extraordinary science” rather than “normal science” • My quarrel with much history of science: attention to normal science only in geographically and temporally local studies of groups of individuals “making knowledge” • Whatever claim any science has to epistemic authority, this claim has to be grounded in evidential practices within “normal science” over many generations of scientists

George E. Smith Tufts University