TURNING DATA INTO EVIDENCE Three Lectures on the Role of Theory in Science 1. CLOSING THE LOOP Testing Newtonian Gravity, Then and Now 2. GETTING STARTED Building Theories from Working Hypotheses 3. GAINING ACCESS Using Seismology to Probe

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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 Earths Insides

• George E. Smith
• Tufts University

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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?

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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

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OUTLINE

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

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CATHODE RAYS 1880s

• 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

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J. J. THOMSON April 1897

• A second equation from a variation of an
  experiment by Jean Perrin, 1895
• The two equations together give

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J. J. THOMSON October 1897

• A different second equation from figuring out
  how to get electrostatic deflection

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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

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TESTING A PREDICTION vs.PUTTING A QUESTION
TO THE WORLD

• 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 precise m/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

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THOMSONS DATA October 1897
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JJTS 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

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SAFEGUARDS AGAINST A GARDEN PATH

• Wiechart, Kaufmann, Lenard, etc. in 1897, 1898
• JJTs 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

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JJTs 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, 19281933)

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CONSTITUTIVE vs. HEURISTIC

• JJTs 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

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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

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OUTLINE

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

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NEWTONS 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.

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WHAT NEWTON MEANT BY THESE LAWS

• 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 ? (lim QR/?t2)

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ORIGINS OF THE FIRST LAW

• 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

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HUYGENS ON CENTRIFUGAL FORCE

• The tension in the string that retains a body in
  uniform circular motion varies as
• EG ? v2/r
• times the weight of the body

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HUYGENSS CONICAL PENDULUM MEASUREMENT OF
GRAVITY (1659)

• 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

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HUYGENSS CYCLOIDAL 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 dg of fall in 1st second
• is a constant equal to

• dg 15 P. ft., 1 in., 2 lines

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HUYGENSS PARABOLOIDAL CONICAL PENDULUM CLOCK
(1660s)

• 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

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THE EVIDENCE FOR NEWTONS 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 Newtons
  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?

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NEWTONS PRIMARY USE OF HIS FIRST TWO LAWS
OF MOTION

• 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 ? (lim QR/?t2)
• ? mass (lim QR/(QT?SP)2)
• ? mass (lim v2/(? sin SPR))
• where 1/? is the curvature at P

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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 promise in 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

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OUTLINE

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

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ASSUMPTIONS IMPLICIT IN NEWTONS USE OF HIS
THREE LAWS OF MOTION

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

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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.

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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

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• 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.

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• 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.

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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
• Newtons 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

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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?

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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