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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 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
I.
Introduction: the issue
II.
The concept of a working hypothesis: J.J. Thomson
III.
The fundamental assumptions of Newtonian science
IV.
A.
Newton’s laws of motion as working hypotheses
B.
Still more fundamental Newtonian assumptions
Concluding remarks
CATHODE RAYS : 1880s
Heinrich Hertz: 1883
Arthur Schuster: 1884, 1890
Cathode rays do not consist
of charged particles: e.g.
they are not deflected by an
electric field across a pair of
parallel plates
Deflection by a magnetic
field yields an equation in
two unknowns, the velocity
of the charged particles and
their mass-to-charge ratio
J. J. THOMSON: April 1897
A second equation from a
variation of an experiment
by Jean Perrin, 1895
The two equations together
give:
J. J. THOMSON: October 1897
A different second equation
from figuring out how to get
electrostatic deflection:
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
TESTING A PREDICTION vs.
PUTTING A QUESTION TO THE WORLD
The prediction:
1. Each experiment will yield
a stable value of m/e as the
dimensions, voltage, etc.
are varied
2. The two experiments will
yield converging values
for m/e
3. (The experimental design
can be refined to produce
increasingly precise m/e)
The questions:
1. What is the value of m/e for
the cathode ray particles?
2. 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
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 characteristic 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
SAFEGUARDS AGAINST A GARDEN PATH
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 photoelectric discharges consist of
negatively charged particles with
the same order of magnitude m/e
and the same order of magnitude e
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 importance 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 processes 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 electricity; 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)
CONSTITUTIVE vs. HEURISTIC
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
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
OUTLINE
I.
Introduction: the issue
II.
The concept of a working hypothesis: J.J. Thomson
III.
The fundamental assumptions of Newtonian science
IV.
A.
Newton’s laws of motion as working hypotheses
B.
Still more fundamental Newtonian assumptions
Concluding remarks
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 corollaries, and this is supported by daily experience with clocks.”
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)
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 quantity of this force by the tension.
Descartes, Principia, III, 59
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
HUYGENS’S 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
HUYGENS’S 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
HUYGENS’S 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
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?
NEWTON’S 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 curvilinear 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/(ρ sin SPR))
where 1/ρ is the curvature at P
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
OUTLINE
I.
Introduction: the issue
II.
The concept of a working hypothesis: J.J. Thomson
III.
The fundamental assumptions of Newtonian science
A.
Newton’s laws of motion as working hypotheses
B. Still more fundamental Newtonian assumptions
IV.
Concluding remarks
ASSUMPTIONS IMPLICIT IN NEWTON’S
USE OF HIS THREE LAWS OF MOTION
1.
2.
3.
4.
5.
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
2.
Physics must contain its own theory of measurement
3.
All measurement is provisional, and hence so too are
lawlike relationships among quantities
4.
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 possible 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