Download Outline of Lecture on Copernican Revolution: 1. Source of word

Outline of Lecture on Copernican Revolution:
1. Source of word “revolution” with its present meaning.
2. Why did people care where the planets were?
a. Agriculture.
b. Auguries.
g
c. Cyclic behavior suggests some law, difficult to divine.
3. Why the sun, stars, and planets all should revolve around us.
a. We are the center of everything, of course.
b. Most observed motions immediately explained.
c. Seasons caused byy inclination and speed
p
of sun’s motion.
d. Moon’s phases come out fine.
e. But there are small, nagging problems.
Outline of Lecture on Copernican Revolution:
4. Problems with the geocentric model:
a. Retrograde motion of the planets.
Particularly, Mars, Jupiter, and Saturn occasionally slow
down relative to the stars and actually go backwards for a
time. This seemed strange.
b. Phases of Venus (an objection more notable after the
invention of the telescope).
Full cycle of phases, correlated with Venus’ apparent size.
5. Retrograde motion “explained” in geocentric model:
a Explained by epicyclic motion.
a.
motion
b. Imperfect, but still circles, just more of them.
c. This idea came from the Greek, Hipparchus, and was
elaborated by Ptolemy, who lived in Alexandria in the
second century AD.
1
The problem with the retrograde motion was:
• Hard to see why a god would have established so complex a
motion.
• This going forward and then occasionally backward, and then
forward again would seem to demand constant attention from a
god, who should more properly have better things to be
attending to.
Ptolemy’s epicycles derived the back and forth motion of the
planets from circles turning on circles.
• This motion might seem possible for a god to set going and
then have it run on forever, since uniform circular motion
seemed like something that could go on forever without
attention. People had been able to build devices (wheels) that
acted this way, although our human imperfection resulted in
the wheels eventually slowing down and coming to rest.
However divine wheels would be perfect and keep on turning.
But Ptolemy’s epicyclic motions were actually not built out of
uniform circular motions.
•
•
The motion of the planet around the epicycle was uniform.
But the motion of the guiding center of the epicycle about its
orbit circle was non-uniform.
• But it was only slightly non-uniform.
• This imperfection of Ptolemy’s model no doubt bothered the
experts who thought about it, but then there weren’t very many
experts around.
There was another problem with Ptolemy’s epicycles, they were
uncomfortably large.
large
• This made the motions of the planets quite bizarre.
• Ptolemy’s model might never have caught on had he used the
epicycles for the outer planets that describe their actual motion
about the sun from our perspective. More on this in a moment.
2
The epicycles in this
diagram from
your textbook
are not drawn
correctly.
In Ptolemy’s
model,
for most
of these
planets the
epicycles
are much
larger than
these in relation
to the radii of the
planets’ orbits about the earth.
For the curious: In fact,
to get the motion of
a planet correct,
the ratio of the
radius of its
epicycle
i l to
that of its
orbit must
equal the
ratio of the
radius of its
orbit about the
sun to that of the
earth, or the inverse
of that ratio,
whichever is
smaller.
Copernicus explained the retrograde motion by
our changing point of view as we pass in our
orbit close by another planet.
Here we can see how Mars would appear
to move backwards as we pass by it riding
on the more rapidly orbiting earth. Its actual retrograde
motion is shown on the next slide.
Copernicus had a much easier and simpler explanation than
Ptolemy did for the retrograde motion of the other planets.
3
Through a telescope, Mars actually
appears larger during its retrograde
motion, because it is closer to the
earth at that time.
The line of dots in the
b k
background
d are
the distant
planet
Uranus.
Some additional detail for the curious student
(this will not be on the test):
Because both earth and Mars orbit the
sun, from
f
our perspective
i on the
h earthh
the sun would orbit us, and Mars would orbit the orbiting
sun. To the extent that both orbits are circular, this means
that the motion of Mars from our perspective actually is an
epicycle, as Ptolemy said it was.
4
Some additional detail for the curious student
(this will not be on the test):
But . . .
I Ptolemy’s
In
P l
’ model,
d l the
h guiding
idi center
orbit for Mars was not the orbit of the sun about us.
This was not allowed, because we must not let Mars orbit
anyone else. Ptolemy could not have used the real epicycle
for the motion of Mars, or he would have had Mars orbiting
the sun!
Some additional detail for the curious student
(this will not be on the test):
Ptolemy solved this problem by
i
interchanging
h i the
h two circles
i l involved
i
l d
in the motion of Mars. He used the radius of Mars’ actual
orbit about the sun as the radius of the guiding center motion
for Mars’ epicycle, and he used the radius of the sun’s
“orbit” about the earth as the radius of Mars epicycle. This
interchange produced precisely the same motion!
5
Some additional detail for the curious student
(this will not be on the test):
We obtain the same apparent motion by letting the small circle
move along the large one as we do by letting the large circle
move along the small one.
Here the motion along each circle is by the same amount from dot to dot as in
the original diagram from your textbook.
Some additional detail for the curious student
(this will not be on the test):
We get precisely the same motion, because it does not matter whether, as on the left, we
go first along the vector with length equal to the radius of Mars’ orbit and then along the
one with length equal to the radius of Earth’s orbit, or if, as on the right, we travel along
these vectors in the opposite order.
For the case of perfectly circular orbits and perfectly uniform motion along the circles,
the paths traced out by the planet’s motion relative to us are identical.
The two constructions are different, but the resulting paths of the planet are the same.
6
Some additional detail for the curious student
(this will not be on the test)
Here we see how the two different constructions do indeed
produce the identical result.
In this diagram,
diagram we see Ptolemy’s
Ptolemy s construction
construction, with Mars riding on an epicycle
the size of the earth’s orbit about the sun, and with the guiding center circle the
size of Mar’s orbit about the sun.
Actually, Mars orbits the sun, and from our perspective the sun appears to orbit
us. Thus the “real” guiding center circle and epicycle circle radii have been
reversed in Ptolemy’s construction, but the resulting motion of Mars is the same
either way.
7
These are the actual “orbits” of Venus
and Mercury as observed regarding the
Earth as fixed. Hopefully, you can see from these last few
slides why the idea of epicyclic motion was quite fitting as
a description of the observed motions of the planets.
At the left is Kepler’s
p
rendering
g of the orbit of Mars as seen from an imagined
g
point above the earth. At the right is a modern rendering. As Mars appears to
come close to the earth, the loops caused by its apparent epicyclic motion are
not all the same. This is caused by the nonuniform motion of the guiding center
along the deferent circle in Ptolemy’s model. In Kepler’s model, this feature
results because the orbit of Mars is an ellipse and not a circle. The apparent
motion of Mercury on the previous slide shows a similar nonuniform character,
but to a lesser degree.
8
5a: So, what was wrong with Ptolemy’s model to a contemporary
mind?
We see from the above that Ptolemy’s model was not really so bad.
It provided a very good description of observed reality, because the
actual motions of the planets from our perspective are
essentially
ti ll epicyclic.
i li
But Ptolemy missed several points that were clues to what was
“really” going on. As a result, no reasonable mechanism for
the motions emerged.
[Here I am assuming that it is not reasonable that a god had built
a set of wheels, gears, and pulleys to produce the epicycles in
Ptolemy’s model.]
A Greek had already pointed out, hundreds of years before, that if
we orbited the sun, retrograde motion of the other planets was
a natural consequence.
The clues Ptolemy ignored:
1) The guiding centers for the planets Mercury and Venus are
always located precisely on the line joining the earth and the
sun.
2) The periods of the motions of all 3 outer planets then known
are exactly
tl equall to
t the
th period
i d off the
th sun’s
’ motion
ti about
b t the
th
earth.
As modern scientists, we know that it was unreasonable to say that
these facts were mere coincidences.
Contemporary people working with Ptolemy’s model must have
noticed these coincidences and wondered why things just
happened to work out this way.
It was not until Copernicus proposed his heliocentric model that
the explanation for all these apparent coincidences emerged.
They all result because we are observing the motion of the
planets from the orbiting earth.
9
Copernicus’
model clearly
had an impact on
other scientists,
but the fact that
no star showed
any parallax
called the
motion of the
earth in the
model into
qquestion.
Brahe invited the
young scientist
Kepler to come
work with his
detailed
observations in
order to sort this
out. (More on
Kepler later.)
A diagram of the solar system made by Tycho Brahe in 1588.
The identical orbital periods of the sun, Mercury, and Venus are explained by these two
planets orbiting the sun as it in turn orbits the earth.
In this picture, the sun carries along Mars, Jupiter, and Saturn as well. The role of the
sun is clearly influenced by Copernicus’ ideas, but in this model of Tycho’s the earth
does not move. Tycho believed that the earth was stationary because he could not
observe any parallax of any star.
5a: Is this simply a history lesson, or do these things have
contemporary significance?
The geocentric and heliocentric models are a nice, extremely clear
and simple example of a general principle that guides scientists
today.
A model that involves a large number of unexplained constants
that must have specific values for the theory to work, but
whose values are not in any way explained or related to other
theories is likely to be wrong.
It might provide an adequate quantitative description of the
phenomena in question, but it is unlikely to lead to a good
understandingg of them..
10
5a: Is this simply a history lesson, or do these things have
contemporary significance?
A model in which the behavior described is strange or weird could
perhaps arise from observing the behavior from a viewpoint
that confuses the behavior we wish to understand with the
dynamics
y
of the pperspective
p
from which we view it.
Example: The laws governing the behavior of gases are most
simply expressed and understood in a frame of reference that
moves with the gas.
(This one tripped up a member of the US National Academy of
Sciences.)
You know when yyou are on the right
g track ((and so do they):
y)
When you’ve got it right, constants that once appeared
arbitrary are explained as coming necessarily from your new
model, and a whole list of productive new questions and
investigations is indicated. When you’ve got it wrong, you
usually find yourself stuck in an intellectual dead end.
5a: Is this simply a history lesson, or do these things have contemporary
significance?
The geocentric and heliocentric models are a nice, extremely clear and simple
example of a general principle that guides scientists today.
It is often inconvenient to embrace a new model, but resistence is futile in the
long run and not usually the best course of action in the short run either.
Example: Global Warming.
The deniers of this phenomenon suggest that the observed warming of the planet
is simply a statistical fluctuation.
But are they willing to put this hypothesis to an objective test, and then accept
the result, even if it goes against them?
After this suggestion was first advanced, people dug down into the Greenland
ice pack and discovered that there had not been a fluctuation like the
present one in the last 300,000 years. If today’s warming is just a
fluctuation, there should have been other ones like it. But there weren’t.
Did those denying global warming accept this result? No. This is an
indication that their motives go beyond scientific curiosity and are likely to
include non-scientific motivations and reasoning.
11
Let’s quickly see where Copernicus’ suggestion of a heliocentric
model led:
1) It led Copernicus to determine the radii of the orbits of all the
planets in terms of the radius of the earth’s orbit – the
“astronomical unit,” or A.U.
2) It resulted in the proper ordering of the planets in terms of
distance from the sun.
3) Copernicus was then able to determine the proper periods of
the orbits of all the planets, measured in years (the period of
our orbit). To do this, he had to account for our motion about
the sun.
4) When Copernicus had figured all this out – for the first time –
he discovered a beautiful progression of orbital period with
orbital radius, which Kepler later stated as his third law of
planetary motion.
12
Role of Copernicus:
12. Nicolaus Copernicus, born in Poland in 1473 (to a wealthy
family), decided in the early 1500s to try to simplify the
Ptolemaic model by putting the sun at the center.
13. Radii of planets from the sun
a. Determined by elongation angles.
b. Results were good to 1% for all but Saturn.
c. Ptolemaic model cannot determine these radii.
14. Introduced small epicycles to get varying orbital speeds.
(Planets orbit faster when nearer to the sun.)
15 D
15.
De R
Revolutionibus
l ti ib Orbium
O bi Celestium,
C l ti
published
bli h d iin 1543
1543, the
th
year Copernicus died.
16. His circular orbits required small epicycles, so still inaccurate.
17. Therefore not adopted, but this model was VERY influential on
later developments.
Copernicus figured
out that observations
of the elongation
angles of planets
could be used to
determine which
orbited nearer and
which farther from
the sun.
13
Copernicus figured out how to use right triangles to determine
the orbital radii of the planets.
He got the radii of all but Saturn’s orbit to 1% accuracy.
Copernicus
figured out how
to calculate the
sidereal period
p
of a planet’s
orbit from its
synodic period
(the period
observed from
the orbiting
earth).
14
Let’s quickly see where Copernicus’ suggestion of a heliocentric
model led:
5) The heliocentric model naturally led to the correct picture of
the mechanism responsible for planetary motions – the
gravitational pull of the sun.
This was not formulated until Newton, but it was no longer
hidden by the peculiar epicyclic gyrations that simply result
from the motion of our observing platform, the earth.
6) The nice progression of orbital periods with orbital radii serves
to nail down how the gravitational force between 2 objects
varies with the distance between them.
7) Newton had to invent the calculus to finish this job, but it was
a real revolution in science.
I see that I have omitted the contributions of Tycho Brahe and
Galileo.
Brahe made his careful observations of planetary motion in order
to test Copernicus’ theory. In the absence of the new theory, he
would most likely not have bothered to make his painstaking
observations.
b
ti
Without those observations, Kepler would not have been forced to
give up on circles and epicycles and discover the true elliptical
nature of the planetary orbits.
Before Brahe and Kepler, we were misled by the nearly circular
nature of planetary orbits. The more elliptical orbit of Mars,
and Brahe’s careful observations, forced ellipses upon us.
15
Role of Tycho Brahe:
18. New, detailed observations of the planetary motions obtained,
with the naked eye, by Tycho Brahe (1546-1601), a Danish
nobleman, over 30 year period.
19. Accurate to one arc minute.
20. Found no parallax of any star.
a. Earth must be stationary.
b. Copernicus must have been wrong.
c. Largest stellar parallax is actually about one arc second.
d. Nearest star is really far away from us.
21. Tycho charged his assistant, Johannes Kepler, hired in 1600,
a year before Tycho’s death, to analyze his data,
so that he should not have worked in vain.
16
Copernicus’
model clearly
had an impact on
other scientists,
but the fact that
no star showed
any parallax
called the
motion of the
earth in the
model into
qquestion.
Brahe invited the
young scientist
Kepler to come
work with his
detailed
observations in
order to sort this
out. (More on
Kepler later.)
A diagram of the solar system made by Tycho Brahe in 1588.
The identical orbital periods of the sun, Mercury, and Venus are explained by these two
planets orbiting the sun as it in turn orbits the earth.
In this picture, the sun carries along Mars, Jupiter, and Saturn as well. The role of the
sun is clearly influenced by Copernicus’ ideas, but in this model of Tycho’s the earth
does not move. Tycho believed that the earth was stationary because he could not
observe any parallax of any star.
17
Role of Johannes Kepler:
22. Kepler tried to fit circular orbits to Tycho’s observations.
a. Mars most difficult.
b. Best circular orbit deviated from Tycho’s observations by
no more than 2 arc minutes, except for two isolated
observations, for which the deviation was 8 arc minutes.
c. Kepler’s refusal to ignore these 2 observations, and
Tycho’s care in making them, which made them
unignorable, are key features of science, as opposed to the
many activities that seek the respect accorded to science
without having to submit to the rigor of the scientific
method.
d. Kepler was able to fit all Tycho’s observations by using
elliptical, rather than circular, orbits.
18
An ellipse is one member of a family of curves, called
conic sections.
Newton showed that the most general orbits are conic sections,
either circles, ellipses, parabolae, or hyperbolae.
To do this, he needed to invent the calculus; one of the greatest
mathematical advances of all time.
Outline of Lecture on Copernican Revolution:
23. Kepler’s three laws of planetary motion:
a. The orbit of each planet about the sun is an ellipse, with the
sun at one focus.
b. As a planet moves along its orbit, it sweeps out equal areas
in equal times.
c. (orbital period, in years)2 = (average distance, in AU)3
24. First two laws predict changes in speed without epicycles.
25. Third law relates distance from sun and orbital speed.
The CD that comes with your textbook illustrates the 3 laws.
Your textbook says these laws are “empirical” and do not explain
“why” the planets move the way they do, while Newton’s laws
do. Not so. Newton’s laws are just as “empirical.” But they
describe more phenomena with a simpler mechanism.
19
20
21
Outline of Lecture on Copernican Revolution:
29. Galileo upset established beliefs with his observations using
the telescope in several ways:
a. He observed sunspots, imperfections of the solar surface.
b. He observed mountains on the moon, imperfections as well
c. He observed the phases of Venus, which demonstrate that it
orbits the sun, not the earth.
d. He observed four “stars” orbiting the planet Jupiter, which
caused a sensation.
30. Items c and d above caused near unanimous adoption by the
scientific communityy ((such as it was)) of the heliocentric model
of Copernicus and Kepler by the mid 1600s.
31. In 1687, Newton, in his Philosophiae Naturalis Principia
Mathematica, explained all of Kepler’s laws (and much more)
with a single concept, universal gravitation.
Near the Uffizi
http://www.museogalileo.it/en/explore/virtualmuseum.html
22
Jupiter with its four Galilean satellites
Galileo’s observations of
Jupiter’s moons.
23
Galileo was able to definitively reject Ptolemy’s model by
observing the full set of phases of the planet Venus, which are
impossible in that model.
Newton’s idea of gravity had to produce Kepler’s three laws in
p had used to come upp
order to fit the observations that Kepler
with these laws.
This forced the inverse square law for the gravitaitonal force onto
Newton’s theory; otherwise he could not come up with
Kepler’s third law.
Not only did gravity produce elliptical orbits, but Newton’s laws of
mechanics which incorporated results of Galileo,
mechanics,
Galileo explained
the speeding up of planets when they are closer to the sun in
terms of the conservation of angular momentum (we will
discuss that later this week).
The motions of Venus in the Ptolemaic model (left) and the
Copernican one (right) predict a different sequence of phases for
the planet Venus. With his telescope, Galileo found that the phases
at the right are observed, so Venus does orbit the sun.
24
Outline of Lecture on Copernican Revolution:
32. Galileo’s work on the motion of bodies (on the earth) laid the groundwork
for Newton’s amazing synthesis, which produced Newton’s 3 laws of
motion and of universal gravitation:
a. He developed the concept of inertia:
1) Aristotle had asserted that all bodies tended toward their most
natural state – a state of rest.
2) Galileo said that a body in uniform motion (i.e. at a constant speed
in an unchanging direction) would, by its inertia resist any
change in that motion and hence remain in uniform motion unless
acted on by a force.
3) Newton adopted this law of inertia as his 1st law of motion.
4)) Galileo asserted that the behavior of bodies follows the same laws
in any inertial frame of reference.
5) Transforming our view point from one such frame of reference to
another is now called a Galilean transformation.
6) The invariance of the laws of motion under Galilean
transformations is called Galilean invariance.
Outline of Lecture on Copernican Revolution:
b. He demonstrated that bodies of all masses fall toward the
earth at the same speed. (Leaning tower of Pisa.)
This observation helped determine the form of Newton’s
law of gravitation. (We will see how later.)
33. Galileo’s tract, Dialogue on the Two Great World Systems,
published in 1632, set out the arguments for the heliocentric
model in a format that did not unequivocally commit Galileo to
either view, but this was not enough to keep him out of trouble.
a. Apparently Galileo could not resist putting the standard
arguments in the mouth of Simplicio (an obvious
simpleton).
b. The book was written in the vernacular, and was popular.
c. Galileo, despite his powerful friends, was put under house
arrest, after first recanting his beliefs publicly.
25
Copernicus
Heliocentric model
Kepler
Corrected heliocentric
model by rejecting circular
in favor of elliptical orbits
Brahe
B
h
Detailed observations
Galileo
Telescope discoveries
Inertia
Outline of Lecture on Copernican Revolution:
34. Despite Galileo’s enormous advances in understanding, it was
Newton who performed the vital and amazing synthesis:
a. Newton realized that the laws of motion that apply to balls
(or apples) falling to the earth or billiard balls colliding on
a pool table are identical to those that apply to and govern
the motions of the sun, earth, moon, and planets.
b. This amazing insight permits one set of simple principles to
describe and predict the motions of all these things, in
fact of every thing.
p is therefore supported
pp
byy all
c. This set of pprinciples
observations of all mechanical behavior, and is therefore
essentially unassailable.
d. This is an example of the force of science. To credibly
claim that it is not true, you have to come up with an
equally voluminous body of evidence. Forget it!
26
Outline of Lecture on Copernican Revolution:
35. In 1687, Newton, in his Philosophiae Naturalis Principia
Mathematica, explained all of Kepler’s laws (and much more)
with a single concept, universal gravitation.
a. His theory tied together the motions of the planets with the
motion of everyday objects falling to earth.
earth
b. The gravitational force constant could be measured in the
laboratory, and then applied to yield the masses of the
planets, information previously unobtainable.
c. The theory applied to the orbit of the planet Uranus (not in
Newton’s life time) predicted the location of the then
unknown planet Neptune to within 1º.
d. The theory explained the tides, caused by the gravitational
attraction of the sun and moon, as well as the very slow
precession of the earth’s rotational axis.
27
28
29
Newton’s concept of universal gravitation allows us to measure
the universal constant of gravitation, G, here on earth and then to
apply that knowledge to weigh other planets, star, and galaxies.
Outline of Lecture on Copernican Revolution:
36. The Copernican revolution is a classic example of the scientific
method. It exemplifies the following philosophical issues that
lie behind the scientific approach:
a. If two conjectures
j
or theories explain
p
all available objective
j
facts equally well, it is impossible to claim that one is
“true” and another “false.” Instead, to prefer one of them
one must devise a new, objectively verifiable and
repeatable experiment, based upon differing predictions
of the two theories, and one must be willing to accept the
result.
b. Kepler’s laws and Newton’s laws make the same
predictions for the planetary motions, but Newton’s laws
are simpler and far more general. Therefore Newton’s
laws are “better;” they are verified and supported by a
vastly larger store of experience and observation.
30
Outline of Lecture on Copernican Revolution:
36. The Copernican revolution is a classic example of the scientific
method. It exemplifies the following philosophical issues that
lie behind the scientific approach:
c. If two models of some pphenomenon explain
p
all
observations to date, we may believe either one of them is
“real.” Only objectively verifiable and repeatable
experiments may be used to reject the “reality” of a
theoretical model. Since both are equally “real,” it is wise
to use the simpler model.
d Copernicus’
d.
Copernicus and Ptolemy
Ptolemy’ss models
models, in the light of
knowledge in Copernicus’ time, were equally real, but
Copernicus’ was simpler.
e. The models, however, made different predictions for the
phases of Venus (unobservable at the time), which later
were used to reject one of them.
Outline of Lecture on Copernican Revolution:
37. Let’s think about science and non-science.
a. Science chooses to address only those questions that can
be answered by an objective test or experiment.
b. In astronomy, because of the paucity of observational
data due to the difficulty in collecting it,
it conjectures
abound, but none of these has the force of established
theory.
c. Thus matters of opinion and plausibility are often
discussed.
d. However, all participants agree to abide by the evidence
of objective observation.
observation
e. For example, the Hubble Space Telescope’s “deep field”
dispatches the steady state theory of the universe, because
it clearly shows that the universe looked different in the
past than it looks today. Therefore the steady state theory
has been discarded.
31
Outline of Lecture on Copernican Revolution:
37. Let’s think about science and non-science.
f. The textbook’s authors, in the first edition, say that
when science and tradition or faith come into conflict,
science should be silent.
g. However, science, if it can speak to an issue, is willing to
make predictions and to stand by them. Science is
always willing to submit to objective experiment. This is a
reason to consider it more seriously than a framework of
belief that will not submit to prediction and objective test.
h. You may think these remarks are related to religion, but in
fact there are many reasons, besides arriving at an answer
in an area where science cannot provide one, for which one
may wish to escape the rigor of the scientific method.
Outline of Lecture on Copernican Revolution:
37. Let’s think about science and non-science.
i. Consider, for example, global warming.
j. Or genetically engineered plants as food.
k. Or tobacco.
l. Or marijuana.
m. Or acid rain.
n. Or substitutes for oil as fuels.
38. Science often comes into conflict with political and/or
economic interests of all types.
39. An advantage of science as a method is its ability to settle
arguments through experiment and demonstration, not
through war or deceit. Think about it.
32
Outline of Lecture on Copernican Revolution:
40. Science can be viewed as the study and discovery of things that
we can all agree about.
a. Science is about consensus, not argument.
b Science finds concepts that can be demonstrated by
b.
experiments that can be performed by anybody (you get
the result too, it doesn’t only happen when I do the
experiment) at any time (not just when I say) and any
place (not just in my laboratory).
c. Scientific concepts grow to be supported by mountains of
compelling evidence, so there is no further argument.
41. The agreement that is built by the scientific method is enviable.
a. Suppose you had a theory that if you and your friends paid
no taxes, while everybody else did, everyone would be
better off. Wouldn’t you like scientific agreement?
Outline of Lecture on Copernican Revolution:
42. The consensus that science builds is so powerful that other
endeavors try to capture some of its effects.
Once you understand how science works, you will learn to
recognize it when you see it.
a Is political science science?
a.
b. What about social science?
c. Or economics?
d. Is the law of supply and demand a law like the universal
law of gravity?
e Is Adam Smith
e.
Smith’ss theory of rent a theory with the force of
the theory of gravity?
43. What a shame it is that science seems to be restricted in
applicability to systems that do not interest many of us.
33