I.
Nicolas Copernicus (1473-1543)
A.
Astronomical Background.
1.
Ptolemaic astronomy, within the general framework of Aristotelian physics,
dominated contemporary astronomical thought--a mathematical, nonobservational
approach concerned with 'saving the phenomena'.
2.
Basic premises of ancient astronomy:
a.
Geostatic and geocentric cosmos.
b.
Celestial bodies possess uniform, circular motion around a central point.
c.
Celestial bodies are composed of a fifth element, the quintessence.
d.
The cosmos is finite.
3. Difficulty
developed concerning the Ptolemaic use of the equant, which violated the
aesthetic concept of uniform motion, and the use of epicycles, which put
the center of motion on a geometric point other than a center of a deferent.
4.
Primary weakness of the existing Ptolemaic schema: it did not entirely
"save the phenomena," that is, observational-theoretical discrepancies
had become apparent.
B. The
Copernican System.
1.
Introduced three celestial motions.
a.
Diurnal rotation of the earth on its axis.
b.
The earth, and the planets, revolve around the sun.
c.
A conical axial motion of earth to explain the fixed orientation of earth
in space.
2. Copernicus
was a mathematical, not an observational, astronomer, and the mathematical
apparatus of his system was as complex as Ptolemy's, employing the same
geometrical devices (except the equant).
3.
Copernicus sought to purify ancient astronomy, not to overthrow Ptolemy;
not a 'revolution' in the technical sense, in that either system would
'save the phenomena' to some degree; the Copernican system only altered
the geostatic and geocentric premise of ancient astronomy.
4.
Copernican advantages were limited to a somewhat simpler computational
technique and the introduction of a more intelligible order in the heavens,
for example, removal of the ad hoc constructions needed to describe
retrograde motion and the ordering of planets.
5.
The main disadvantage of the Copernican system was its violation of Aristotelian
physics--the physical problems involved with the heliocentric system called
for a new, as yet nonexistent, physics.
C. Motivation
for the Copernican System.
1.
Copernicus was educated at Cracow and Bologna in a critical atmosphere
that called for the reform of Ptolemaic astronomy and cosmology.
2.
Renaissance Platonic-Pythagorean influences stressed unity, coherence,
and harmony in the cosmos in addition to accounting for observed phenomena.
D. The
Copernican 'Revolution'
1.
A 'revolution' inadvertently, in that Copernicus was a conservative who
sought to purify, not destroy, ancient astronomy.
2.
Its revolutionary aspect lay in its violation of Aristotelian physics and
the implicit requirement of a 'new' physics which caused natural philosophers
to think, and look, in a new astronomical frame of reference.
II. Johannes
Kepler (1571-1630)
A.
Background of Keplerian Astronomy.
1.
Platonic and Pythagorean elements, especially a mystical sense of mathematical
harmony in the cosmos, for example, the use of the five regular polyhedra
to account for the planetary orbits,
The Cosmographic Mystery (1596).
2.
The heliocentric Copernican cosmos with uniform circular motion.
3.
The mechanical ideas of the Renaissance, particularly "clockwork" as a
suggestive conceptual model for celestial physics.
4.
Existence of 'powers' such as magnetism and light which could be used to
account for the physical force necessary to drive the celestial machine.
5.
Kepler was a highly competent mathematician.
B. Kepler
and the Tychonic System.
1.
Brahe provided Kepler with the best collection of observational (empirical)
data in existence.
2.
He set Kepler to work on the problem of the orbit of Mars, that is, the
planet's nonuniform motion with respect to the center of its orbit:
a.
Disregarded the use of equants and epicycles as a solution.
b.
Formulated the Area Law: in equal time intervals a planet will sweep out
equal areas (Second Law).
c.
Kepler settled on the ellipse as an orbital path, that is, planetary orbits
are elliptical (First Law).
C. Synopsis
of Keplerian Astronomy.
1.
A nonempirical, mathematical commitment to the area law and the geometrical
cosmos of elliptical orbits--the data were observational but the commitment
was philosophical.
2.
Introduced a type of 'physical' unity, that is, a solar 'power' or 'virtue'
moves the planets in their orbits.
3.
The account of elliptical orbits was based on the assumption that the sun
and the planets were magnets, an action between "animate souls" which served
to attract, or be attracted by, the sun thus drawing the planets into elliptical
paths.
4.
No quantitative elements have been introduced--a qualitative analysis expressed
in terms of mathematical harmonies, for example, the square of a planetary
period is proportional to the planet's mean distance from the sun, T [squared]
is proportional R [cubed] (Kepler's Third Law ).
5.
Kepler thought he had penetrated the structural reality of the cosmos and
in so doing, was forced to seek a 'new' celestial physics.
III.
Galileo Galilei (1564-1642)
A.
Intellectual Roots of Galileo's Science.
1.
Copernican astronomy and the implicit necessity of a 'new' physics to replace
Aristotelian mechanics.
2.
A long tradition in mechanics extending from the ancient world and middle
ages through the Renaissance (for example, Aristotle, Philoponus, Avempace,
the Merton and Parisian schools, Padua), and especially the works of Archimedes.
B. Galileo
and Astronomy.
1.
Galileo was a confirmed Copernican and given to the concept of circular
motion.
2.
Galileo wrote for a literate but nontechnical reader in his defense of
Copernicus, and not as a professional astronomer--his arguments and evidence
were polemical and perhaps propagandistic.
3.
Galileo's 'facts' differed from the traditional data of astronomy in that
they were derived from qualitative telescopic observations.
4.
Observational data obtained with the telescope:
a.
Stellar 'population explosion' implying an expanded cosmos.
b.
The topography of the moon was similar to, or more pronounced than, that
of the earth; the earth-like moon moves around the earth--why can't the
earth move around the sun?
c.
The phases of Venus were inexplicable in terms of Ptolemaic cosmology;
Ptolemaic scheme no longer viable.
d.
The satellites of Jupiter, moving with, and approximately in the same plane
as the planet, suggested more than one center of rotation in the solar
system and, by analogy, the earth's rotation around the sun.
e.
Sun spots implied that the heavens are not perfect (to reinforce the argument
of the moon's topography); these data were obviously unknown to Aristotle
or Ptolemy.
C.
The Problem of Falling Bodies.
1.
His early work in the 1 590s dealt with falling bodies as a problem in
dynamics approached in terms of the self-expending impetus theory of Oresme
and Avempace, V is proportional to W-R.
2.
Inspired by Archimedes and Benedetti, Galileo used hydrostatics as a model
for his science.
3.
In his later work, Galileo abandoned the dynamical approach in favor of
kinematics.
4.
He proceeded to clarify, restate, and systematize medieval problems in
kinematics while giving them a more complete mathematical expression, for
example, problems suggested by the Odd Numbers Law relating distance to
time (S proportional to t squared) and velocity to distance (V proportional
to S), out of which he came to relate velocity to time (V proportional
to T), and eventually, S = 1/2at [squared].
5.
After 1609, Galileo's kinematic treatment of an idealized model identified
falling bodies as a case of uniformly accelerated motion and thereafter
demonstrated it with his inclined plane experiment.
D. Projectile
Motion.
1.
Galileo's work developed out of the impetus theories of contemporary physics,
especially those of Tartaglia and Benedetti.
2.
In his later theory (1632), no force is necessary to keep a body moving
on a level (frictionless) plane; a body, as such, has no inclination to
move or remain at rest, it is indifferent.
3.
Thus, if a body is indifferent to motion, no mover is required to sustain
movement once a body is in motion.
4.
Motion is now a state rather than a process, and rest is motion of zero
speed in a continuum.
5.
Galileo's conception of inertia as circular motion was an attempt to save
Copernican circularity, particularly in the absence of any known force
which could 'bend' rectilinear motion into an orbit.
E. Galileo's
Method.
1.
Galileo argued that theoretical conclusions required experimental verification
even if the experimentation was mental rather than empirical.
2.
He was a thinker about nature and thought in terms of ideal situations
rather than the complexities of the sensate world.
3.
Expressed confidence in deductive, reasoned conclusions: Archimedean mathematics
applied to physical problems rather than extensive experimental programs.
IV. René
Descartes (1596-1650) and the Mechanical Philosophy
A.
Background of the Mechanical Philosophy.
1.
Derived from ancient atomism but reworked by 17th century thinkers such
as Descartes, Gassendi, Huygens, Hooke, and Boyle.
2.
Reaction against the animistic philosophies of the Renaissance, notably
Hermetism.
3.
Conceived as an alternative to existing Aristotelian metaphysics.
B. Basic
Tenets of the Mechanical Philosophy.
1.
Viewed nature as composed of inert (without quality) matter in motion.
2.
All causality involved matter in contact with matter--no action at-a-distance.
C. Cartesian
Mechanical Philosophy.
1.
Descartes, reacting against Renaissance skepticism, sought to affirm the
existence of certain knowledge.
2.
The conclusions of mathematics, especially those of geometry, are demonstrable,
that is, start with true premises (clear and distinct ideas) and proceed
deductively to certain conclusions.
3.
Mathematics accepted as a model, though not the essence, of knowledge.
4.
Descartes' methodical doubt reduces existing substances to two types:
a.
Res
cogitans (thinking stuff): immaterial thought or mind.
b.
Res
extensa (extended stuff): geometrical extension or matter.
5. All
that exists outside the mind is matter: only primary qualities exist, that
is, motion, size, shape, number, location, place; secondary qualities are
illusory (soft, hard, hot, cold, wet, dry, etc.).
6.
The universe is a plenum, that is, it is 'full' with no void possible.
7.
Matter is of three types, classified as to size: First matter, fine (chips);
second matter, medium (spheres); and third matter, gross (chunks), that
is, respectively, material light, aether, and ordinary, visible matter.
8.
The interaction between the various forms of matter occur as the result
of vortex action; the universe is composed of vortices or whirlpools of
matter. Vortices explain the varying periods and uniform orbital directions
and inclinations of the planets.
9.
Formulated the concepts of rectilinear inertia and the conservation of
motion.
V.
Francis Bacon (1561-1626) and the Baconian Method
A.
Opposition to Scholastic and Renaissance Philosophy: The Idols.
1.
The Tribe: weaknesses of human nature, that is, prejudice, passions, limited
mental and sensory faculties.
2.
The Cave: weaknesses of environment, that is, education, habit, prejudice,
predisposition of approach to philosophical-scientific questions.
3.
The Market Place: semantic difficulties arising from confusing words with
things.
4.
The Theatre: philosophical systems or theories which direct the mind beyond
the data of experience to unsupported generalities.
B. Basic
Assumption: The Simplicity of Nature.
1.
Scientific progress is a matter of finding the correct method, that is,
the correct method is equivalent to truth:
a.
If nature is approached in the appropriate manner, the truth can be found.
b.
Error is the result of defective methods.
2. The
ultimate goal of science is practical utility for the benefit of mankind.
3.
The method is the 'tool' of the intellect: it enables the mind to overcome
its weaknesses, and can compensate for disparity of mental ability.
4.
The function of method is to collect data from the natural world and refashion
it (the bee)--it is not just empirical cataloguing (the ant) and it is
not a matter of pure speculation (the spider).
C. The
Baconian Method.
1.
The basic premise: observe nature with the senses--proceed inductively
from observations (data) to generalities (axioms), and form deductive conclusions
which can be tested by experimental evidence.
2.
The method of exclusion:
a.
Tabulate all possible causes of an observed effect.
b.
Observe
nature to see what causes actually exist in the given physical circumstances.
c.
Exclude all but one, that is, the result of the crucial experiment.
VI. Isaac
Newton (1642-1727) and the Newtonian Synthesis
A.
Elements of the Synthetic, "New" Physics.
1.
Galileo's idealized formulation of the law of freely falling bodies, d
= 1 /2at [squared].
2.
Galileo's analysis of terrestrial inertia: a body is indifferent to uniform
rectilinear motion and is as 'natural' as rest.
3.
Descartes' conception of rectilinear inertia existing in Euclidean space
and the implied rejection of privileged spatial position.
4.
Kepler's 'discovery' of his three laws of celestial motion, especially
the The Third Law, T squared is proportional to the mean Radius cubed.
5.
Huygens' and Borelli's work on centrifugal forces, terrestrial and celestial
respectively, suggested an inverse square relationship, as well as the
analogy from light made explicit by Boulliau.
B. The
Problem and the Test Case: Lunar Motion.
1.
Lunar motion was essential to both Aristotle and Newton:
a.
The lunar orbit was the demarcation line for the Aristotelian two-world
system (sublunar/superlunar regions).
b.
The connection of lunar-terrestrial motion under the same principle was
the crux of the Newtonian argument.
2. Newtonian
assumptions:
a.
The Copernican hypothesis: the earth is a planet.
b.
The hypothesis that inter-planetary space is empty, that is, free space.
3. The
problem was to explain the configuration of planetary orbits, that is,
what mechanism or force can account for the orbital alteration of a planet's
rectilinear path.
C. The
Moon's Orbit and the Unification of Terrestrial-Celestial Physics.
1.
Problem of translating the moon's rectilinear acceleration into the centripetal
acceleration necessary to account for the lunar orbit--assume circular
Copernican orbits.
2.
Problem of demonstrating that lunar acceleration represents a ratio equivalent
to that of free fall on the earth, implying the same gravitational force:
the inverse square law.
3.
Problem of justifying the mathematical treatment of the earth's total mass
as concentrated in a single mass point at the earth's center; Newton's
solution rested upon his invention of the calculus, his "fluxions", which
could be used to consider the intricacies of the problem.
4.
The final stage was to transfer the concept of force for a planetary orbit
in relation to the sun, based on the moon-earth test case to a universal,
reciprocal gravitational relationship which applied to all matter
D.
Components of Newtonian Physics.
1.
Matter:
an infinite number of separate, hard, and unchangeable particles which
are not identical.
2.
Motion:
the relational state which moves particles from place to place in an infinite
void of free space without affecting them.
3.
Space:
the
infinite homogeneous void in which the particles, and the bodies they form,
move.
4.
Attraction:
the undefined unifying force which is not a constructive element but rather
a "hyperphysical" power or mathematical statement describing how the universal
components are connected.
E. The
Destruction of the Aristotelian Cosmos.
1.
Considerations of such concepts as perfection, harmony, teleology, formal
and final causality, and value are removed from scientific discussion.
2.
The world was no longer viewed as finite and hierarchically ordered: quantitative
considerations replace qualitative ones.
3.
The celestial and terrestrial worlds are no longer philosophically and
scientifically distinct; astronomy and physics have been geometrically
unified.
F. The
Mathematical Generation of Homogeneous, Abstract Euclidean Space.
1.
The common sense world of the pre-Galilean cosmos is replaced by an idealized
mathematical universe.
2.
Newtonian science attempted to synthesize mathematics and experiment: the
integration of theory and experience under the 'direction' of the inverse
square law.
3.
The Newtonian pattern of empirical-deductive knowledge provided both physical
and intellectual unity for the 18th-century universe. Alexander Pope
suggested:
Nature
and nature's laws
Lay
hid in night,
And
God said
'Let
Newton be'
And
all was light.
The
Enlightenment is sometimes called 'Newton's Century.'
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