The Ptolemaic System
Intellectual Background
Aristotle’s cosmology:
Universe as finite, spherical, and hierarchical
Earth sits motionless at the centre, made out of 4 elements: fire, water, air, earth
The heavens made up of a fifth element: the aether (perfect, unchanging)
Celestial motion should be uniform and circular (since circles were considered to be
perfect)
Claudius Ptolemy was born into Aristotle’s cosmology
Greco-Roman mathematician, astronomer, and geographer who lived around
100 to 170 AD in Alexandria, Egypt
In his book Almagest he produced the most mathematically detailed and
predictive version of the geocentric model
Goal: ‘save the phenomena’ Moet kloppen met wat we zien, niet noodzakelijk
waar zijn.
o Plato: describe observed phenomena (mathematically)
o By Ptolemy’s time: describe observed phenomena but also predict others
Het model moet zeggen: “Als je dit ziet, dan gebeurt dat”
Niet: “Zo zit de wereld echt in elkaar”
Astronomical tables based on Ptolemy’s system used for calendars, navigation,
and astrology Bleek het later niet de juiste beschrijving van de werkelijkheid
Circles upon circles; Movement of the Planets
Deferent: A large circular path centered roughly on Earth.
Epicycle: A smaller circle whose center moves along the deferent. Planets move
on epicycles
o Allows to explain retrograde motion, i.e. the apparent backward loops
planets make against the background stars
Eccentric and Equant points: Deferents are centered on the eccentric; the
Earth is slightly displaced from the eccentric. Epicycles are centered around the
equant.
o Breaks with Aristole’s demand for strictly uniform circular motion
o Preserves empirical accuracy (if the Earth is taken as geometrical centre
of the deferent, then the varying observed speeds of the planets cannot
be explained)
Movement of the stars
Daily motion: All stars are embedded in the celestial sphere, which rotates once
per day around the Earth. This accounts for the nightly east-to-west arcs of stars.
Fixed stars: Stars as “fixed” relative to one another, i.e. the constellations maintain
their shape. Any slow drift over years (precession) treated as a separate
phenomenon [which Ptolemy could also explain]
No detectable parallax: Ptolemy reasoned that if Earth were moving, nearby stars
should shift against the background stars. Since no such parallax was observed,
the Earth must be stationary. Als de Aarde beweegt, zouden de sterren een beetje
moeten “verschuiven” (parallax). Hij zag die verschuiving niet met het blote oog.
DUS: de Aarde staat stil, want als hij bewoog, zou je parallax zien.
Why Ptolemy’s system persisted
Empirical adequacy “Als je dit rekent, staan de planeten daar”: klopt met wat je ziet
, Conceptual coherence with Aristotelian physics and Christian theology; Paste bij het
wereldbeeld. Aristoteles: Aarde in het midden, Christendom: mens & aarde centraal
Lack of observational alternatives
o Phenomena like stellar parallax (the apparent shift of stars due to Earth’s
motion) were not observable with naked-eye precision. Dus: geen zichtbare
reden om te twijfelen
Institutional authority: Ptolemy’s Almagest became a cornerstone of the
medieval university curriculum and Islamic astronomy (Copernicus (1473–1543)
only came along roughly 1400 years later!)
Some insights
Empirical success ≠ truth: A theory can predict phenomena extremely well while
still being conceptually false
The power of background assumptions: metaphysical and aesthetic
commitments shape scientific models Iedereen heeft ideeën over hoe de wereld
zou moeten werken (metafysica) of wat mooi/logisch is (esthetiek). Bv. Aristoteles
dacht dat de aarde stil in het midden stond en dat alles in perfecte cirkels beweegt.
Theory shapes observation: what counts as “evidence of motion” depends on
your theoretical framework. Bv. sterrenparallax kon je alleen zien als je dacht: “De
aarde beweegt”. Mensen die dachten dat de aarde stil stond, zagen die
verschuiving niet als bewijs of merkten het simpelweg niet op.
Absence of evidence is not always evidence of absence, especially given
technological limits (e.g. parallax)
Towards heliocentrism
Copernicus (1473–1543)
Proposed the heliocentric model: the planets revolve around the sun instead of
around the earth (as the geocentric model proposed)
o This was a radical position that conflicted with an account of the heavenly
bodies that was held for hundreds of years by the most renowned scholars of
their time
Copernicus’ model preserved circular orbits and epicycles
o Not much simpler than Ptolemy’s model
Born in problems: no observed parallax of the stars (only measured by Friedrich
Bessel in 1838)
A search for simplicity and harmony
Copernicus was motivated by philosophical ideals:
o He believed the cosmos was created according to divine order, harmony, and
simplicity
o A good model should reflect that order, not just fit the data. The equant in
particular bothered him
By placing the Sun at the center, Copernicus found he could…
o Eliminate the equant
o Make the retrograde motions of planets natural consequences of Earth’s own
motion
o Preserve circular and uniform motions (for the most part)
So, heliocentrism offered a conceptual simplification, even though it didn’t
immediately improve predictive accuracy.
,Brightness variations of the planets (example for simplification)
Empirical observation: all planets change in brightness. Venus and Mercury only
ever visible close to sunset or sunrise. Mars, Jupiter, and Saturn are brightest when
opposite to the Sun (= rise when Sun sets)
Ptolemaic explanation: tweaking epicycles and deferents for each planet individually
to fit the phenomena
o Ad hoc explanation: a modification or added assumption made solely to
save a theory from conflicting evidence, without independently testable
consequences "Ik plak iets erop zodat mijn theorie klopt, maar het is niet
echt bewijs.”
Copernican explanation: Mercury and Venus are inside the Earth’s orbit around the
Sun. Mars, Jupiter and Saturn are outside of that orbit (= further away from the Sun)
Tycho Brahe (1546–1601)
Danish astronomer and nobleman
Ambition: truly accurate, empirical foundation for astronomy
Tychonic model:
o Earth at the centre
o Sun and Moon revolve around the Earth
o The planets revolve around the Sun
This is geocentrism, but with some heliocentristic flavour
Johannes Kepler (1571–1630)
Ardent (= vurig) Copernican
Worked on Tycho’s data
Believed that Mars’s motion could not be explained by any circular model
o “If I had believed that we could ignore 8 minutes of arc, I would have patched
up my hypothesis accordingly. But since it was not permissible to ignore,
these 8 minutes pointed the road to a complete reformation of astronomy.”
Dat zou een ad hoc oplossing zijn geweest, maar hij vond die afwijking
belangrijk → leidde naar een hele nieuwe theorie
Suggested that orbits are elliptical not circular
Galileo Galilei (1564–1642)
Copernican sympathiser
Telescopic observations
o Mountains on the moon: heavens not perfect (zoals Aristoteles dacht)
o 4 moons orbiting around Jupiter: not everything revolves around the Earth
o The phases of Venus: this is sometimes regarded as a crucial experiment
that showed that Ptolemy’s geocentrism was wrong and Copernicus’s
heliocentrism true/more adequate
The Phases of Venus
Ptolemy’s system: Venus’s epicycle always lies between Earth and the Sun
Venus can only ever been seen in crescent-like phases, never full
Copernicus’s system: Venus sometimes passes behind the Sun (from Earth’s
perspective), so it can appear fully illuminated.
Galileo observed all phases (crescent and full), thereby “disconfirming” geocentrism
,Crucial Experiments
“Propose theories which can be criticized. Think about possible decisive falsifying
experiments - crucial experiments. But do not give up your theories too easily—not, at
any rate, before you have critically examined your criticism.”
(Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (1963), p. 170-
171, emphasis added)
Crucial experiments: experiments which could decisively falsify a theory
Were the phases of Venus a crucial experiment?
Yes:
- Decisive test between conflicting theories (geocentrism & heliocentrism make
different predictions about the phases of Venus)
- Historical impact
No:
- Theory-laden observations: experimental evidence presupposes theory. E.g.
telescopic evidence is only evidence when we subscribe to the theories that we
used to build the telescope. Wat je ziet in een experiment hangt af van de theorieën
die je al hebt. Zonder achtergrondtheorie zou je bewijsmateriaal niet kunnen
interpreteren.
- Underdetermination of auxiliary hypothesis: any observation is made against
the background of numerous additional (auxiliary) hypotheses, e.g. that Galileo did
not by accident look at the moon, that his telescope was clean, etc. Je observatie
zegt op zichzelf niks; een waarneming kan meerdere verklaringen hebben,
afhankelijk van wat je aanneemt.
Was Mars’s motion a crucial experiment?
Yes:
- Empirical “refutation” of an entrenched principle
- Historical outcome
No:
- Not an “experiment” (Kepler analysed existing data; no controlled manipulation or
intervention)
- Underdetermination of theory by data (Duhem/Quine thesis): the same
observational data can be accounted for by different theoretical frameworks. E.g.
both Copernicus’s heliocentric and Tycho’s geocentric model account equally well
for Mars’s motion. Data kan meerdere theorieën “ondersteunen” → je hebt niet
genoeg alleen aan observaties om te kiezen welke theorie waar is. Het feit dat iets
gebeurt, zegt niet automatisch welke theorie klopt.”
Relevant take-aways
Empirical success ≠ truth
The notion of a crucial experiment (Popper): is ‘decisive evidence’ a myth?
Ad hoc explanations/changes to theory
The power of background assumptions**
o Metaphysical and aesthetic commitments shape scientific models
o Underdetermination of theory by data (Duhem/Quine thesis)
Underdetermination of auxiliary hypothesis
o Observations are theory-laden (Hanson/Kuhn)
, Case studies as a method
Some words about case studies as method
We observed some points about the Copernican revolution (e.g. relevance of background
assumptions) and then suggested that these points appear in science generally. Is this not
just induction (bijzonder -> algemeen) from a single instance?
- Yes, if we say that what we have observed holds generally
- No, if we say that what we have observed can happen in the sciences
Is this enough? That will depend on our aims
Let’s deepen the worry about case studies
The dilemma of case studies (Pitt, 2001):
o First horn: we already hold a certain view and then cherry-pick our case
studies to support this view
o Second horn: we do not have a view yet and wish to “be led by our findings”,
which runs into the problem of induction
Chang’s (2011) criticises Pitt for viewing case studies as the particular and theory
as the general. Better: abstract vs. concrete.
Chang’s ‘never-ending’ process of abstracting from the concrete and testing the
abstract against some concrete instances.
** Achterliggende aannames = dingen die je stiekem gelooft of aanneemt voordat je iets
onderzoekt of berekent. Het zijn ideeën die je niet altijd expliciet zegt, maar die bepalen hoe je
dingen interpreteert.
Intellectual Background
Aristotle’s cosmology:
Universe as finite, spherical, and hierarchical
Earth sits motionless at the centre, made out of 4 elements: fire, water, air, earth
The heavens made up of a fifth element: the aether (perfect, unchanging)
Celestial motion should be uniform and circular (since circles were considered to be
perfect)
Claudius Ptolemy was born into Aristotle’s cosmology
Greco-Roman mathematician, astronomer, and geographer who lived around
100 to 170 AD in Alexandria, Egypt
In his book Almagest he produced the most mathematically detailed and
predictive version of the geocentric model
Goal: ‘save the phenomena’ Moet kloppen met wat we zien, niet noodzakelijk
waar zijn.
o Plato: describe observed phenomena (mathematically)
o By Ptolemy’s time: describe observed phenomena but also predict others
Het model moet zeggen: “Als je dit ziet, dan gebeurt dat”
Niet: “Zo zit de wereld echt in elkaar”
Astronomical tables based on Ptolemy’s system used for calendars, navigation,
and astrology Bleek het later niet de juiste beschrijving van de werkelijkheid
Circles upon circles; Movement of the Planets
Deferent: A large circular path centered roughly on Earth.
Epicycle: A smaller circle whose center moves along the deferent. Planets move
on epicycles
o Allows to explain retrograde motion, i.e. the apparent backward loops
planets make against the background stars
Eccentric and Equant points: Deferents are centered on the eccentric; the
Earth is slightly displaced from the eccentric. Epicycles are centered around the
equant.
o Breaks with Aristole’s demand for strictly uniform circular motion
o Preserves empirical accuracy (if the Earth is taken as geometrical centre
of the deferent, then the varying observed speeds of the planets cannot
be explained)
Movement of the stars
Daily motion: All stars are embedded in the celestial sphere, which rotates once
per day around the Earth. This accounts for the nightly east-to-west arcs of stars.
Fixed stars: Stars as “fixed” relative to one another, i.e. the constellations maintain
their shape. Any slow drift over years (precession) treated as a separate
phenomenon [which Ptolemy could also explain]
No detectable parallax: Ptolemy reasoned that if Earth were moving, nearby stars
should shift against the background stars. Since no such parallax was observed,
the Earth must be stationary. Als de Aarde beweegt, zouden de sterren een beetje
moeten “verschuiven” (parallax). Hij zag die verschuiving niet met het blote oog.
DUS: de Aarde staat stil, want als hij bewoog, zou je parallax zien.
Why Ptolemy’s system persisted
Empirical adequacy “Als je dit rekent, staan de planeten daar”: klopt met wat je ziet
, Conceptual coherence with Aristotelian physics and Christian theology; Paste bij het
wereldbeeld. Aristoteles: Aarde in het midden, Christendom: mens & aarde centraal
Lack of observational alternatives
o Phenomena like stellar parallax (the apparent shift of stars due to Earth’s
motion) were not observable with naked-eye precision. Dus: geen zichtbare
reden om te twijfelen
Institutional authority: Ptolemy’s Almagest became a cornerstone of the
medieval university curriculum and Islamic astronomy (Copernicus (1473–1543)
only came along roughly 1400 years later!)
Some insights
Empirical success ≠ truth: A theory can predict phenomena extremely well while
still being conceptually false
The power of background assumptions: metaphysical and aesthetic
commitments shape scientific models Iedereen heeft ideeën over hoe de wereld
zou moeten werken (metafysica) of wat mooi/logisch is (esthetiek). Bv. Aristoteles
dacht dat de aarde stil in het midden stond en dat alles in perfecte cirkels beweegt.
Theory shapes observation: what counts as “evidence of motion” depends on
your theoretical framework. Bv. sterrenparallax kon je alleen zien als je dacht: “De
aarde beweegt”. Mensen die dachten dat de aarde stil stond, zagen die
verschuiving niet als bewijs of merkten het simpelweg niet op.
Absence of evidence is not always evidence of absence, especially given
technological limits (e.g. parallax)
Towards heliocentrism
Copernicus (1473–1543)
Proposed the heliocentric model: the planets revolve around the sun instead of
around the earth (as the geocentric model proposed)
o This was a radical position that conflicted with an account of the heavenly
bodies that was held for hundreds of years by the most renowned scholars of
their time
Copernicus’ model preserved circular orbits and epicycles
o Not much simpler than Ptolemy’s model
Born in problems: no observed parallax of the stars (only measured by Friedrich
Bessel in 1838)
A search for simplicity and harmony
Copernicus was motivated by philosophical ideals:
o He believed the cosmos was created according to divine order, harmony, and
simplicity
o A good model should reflect that order, not just fit the data. The equant in
particular bothered him
By placing the Sun at the center, Copernicus found he could…
o Eliminate the equant
o Make the retrograde motions of planets natural consequences of Earth’s own
motion
o Preserve circular and uniform motions (for the most part)
So, heliocentrism offered a conceptual simplification, even though it didn’t
immediately improve predictive accuracy.
,Brightness variations of the planets (example for simplification)
Empirical observation: all planets change in brightness. Venus and Mercury only
ever visible close to sunset or sunrise. Mars, Jupiter, and Saturn are brightest when
opposite to the Sun (= rise when Sun sets)
Ptolemaic explanation: tweaking epicycles and deferents for each planet individually
to fit the phenomena
o Ad hoc explanation: a modification or added assumption made solely to
save a theory from conflicting evidence, without independently testable
consequences "Ik plak iets erop zodat mijn theorie klopt, maar het is niet
echt bewijs.”
Copernican explanation: Mercury and Venus are inside the Earth’s orbit around the
Sun. Mars, Jupiter and Saturn are outside of that orbit (= further away from the Sun)
Tycho Brahe (1546–1601)
Danish astronomer and nobleman
Ambition: truly accurate, empirical foundation for astronomy
Tychonic model:
o Earth at the centre
o Sun and Moon revolve around the Earth
o The planets revolve around the Sun
This is geocentrism, but with some heliocentristic flavour
Johannes Kepler (1571–1630)
Ardent (= vurig) Copernican
Worked on Tycho’s data
Believed that Mars’s motion could not be explained by any circular model
o “If I had believed that we could ignore 8 minutes of arc, I would have patched
up my hypothesis accordingly. But since it was not permissible to ignore,
these 8 minutes pointed the road to a complete reformation of astronomy.”
Dat zou een ad hoc oplossing zijn geweest, maar hij vond die afwijking
belangrijk → leidde naar een hele nieuwe theorie
Suggested that orbits are elliptical not circular
Galileo Galilei (1564–1642)
Copernican sympathiser
Telescopic observations
o Mountains on the moon: heavens not perfect (zoals Aristoteles dacht)
o 4 moons orbiting around Jupiter: not everything revolves around the Earth
o The phases of Venus: this is sometimes regarded as a crucial experiment
that showed that Ptolemy’s geocentrism was wrong and Copernicus’s
heliocentrism true/more adequate
The Phases of Venus
Ptolemy’s system: Venus’s epicycle always lies between Earth and the Sun
Venus can only ever been seen in crescent-like phases, never full
Copernicus’s system: Venus sometimes passes behind the Sun (from Earth’s
perspective), so it can appear fully illuminated.
Galileo observed all phases (crescent and full), thereby “disconfirming” geocentrism
,Crucial Experiments
“Propose theories which can be criticized. Think about possible decisive falsifying
experiments - crucial experiments. But do not give up your theories too easily—not, at
any rate, before you have critically examined your criticism.”
(Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (1963), p. 170-
171, emphasis added)
Crucial experiments: experiments which could decisively falsify a theory
Were the phases of Venus a crucial experiment?
Yes:
- Decisive test between conflicting theories (geocentrism & heliocentrism make
different predictions about the phases of Venus)
- Historical impact
No:
- Theory-laden observations: experimental evidence presupposes theory. E.g.
telescopic evidence is only evidence when we subscribe to the theories that we
used to build the telescope. Wat je ziet in een experiment hangt af van de theorieën
die je al hebt. Zonder achtergrondtheorie zou je bewijsmateriaal niet kunnen
interpreteren.
- Underdetermination of auxiliary hypothesis: any observation is made against
the background of numerous additional (auxiliary) hypotheses, e.g. that Galileo did
not by accident look at the moon, that his telescope was clean, etc. Je observatie
zegt op zichzelf niks; een waarneming kan meerdere verklaringen hebben,
afhankelijk van wat je aanneemt.
Was Mars’s motion a crucial experiment?
Yes:
- Empirical “refutation” of an entrenched principle
- Historical outcome
No:
- Not an “experiment” (Kepler analysed existing data; no controlled manipulation or
intervention)
- Underdetermination of theory by data (Duhem/Quine thesis): the same
observational data can be accounted for by different theoretical frameworks. E.g.
both Copernicus’s heliocentric and Tycho’s geocentric model account equally well
for Mars’s motion. Data kan meerdere theorieën “ondersteunen” → je hebt niet
genoeg alleen aan observaties om te kiezen welke theorie waar is. Het feit dat iets
gebeurt, zegt niet automatisch welke theorie klopt.”
Relevant take-aways
Empirical success ≠ truth
The notion of a crucial experiment (Popper): is ‘decisive evidence’ a myth?
Ad hoc explanations/changes to theory
The power of background assumptions**
o Metaphysical and aesthetic commitments shape scientific models
o Underdetermination of theory by data (Duhem/Quine thesis)
Underdetermination of auxiliary hypothesis
o Observations are theory-laden (Hanson/Kuhn)
, Case studies as a method
Some words about case studies as method
We observed some points about the Copernican revolution (e.g. relevance of background
assumptions) and then suggested that these points appear in science generally. Is this not
just induction (bijzonder -> algemeen) from a single instance?
- Yes, if we say that what we have observed holds generally
- No, if we say that what we have observed can happen in the sciences
Is this enough? That will depend on our aims
Let’s deepen the worry about case studies
The dilemma of case studies (Pitt, 2001):
o First horn: we already hold a certain view and then cherry-pick our case
studies to support this view
o Second horn: we do not have a view yet and wish to “be led by our findings”,
which runs into the problem of induction
Chang’s (2011) criticises Pitt for viewing case studies as the particular and theory
as the general. Better: abstract vs. concrete.
Chang’s ‘never-ending’ process of abstracting from the concrete and testing the
abstract against some concrete instances.
** Achterliggende aannames = dingen die je stiekem gelooft of aanneemt voordat je iets
onderzoekt of berekent. Het zijn ideeën die je niet altijd expliciet zegt, maar die bepalen hoe je
dingen interpreteert.
