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.
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.
