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Great year?

25,800 - 26,000

year cycles are God's diastolic beat.

zeitgeist | what is modern? | worldview | Influence | Background | lesson
dates | Siderius Nuncius | El Dialogo

sketches of the moon

Hipparchus in 127 BC recognized that the equinoxes move with respect to the fixed stars and this is called a:

"precession of the equinoxes."

Precession of the equinoxes

A scientific problem of complex movement

The slow westward movement of the equinoctial points along the plane of the ecliptic by a rate of 50.27 seconds of arc per year resulting from a slow westward shift of the Earth's axis of rotation.

Copernican vs. Ptolemaic world systems

Superior relation of theory to empirical observation:
Eclipses - earliest recorded eclipse is 19 March 721 BC

  • 29.5 days = 1 lunation of moon about the earth
  • 19 year cycle = 235 lunations

On the Julian calendar by 1425 the vernal equinox fell earlier and earlier than March 21

by 1570, the equinox was falling 10 days before 21 March. The October 1582 calendar was calculated on the basis of the Copernican model of the cosmos.

If the Sun is moving to the east, does that mean the moon moves to the west?


The person & the scientist


Foundations of measurement:

then & now



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Eventful moments in the Scientific Revolution

(internal history of science)

1477 earliest reprinting of Ptolemy's Geography [The map from which is below].

Ptolemies map
1492 First of Columbus' four voyages
1503 Vespucci's Novus Mundi -- The New World
1509 Erasmus, In Praise of Folly
1513 landing in Florida of Ponce de Leon
1517 Reformation
1545-63 Council of Trent
1560 Tycho Brahe begins observations of an eclipse
1569 Mercator's Projection of the map of the world
1578 Sir Francis Drake in California
1582 Hakluyt's Voyages published about the world
1590 microscope
1608 telescope
1609 Kepler's Astronomia Nova
1620 Bacon's, Novum Organum
1634 Thomas Hobbes met Galileo Galilei
1636 Galileo's trial before the inquisition
1687 Isaac Newton's Principia Mathematica

Ptolemy's world in the Renaissance was measurable and could readily predict a planet's observed motion and the precession of the equinox.

Ancient western cosmology stressed that our Cosmos was alive; made up of Four elements (earth, air, fire, and water).

This earth was the center of the heavens and made of base matter.

In opposition, celestial realm was dwelling place of perfect forms, this world was a reflection of the celestial quintessence.

Humans were part of a "SCALA NATURA" (a chain of being) and were divinely made (as were all things) of four material humors and an immortal soul.

Two opposed forces called gravity and levity account for the movement of the heavens and the disc-like earth.

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Natural Philosophy was set against empirical philosophy

1500 - 1600

Essentialism -- ""the animals and plants we observe as merely imperfect copies of the ideal or archetypal patterns defined and maintained on a supernatural plane of existence."

p. 35, Peter J. Bowler.

"Natural philosophers of the Renaissance could now appreciate the need for observation and mathematical analysis. and soon went on to transcend the theoretical achievements of the ancients."

p. 66, Peter J. Bowler.

Aristotle "the Master of those who know" said Dante (8)
the most profound characteristic of nature is change (process)

Euclid's Elements, Book V theory of proportionality was the most read book of the ancient world (Greco-Roman period of 1st century through the medieval period of the 15th century).

techne the Greek idiom for practical knowledge experience
episteme the Greek idiom for scientific knowledge reason

Their sources & goals were very different; prediction of events vs. fundamental causes of conditions in which events occurred.

"But even in astronomy and physics it was necessary to combine the mathematical spirit with an increased accuracy of observation."

p. 67, Peter J. Bowler.


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Euclid's Elements most widely read book of antiquity
Archimedes -- measurement & predictable laws of behavior
Aristarchus -- measurement & heliocentric cosmos
Copernicus -- corrected the error in measurement - heliocentric
Kepler (1598 saw his work) combined observation & math.


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In rejecting the geocentric or Ptolemaic model of the heavens, the precession of the equinoxes had to be explained as Galileo proposed that the Copernican model based on the heliocentric conception of the solar system.

sketches of the moon

"I have discovered four planets, neither known nor observed by any one of the astronomers before my time, which have orbits round a certain bright star, one of those previously known, like Venus & Mercury round the Sun, and are sometimes in front of it, sometimes behind it, though they never depart from it beyond certain limits."

venus phases

"Now let me review the observations made by me . . . inviting the attention of all who are eager for true philosophy. . . ."

"just as the shadows in the hollows of the Earth diminish in size as the Sun rises higher, so also the spots on the Moon lose their blackness as the illuminated part grows larger and larger."

"The grandeur of such prominences and depressions in the Moon seems to surpass both in magnitude and extent the ruggedness of the Earth's surface. . . ."

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Trial of Galileo was started on April 12, 1633:

Files of his trial include information on Galileo from 1611
1616 Holy Inquisition had banned the profession of belief in Copernicus as heretical

1632 Pope Urban VIII wrote: "Your Galileo has ventured to meddle with things that he ought not to and with the most important and dangerous subjects which can be stirred up these days,"

Trial presided over by Ten judges; all Cardinals of the Dominican Order

neither charges nor evidence was shared with the accused
written documents need not be produced

"I abjure, curse & detest the aforesaid errors and heresies, and generally every other error & sect whatsoever contrary to the said Holy Church,"

G. Galilei, 22 June 1633

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ethics or moral certainty

Special circumstances:
• vernacular (Italian) challenge to authority [Latin]
• anomalies in the heavens; comets, Medicean moons, Venus
• wars of the Reformation (1517-1648)
• empirical evidence for heliocentricity, precession of the equinox

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Galileo's significance:

    1. Assault on Aristotelian doctrines
    2. NeoPlatonism & new mathematics
    3. Conservation of motion
    4. Copernican
    5. observational & experimental method
    6. mathematical proof
    7. practical crafts people
    8. useful science
    9. inventive viewpoint
    10. modern worldview
    11. mechanism
    12. atomism
    13. mercantilism
    14. heliocentric - solar system

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According to Gerald Holton an historian at Harvard any description in order to be scientific must be refutable and be consistent across three different perspectives to have integrity such as Galileo's ideas about the earth moving around the sun, or the precession of the equinoxes:

1. THEORETICAL or rational -- see Gell-Mann and Einstein
2. EMPIRICAL or experience -- see Newton and Darwin
3. HEURISTIC or discoverable -- see Feynman and Watson

A refutable theory is based on a set of hypotheses that can be tested and scrutinized for any and all possible facts that could undermine the theory.


Comments on the scientific method.

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