MELK (APOD 2009 April 17)

[neufer]

http://apod.nasa.gov/apod/ap090417.html
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• Distribution of Easter Sundays in the Julian Calendar
  
  <<Table lists all the possible dates for Easter Sunday in the Julian calendar (and in the Coptic/Ethiopian calendar) according to the Dionysian reckoning from AD 533 to AD 2128 (spanning three complete Dionysian Easter Cycles). The last two columns give the number of occurrences during a Dionysian Easter Cycle of 532 years, the period after which the dates of Easter Sunday repeat in the same sequence.>>

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Dionysian Easter Cycle of 532 years = 19 year Metonic cycle x 4 year leap year cycle x 7 days a week
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<<In 525, Dionysius prepared a table of the future dates of Easter and a set of "arguments" explaining their calculation (computus) on his own initiative. He ignored the existing tables used by the Church of Rome, which were prepared in 457 by Victorius of Aquitaine, complaining that they did not obey Alexandrian principles, without actually acknowledging their existence. To be sure that his own tables were correct, he simply extended a set of tables prepared by a subordinate of Bishop Cyril of Alexandria shortly before Cyril's death in 444. They covered a period of 95 years or five decennovenal (19-year) cycles with years dated in the Diocletian Era, whose first year was 285 (the modern historical year in progress at Easter). Diocletian years were advantageous because their division by 19 yielded a remainder equal to the year of the decennovenal cycle (1–19).

The epact (the age of the moon on 22 March) of all first decennovenal years was zero, making Dionysius the first known medieval Latin writer to use a precursor of the number zero. The Latin word nulla meaning nothing was used because no Roman numeral for zero existed. To determine the decennovenal year, the Dionysian year plus one was divided by 19. If the result was zero (to be replaced by 19), it was represented by the Latin word nihil, also meaning nothing. Both "zeros" continued to be used by (among others) Bede, by whose extension of Dionysius Exiguus’ Easter table to a great Easter cycle all future Julian calendar dates of Easter Sunday were fixed unambiguously at last. However, in medieval Europe one had to wait as late as the second millennium before one got dispose of the number zero itself, which had come into being around the year 600 in India.

Dionysius copied the last decennovenal cycle of the Cyrillian table ending with Diocletion 247, and then added a new 95-year table with numbered Anni Domini Nostri Jesu Christi (Years of our Lord Jesus Christ) because, as he explained to Petronius, he did not wish to continue the memory of a tyrant who persecuted Christians. The only reason he gave for beginning his new 95-year table with the year 532 was that six years were still left in the Cyrillian table after the year during which he wrote. He did not realize that the dates of the Alexandrian Easter repeated after 532 years. Furthermore, he obviously did not realize that simply multiplying 19 by 4 by 7 (decennovenal cycle x cycle of leap years x days in a week) fixed the Alexandrian cycle at 532 years, otherwise he would have stated such a simple fact.>>

[bystander]

Dionysian Easter Cycle of 532 years = 19 year Metonic cycle x 4 year leap year cycle x 7 days a week

And what does the Greek god of wine, the inspirer of ritual madness and ecstasy, have to do with Easter?

Art, you're slipping. I would have expected your title to be Got MELK?

[CharlieNNC]

Were the optics that good in 1490 that Pluto was observed and cataloged?

[crosscountry]

Not at all, there were no optics in 1490 (maybe hand lenses for reading). In fact after the moon there are only 8 listed things: Mercury, Venus, Sun, Mars, Jupiter, Saturn, and two I cannot understand. Uranus, Neptune, and Pluto had not been discovered yet.

I came here to ask what the last two were.

[bystander]

Not at all, there were no optics in 1490 (maybe hand lenses for reading). In fact after the moon there are only 8 listed things: Mercury, Venus, Sun, Mars, Jupiter, Saturn, and two I cannot understand. Uranus, Neptune, and Pluto had not been discovered yet.

I came here to ask what the last two were.

Ptolemaic system: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, Fixed Stars, and Prime Mover

[neufer]

Dionysian Easter Cycle of 532 years = 19 year Metonic cycle x 4 year leap year cycle x 7 days a week

And what does the Greek god of wine, the inspirer of ritual madness and ecstasy, have to do with Easter?

• ---------------------------------------------------
  Oscar Levant: There's a fine line between
  . genius & insanity. I have erased this line.
  ---------------------------------------------------

Art, you're slipping. I would have expected your title to be Got MELK?

Harvey Milk: Is anyone gonna pay the pizza guy, or are we all just gonna stare?

[aristarchusinexile]

Dionysian Easter Cycle of 532 years = 19 year Metonic cycle x 4 year leap year cycle x 7 days a week

And what does the Greek god of wine, the inspirer of ritual madness and ecstasy, have to do with Easter?

Excellent example of twist. Thanks.

[neufer]

Dionysian Easter Cycle of 532 years = 19 year Metonic cycle x 4 year leap year cycle x 7 days a week

And what does the Greek god of wine, the inspirer of ritual madness and ecstasy, have to do with Easter?

Excellent example of twist. Thanks.

thigh....

John 15:5 "I am the vine"
Mark 14:24 "This is my blood"

"Virgin" impregnation by Zeus of Dionysus

<<Dionysus, the son of Zeus and Persephone, the queen of the underworld, is called Zagreus, and was dismembered by the Titans, at the instigation of Hera. Zeus created mead out of Zagreus's heart, which he gave to Semele to drink, and that this was how she became pregnant. Semele later demanded of Zeus that he reveal himself in all his glory as proof of his godhood. Though Zeus begged her not to ask this, she persisted and he agreed. Mortals, however, cannot look upon Zeus without dying, and she perished, consumed in lightning-ignited flame. Zeus rescued the fetal Dionysus, however, by sewing him into his thigh. A few months later, Dionysus was born. This leads to his being called "the twice-born". Dionysus "was also called Dimetor [of two mothers] ... because the two Dionysoi were born of one father, but of two mothers" According to Ellie Crystal, the rebirth in both versions of the story is the primary reason he was worshipped in mystery religions, as his death and rebirth were events of mystical reverence, and this narrative was apparently used in certain Greek and Roman mystery religions.>>

[bystander]

Getting back to beer (or was that another thread)



Sculpture of Dionysus drinking Qingdao Beer,
commissioned to celebrate the 100th anniversary of Qingdao Beer.
Qingdao Beer Museum, Qingdao, Shandong province, China.

[aristarchusinexile]

And what does the Greek god of wine, the inspirer of ritual madness and ecstasy, have to do with Easter?

Excellent example of twist. Thanks.

thigh....

John 15:5 "I am the vine"
Mark 14:24 "This is my blood"

"Ah, 'tis not the blood of madness ritual or otherwise ye drink when ye drink the blood of the Lamb .. beware, beware of false labels and demonic babels and the lure of women fair of face (or not) wanting themselves to be lovers or wives; and leave not off grace."
Book of Bob

[JohnD]

Melk - "The Name of the Rose" was narrated by Adso of Melk in a story set a hundred years before this manuscript. Adso was a gaping naive who told his story from educated old age, of how his master William of Baskerville, by observation, insight and scholarship, solved the apparently demonic series of murders. So Adso's tale was told about the time this was written. An allusion, and illusion, that Eco would love.

John

[apodman]

If the manuscript is from 1490, why is the Earth round in the eclipse diagrams? I thought the Earth was flat until 1492.

[BMAONE23]

My guess would be like a coin, round but flat

[apodman]

Aha, with turtles on the reverse no doubt.

[Chris Peterson]

If the manuscript is from 1490, why is the Earth round in the eclipse diagrams? I thought the Earth was flat until 1492.

Educated people, including Europeans throughout the Middle Ages, were fully aware that the Earth was spherical- knowledge from at least ancient Greece, which was never lost. The sort of person who would have constructed a chart like this would not have believed the world was flat.

[BMAONE23]

What I find interesting about the geocentric manuscript is the Eclipsis Lune image depicts the earths shadow as a cone which can completely cover the moon but ends at a point beyond with a larger sun as the light source. However, in the Eclipsis Solis side, all bodies are the same size and the shadow completely covers the earth with no apparent convergence

[neufer]

If the manuscript is from 1490, why is the Earth round in the eclipse diagrams? I thought the Earth was flat until 1492.

Educated people, including Europeans throughout the Middle Ages, were fully aware that the Earth was spherical- knowledge from at least ancient Greece, which was never lost. The sort of person who would have constructed a chart like this would not have believed the world was flat.

Some even guessed that it was pear shaped!

<<The possibility that the Earth's equator is an ellipse rather than a circle and therefore that the ellipsoid is triaxial has been a matter of scientific controversy for many years. Modern technological developments have furnished new and rapid methods for data collection and since the launch of Sputnik 1, orbital data have been used to investigate the theory of ellipticity. A second theory, more complicated than triaxiality, proposed that observed long periodic orbital variations of the first Earth satellites indicate an additional depression at the south pole accompanied by a bulge of the same degree at the north pole. It is also contended that the northern middle latitudes were slightly flattened and the southern middle latitudes bulged in a similar amount. This concept suggested a slightly pear-shaped Earth and was the subject of much public discussion. Modern geodesy tends to retain the ellipsoid of revolution and treat triaxiality and pear shape as a part of the geoid figure.>>

The same principles which explain the strange world of Cosmas explain also the strange conception of the Earth which we found in the letters of Columbus. According to this latter, it will be remembered, the historic hemisphere was true to the spherical figure, but the hemisphere of his far West explorations rose to a lofty eminence at the equator, in what he supposed to be Asia, but which afterwards proved to be the northern part of South America. This gave to the Earth the figure shown in the adjoining cut,—a figure which he compared to that of a nearly round pear. At first view this conception seems altogether arbitrary, and even whimsical; but if we go back a century or two to Dante's Earth, we find a globe still more eccentric, one on which the Paradise-mount has slipped down full 30° below the equator, as shown in the following figure. A fundamental datum for its construction is found in the description of the Mountain of Purgatory, respecting whose location it is said, "Zion stands with this Mountain in such wise on the earth that both have a single horizon and diverse hemispheres." A commentator on this says, "When the Divina Commedia was written, Jerusalem was believed to be the exact centre of the habitable hemisphere; the other was conceived to be covered with water. Out of this ocean the mountain of the poet's Purgatory rises up, like the Peak of Teneriffe, from the bosom of the waves, and is exactly opposite to Mount Zion, so that the two become the antipodes of each other. The mathematicians in their measurement of Dante's Hell proceeded in this wise: An arc of thirty degrees was measured from the meridian of Jerusalem westward as far as Cuma, near Naples, and here, at the 'Fauces Averni' of Vergil, it pleased them to locate its dreary entrance. Another arc of thirty degrees was next measured from the same meridian eastward, so that both together made up a portion of the earth's circumference of about 4330 English miles, the chord of which would be equal to its semi-diameter. This was made the base of their operations, so that with the world's centre for its apex . . . the Inferno became as broad as it was deep. At this centre of gravity, firmly wedged in everlasting ice, the grim monarch of these dolorous realms is placed.">>

[apodman]

Serious questions this time.

On the eclipse diagrams on the manuscript, the moon is shown on a double orbit. Since the moon is shown at the intersection of these orbits in the solar eclipse diagram, I thought maybe one orbit was to suggest the ecliptic plane and the other the moon's orbital plane so the moon would be located at a rising or falling node as required for an eclipse. Would that have been advanced knowledge for the time? But the moon must be at a node for a lunar eclipse as well, and it's not shown that way. So does anybody know what the deal is with the double lunar orbits?

[neufer]

Serious questions this time.

On the eclipse diagrams on the manuscript, the moon is shown on a double orbit. Since the moon is shown at the intersection of these orbits in the solar eclipse diagram, I thought maybe one orbit was to suggest the ecliptic plane and the other the moon's orbital plane so the moon would be located at a rising or falling node as required for an eclipse. Would that have been advanced knowledge for the time? But the moon must be at a node for a lunar eclipse as well, and it's not shown that way. So does anybody know what the deal is with the double lunar orbits?

The moon only has to be near a node for a lunar eclipse and that is what is shown, isn't it?
(Clearly, these are 'cartoons' with the size of the moon varying, etc.)

[Chris Peterson]

Serious questions this time.

On the eclipse diagrams on the manuscript, the moon is shown on a double orbit. Since the moon is shown at the intersection of these orbits in the solar eclipse diagram, I thought maybe one orbit was to suggest the ecliptic plane and the other the moon's orbital plane so the moon would be located at a rising or falling node as required for an eclipse. Would that have been advanced knowledge for the time? But the moon must be at a node for a lunar eclipse as well, and it's not shown that way. So does anybody know what the deal is with the double lunar orbits?

I was thinking it might be trying to show in some way the varying distance from the Earth to the Moon. At that time they must have been well aware of the difference between a total and an annular eclipse. You would also think they must have some idea that the Earth, Sun, and Moon didn't share a common plane- how else to explain partial eclipses? So your idea may be correct as well.

[iamlucky13]

Serious questions this time.

On the eclipse diagrams on the manuscript, the moon is shown on a double orbit. Since the moon is shown at the intersection of these orbits in the solar eclipse diagram, I thought maybe one orbit was to suggest the ecliptic plane and the other the moon's orbital plane so the moon would be located at a rising or falling node as required for an eclipse. Would that have been advanced knowledge for the time? But the moon must be at a node for a lunar eclipse as well, and it's not shown that way. So does anybody know what the deal is with the double lunar orbits?

I was thinking it might be trying to show in some way the varying distance from the Earth to the Moon. At that time they must have been well aware of the difference between a total and an annular eclipse. You would also think they must have some idea that the Earth, Sun, and Moon didn't share a common plane- how else to explain partial eclipses? So your idea may be correct as well.

My thoughts exactly. I was actually rather surprised to see what appeared to be a drawing of elliptical orbits.

My guess would be like a coin, round but flat

Once the Greeks had spread over a geographically large area and had regular exchange of knowledge, they noticed that the sun reached different angles in the sky at noon depending on the location. They were also well aware of the horizon effect.

After some exercise in geometry, Eratosthenes calculated the circumference of the accurate to within just a few percent around the year 240 BC. His calculations were actually far more accurate than Columbus' were. I tend to think Columbus duped himself to convince himself and others that the land Norse sailors reported to the west was Siberia, not Canada.

[vofl]

There is no "Tycho de Brahe". He is named Tycho Brahe. Tycho is a latinification of the name Tyge, which still is used in Denmark. Brahe is a family-name - also still in use.

[neufer]

On the eclipse diagrams on the manuscript, the moon is shown on a double orbit. Since the moon is shown at the intersection of these orbits in the solar eclipse diagram, I thought maybe one orbit was to suggest the ecliptic plane and the other the moon's orbital plane so the moon would be located at a rising or falling node as required for an eclipse. Would that have been advanced knowledge for the time? But the moon must be at a node for a lunar eclipse as well, and it's not shown that way. So does anybody know what the deal is with the double lunar orbits?

I was thinking it might be trying to show in some way the varying distance from the Earth to the Moon. At that time they must have been well aware of the difference between a total and an annular eclipse. You would also think they must have some idea that the Earth, Sun, and Moon didn't share a common plane- how else to explain partial eclipses? So your idea may be correct as well.

My thoughts exactly. I was actually rather surprised to see what appeared to be a drawing of elliptical orbits.

To explain both Mars's retrograde motion and variable distance
in a geocentric model always required epicycles which,
if small enough, resembled off center circles NOT ellipses.

[Chris Peterson]

To explain both Mars's retrograde motion and variable distance
in a geocentric model always required epicycles which,
if small enough, resembled off center circles NOT ellipses.

Yes, but have you seen epicycles used to explain the varying distance of the Moon? I don't recall seeing that explicitly. While epicycles cause a planet's distance from Earth to change, I don't think that effect was observed, only the effect on position- retrograde and prograde motion.

[neufer]

To explain both Mars's retrograde motion and variable distance
in a geocentric model always required epicycles which,
if small enough, resembled off center circles NOT ellipses.

Yes, but have you seen epicycles used to explain the varying distance of the Moon? I don't recall seeing that explicitly. While epicycles cause a planet's distance from Earth to change, I don't think that effect was observed, only the effect on position- retrograde and prograde motion.

The moon is not treated explicitly
(except for the "unusual" fact that it shines by reflected light from the sun)
because ALL planets are on epicycles.
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<<In the Ptolemaic system of astronomy, the epicycle (literally: on the circle in Greek) was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. It was designed by Apollonius of Perga at the end of the 3rd century BC. In particular it explained the retrograde motion of the five planets known at the time. Secondarily, it also explained changes in the apparent distances of the planets from Earth.

<<Apollonius of Perga [Pergaeus] (Ancient Greek: Ἀπολλώνιος) (ca. 262 BC–ca. 190 BC) was a Greek geometer and astronomer noted for his writings on conic sections. His innovative methodology and terminology, especially in the field of conics, influenced many later scholars including Ptolemy, Francesco Maurolico, Isaac Newton, and René Descartes. It was Apollonius who gave the ellipse, the parabola, and the hyperbola the names by which we know them. The hypothesis of eccentric orbits, or equivalently, deferent and epicycles, to explain the apparent motion of the planets and the varying speed of the Moon, are also attributed to him. Apollonius' theorem demonstrates that the two models are equivalent given the right parameters. Ptolemy describes this theorem in the Almagest XII.1. Apollonius also researched the lunar theory, for which he is said to have been called Epsilon (ε). The crater Apollonius on the Moon is named in his honor.>>

In the Ptolemaic system, the planets are assumed to move in a small circle, called an epicycle, which in turn moves along a larger circle called a deferent. Both circles rotate eastward and are roughly parallel to the plane of the Sun's orbit (ecliptic). The orbits of planets in this system are epitrochoids.

The deferent was a circle centered around a point halfway between the equant and the earth. The epicycle rotated on the deferent with uniform motion, not with respect to the center, but with respect to the off-center point called the equant. The rate at which the planet moved on the epicycle was fixed such that the angle between the center of the epicycle and the planet was the same as the angle between the earth and the sun.

Ptolemy did not predict the relative sizes of the planetary deferents in the Almagest. All of his calculations were done with respect to a normalized deferent. This is not to say that he believed the planets were all equidistant. He did guess at an ordering of the planets. Later he calculated their distances in the Planetary Hypotheses.

For superior planets the planet would typically rotate in the night sky slower than the stars. Each night the planet would "lag" a little behind the star. This is prograde motion. Occasionally, near opposition, the planet would appear to rotate in the night sky faster than the stars. This is retrograde motion. Ptolemy's model, in part, sought to explain this behavior.

The inferior planets were always observed to be near the sun, appearing only shortly before sunrise or shortly after sunset. To accommodate this, Ptolemy's model fixed the motion of Mercury and Venus so that the line from the equant point to the center of the epicycle was always parallel to the earth-sun line.>>

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<<In the 4th century BC, two influential Greek philosophers wrote works based on the geocentric model. These were Plato and his student Aristotle. According to Plato, the Earth was a sphere, stationary at the center of the universe. The stars and planets were carried around the Earth on spheres or circles, arranged in the order (outwards from the center): Moon, Sun, Venus, Mercury, Mars, Jupiter, Saturn, fixed stars. In the "Myth of Er," a section of the Republic, Plato describes the cosmos as the Spindle of Necessity, attended by the Sirens and turned by the three Fates. Eudoxus of Cnidus, who worked with Plato, developed a less mythical, more mathematical explanation of the planets' motion based on Plato's dictum stating that all phenomena in the heavens can be explained with uniform circular motion. Aristotle elaborated on Eudoxus' system. In the fully developed Aristotelian system, the spherical Earth is at the center of the universe. All heavenly bodies are attached to 56 concentric spheres which rotate around the Earth . (The number is so high because several transparent spheres are needed for each planet.) The Moon is on the innermost sphere. Thus it touches the realm of Earth, which contaminates it, causing the dark spots (macula) and the ability to go through lunar phases. It is not perfect like the other heavenly bodies, which shine by their own light.>>

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