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Pythagorus' Spherical Earth

by baywax
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baywax
#1
Aug18-08, 05:35 PM
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Has anyone else heard of Pythagorus' spherical earth model?

Classical Mediterranean

Pythagoras

Early Greek philosophers alluded to a spherical earth, though with some ambiguity.[3]
This idea influenced Pythagoras (b. 570 BCE), who saw harmony in the universe and sought to explain it. He reasoned that Earth and the other planets must be spheres, since the most harmonious geometric solid form is a sphere[1]. After the fifth century BCE, no Greek writer of repute thought the world was anything but round.[3]

Herodotus

In The Histories, written 431 BCE - 425 BCE, Herodotus dismisses a report of the sun observed shining from the north. This arises when discussing the circumnavigation of Africa undertaken c. 615-595 BCE. (The Histories, 4.43) His dismissive comment attests to a widespread ignorance of the ecliptic's inverted declination in a southern hemisphere.

Plato

Plato (427 BCE - 347 BCE) travelled to southern Italy to study Pythagorean mathematics. When he returned to Athens and established his school, Plato also taught his students that Earth was a sphere. If man could soar high above the clouds, Earth would resemble "a ball made of twelve pieces of leather, variegated, a patchwork of colours."[citation needed]

Aristotle

When a ship is at the horizon its lower part is invisible due to Earth's curvature. This was one of the first arguments favoring a round-earth model.
Aristotle (384 BCE - 322 BCE) was Plato's prize student and "the mind of the school." Aristotle observed "there are stars seen in Egypt and [...] Cyprus which are not seen in the northerly regions." Since this could only happen on a curved surface, he too believed Earth was a sphere "of no great size, for otherwise the effect of so slight a change of place would not be quickly apparent." (De caelo, 298a2-10)

Aristotle provided physical and observational arguments supporting the idea of a spherical Earth:
Every portion of the earth tends toward the center until by compression and convergence they form a sphere. (De caelo, 297a9-21)

Travelers going south see southern constellations rise higher above the horizon; and
The shadow of Earth on the Moon during a lunar eclipse is round. (De caelo, 297b31-298a10)
http://en.wikipedia.org/wiki/Spherical_Earth

There is a link on this page to a Philosophy out of India that claimed the earth was spherical as well... but I couldn't find it.

I'm just in awe of these early observations, and find it hard to believe they were lost for so long until only just recently.
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mgb_phys
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Aug18-08, 06:01 PM
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Quote Quote by baywax View Post
I'm just in awe of these early observations, and find it hard to believe they were lost for so long until only just recently.
I don't think they were lost, nobody in the years since Hipparchus believed the Earth was flat. Washington Irvine famously wrote a story about Columbus being stopped by the church because the earth was flat - but this story was just a bit of political trouble making.

On the other hand pythagorus thinking the Earth was a sphere because a sphere is the perfect shape is no more justified than the elephants on the back of a turtle model.
baywax
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Aug18-08, 06:45 PM
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Quote Quote by mgb_phys View Post
On the other hand pythagorus thinking the Earth was a sphere because a sphere in is the perfect shape is no more justified than the elephants on the back of a turtle model.
Well, we don't know if it was Pythagorus' thinking that came up with earth as a sphere 600 BC. He quite possibly got the idea from earlier documents, the likes of which could have been found at the Library of Alexandria. In fact... 600 years after Pythagorus, Ptolemy based his maps on those of the Phoenician Marinus of Tyre, who in turn drew on even earlier mapmakers for inspiration. Ptolemy lived from around 85 ad to 165 ad and actually had a chance to study the charts in the Library of Alexandria since he lived in Alexandria for most of his life. He never made more than one or two maps of the known world but he brought to Cartography a new system of longitude and latitude which we can guess came from his studies at the library. It was by this system that many maps were calculated and many were quite accurate, to a degree.

Ptolemy's hypotheses of astronomy

That the Heaven Rotates as a Sphere

3. It is reasonable to assume that the first ideas on these matters came to the ancients from observation such as the following. They saw the sun and the moon and the other stars moving from east to west in circles always parallel to each other; they saw the bodies begin to rise from below, as if from the earth itself, and gradually to rise to their highest point, and then, with a correspondingly gradual decline, to trace a downward course until they finally disappeared, apparently sinking into the earth. And then they saw these stars, once more, after remaining invisible for a time, make a fresh start and in rising and setting repeat the same periods of time and the same places of rising and setting with regularity and virtual similarity.

They were, however, led to the view of a spherical heaven chiefly by the observed circular motion described about one and the same centre by those stars that are always above the horizon. For this point was, necessarily, the pole of the heavenly sphere, since the stars that are nearer this pole revolve in smaller circles, whereas those further away make larger circles, proportionately to their distance, until the distance reaches that of the stars not always visible.
http://www-groups.dcs.st-and.ac.uk/~...s/Ptolemy.html

So I see no reason to assume that Pythagorus came up with the idea of a Spherical Earth on his own. He was also Greek, like Ptolemy and the Greeks were often guests in Egypt as intellectual tourists etc.

DEMcMillan
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Aug20-08, 11:50 AM
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Pythagorus' Spherical Earth

baywax, your great start should go on a bit further with the mention of the name of Eratothenes http://en.wikipedia.org/wiki/Eratosthenes who measured the “spherical” Earth’s circumference with real accuracy before 200 BC. Confusion that followed led Columbus to underestimate Earth’s size and discover the New World. http://users.zoominternet.net/~matto...size_shape.htm The more precise but not quite complete oblate ellipsoidal shape developed more recently as a part of geodesy. http://en.wikipedia.org/wiki/History_of_geodesy I suspect that we can still get into trouble from oversimplifying the Earth’s shape.
baywax
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Aug20-08, 01:19 PM
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Quote Quote by DEMcMillan View Post
baywax, your great start should go on a bit further with the mention of the name of Eratothenes http://en.wikipedia.org/wiki/Eratosthenes who measured the “spherical” Earth’s circumference with real accuracy before 200 BC. Confusion that followed led Columbus to underestimate Earth’s size and discover the New World. http://users.zoominternet.net/~matto...size_shape.htm The more precise but not quite complete oblate ellipsoidal shape developed more recently as a part of geodesy. http://en.wikipedia.org/wiki/History_of_geodesy I suspect that we can still get into trouble from oversimplifying the Earth’s shape.
Thank you DEMcMillan,

Its becoming quite disconcerting to find that these great minds, like Ptolemy, were practically permanent fixtures of the Alexandria Library. I get the feeling that they found records of methods for doing and recording geological and astronomical measurements at the library, there, waiting for someone with an open mind to interpret and try out in what was the modern world of the time.

Ptolemy himself points out that "It is reasonable to assume that the first ideas on these matters came to the ancients from observation such as the following"... here he's refering to the idea that the "heavens" are spherical.

Eratosthenes was born in Cyrene (in modern-day Libya). He was the chief librarian of the Great Library of Alexandria and died in the capital of Ptolemaic Egypt. He never married.
Eratosthenes studied in Alexandria and claimed to have also studied for some years in Athens. In 236 BC he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library, succeeding the first librarian, Apollonius of Rhodes, in that post[2]. He made several important contributions to mathematics and science, and was a good friend to Archimedes. Around 255 BC he invented[citation needed] the armillary sphere, which was widely used until the invention of the orrery in the 18th century.
http://en.wikipedia.org/wiki/Eratosthenes

What I don't know is exactly what books and papyrus were in the Alexandria Library. Who are the "ancients" that seem to have invented many of the ideas that were eagerly taken up and continued by the Greeks and others who had the opportunity to study there?

Apparently they spurred quite a movement. Accurate measurements of the distance to the sun from earth, systems of longitude and latitude with compensations for the curvature of the earth, a spherical earth at that.... and so on.

It was always my impression through elementary and high school that no one figured out the world was a sphere until Marco Polo or even the 1400s. And no one taught anything to the contrary.
baywax
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Aug20-08, 01:39 PM
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I'm looking into a bit of the history of the Alexandria Library...

Here's a good link and some quotes from it..


Alexander the Great built the city in 331 BC, and upon his death his widespread empire was divided among several rulers. Ptolemy, one of his generals, chose Egypt and started a new royal house. Alexandria became the capital of the state, and by the year 200 B.C., it grew into the largest metropolis in the world, and became the world's scientific and intellectual Mecca.

THE ANCIENT LIBRARY

The Mouseion was built in the district known as ‚€œBrucheium‚€Ě within the vicinity of the royal palace. Strabo described it as a large complex of buildings and gardens with richly decorated lecture and banquet halls linked by colonnaded walks.

"It was part of the royal palaces, it had a walk [peripatos], an arcade [exedera], a large house in which was a refectory for members of the Mouseion. They formed a community who held property in common with a priest appointed by the kings in charge of the Mouseion."

The University and renowned Library were built as part of the Museum in 290 BC by Ptolemy I-Soter, though some sources suggest that it started during the reign of his son, Ptolemy II- Philadelphus. The actual founder was ‚€œDemetrius Phalereus‚€œ, a follower of Aristotle and counselor of Ptolemy I-Soter, who suggested to the king the idea of establishing a great research center with a universal library attached to it. Such a suggestion fitted perfectly with Soter's desire to render Alexandria not only the capital of a powerful kingdom but also a center of culture and civilization.
So Pythagorus, in 600 BC did not have access to the Library since it was not built in his time. But, he did have access to the Egyptian records. And the Egyptians already had the value of Pi built into their pyramids on the Gaza Plateau. Is this where Pythagorus got the formula?

Apparently, the relation between the slope of the pyramids and Pi may have simply happened by accident rather than by design... but, that doesn't mean it went unnoticed and unrecorded...

The main point that I will make in this essay is that when one takes into account what we know about ancient Egyptian mathematics (based primarily on the Rhind Papyrus), especially their ways of representing lengths and slopes, then the relationship between π and the Great Pyramid no longer seems very remarkable. The essential point is that the measurement system which the ancient Egyptians used would lead the architects to use certain slopes in the design of pyramids. One of those slopes just happens to be an excellent approximation to the number 4/π, and if the architect chooses that slope, then the pyramid would exhibit the famous π relationship. From this point of view, the probability that the architect might choose that particular slope for at least one of the pyramids is actually rather high. It then becomes quite reasonable to believe that the relationship between π and the Great Pyramid is just an accidental consequence of their Mathematics.
http://www.math.washington.edu/~greenber/PiPyr.html

Eratosthenes (275 - 195 BC), the poet, philosopher, astronomer and chief librarian in the 3rd century BC, calculated the Earth diameter - more than 15 centuries before Copernicus and Galileo. Since he believed the Earth was round, and knowing the distance between Alexandria and Aswan, Eratosthenes measured the shadows in both cities on the same day on two successive years. With simple calculations, he estimated the diameter at 7,850 miles, only about 0.5% off today‚€™s measure. His co-worker, Aristarchus of Samos, suggested the heliocentric hypothesis, which stated that the Earth and the planets revolve around the Sun.
All these quotes: http://www.arabworldbooks.com/biblio...lexandrina.htm

I don't want to suggest that these librarians and their assistants were too dumb to come up with these calculations and methods on their own, but, it seems just a bit to coincidental that these revolutionary ideas always seem to pop up in Alexandria.

So far all I know about the contents of the Alexandria Library are that the catalog was called a "Pinakes". The poet Callimachus (another Head Librarian at Alexandria) solved the problem (without the Dewy Decimal System) of cataloging by compiling a catalogue called The Pinakes... or "subject launch pad".
baywax
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Aug20-08, 02:10 PM
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Don't freak out but here's what Wicipedia states is the Earliest model of the Armillary Sphere ( (variations are known as spherical astrolabe, armilla, or armil) is a model of the celestial sphere.).

The earliest known armillary sphere was invented by Shi Shen and Gan De in the 4th century BC (China), as they were equipped with a primitive single-ring armillary instrument.
The Greek Eratosthenes developed the armillary sphere in 255 BC[citation needed]
http://en.wikipedia.org/wiki/Armillary_sphere

So... you can see that attributing "the first" to someone is always a gamble because it seems that, whatever the invention, it has been thought of somewhere else with less fan fare.

PS. "Before the advent of the European telescope in the 17th century, the armillary sphere was the prime instrument of all astronomers in determining celestial positions."...

but was the 17th Century really the first time period to have a telescope???
mgb_phys
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Aug20-08, 02:22 PM
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Quote Quote by baywax View Post
PS. "Before the advent of the European telescope in the 17th century, the armillary sphere was the prime instrument of all astronomers in determining celestial positions."...

but was the 17th Century really the first time period to have a telescope???
Even after the invention of the telescope the astrolab was still much better for astrometric (star position) measurements.
You can make more accurate measurements merely by making the astrolabe bigger, so Tycho's was a basically a building sized sundial - similar to the observatories all over the middle east and india (http://en.wikipedia.org/wiki/Yantra_Mandir)

Telescopes were distrusted because although they made the stars brighter any faults in the optics could move the position of the star and invalidate your measurements.
Even today it's hard to make accurate star position measurements with an ordinary telescope eyepiece.
baywax
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Aug20-08, 04:29 PM
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Quote Quote by mgb_phys View Post
Even after the invention of the telescope the astrolab was still much better for astrometric (star position) measurements.
You can make more accurate measurements merely by making the astrolabe bigger, so Tycho's was a basically a building sized sundial - similar to the observatories all over the middle east and india (http://en.wikipedia.org/wiki/Yantra_Mandir)

Telescopes were distrusted because although they made the stars brighter any faults in the optics could move the position of the star and invalidate your measurements.
Even today it's hard to make accurate star position measurements with an ordinary telescope eyepiece.
I had no idea mgb_phys. That's incredible. Was the Aztec Calendar the same sort of astrological record only flat? Are there examples of the astrolab in the Egyptian or South American cultures? I should have a look for that.
mgb_phys
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Aug20-08, 09:48 PM
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Quote Quote by baywax View Post
Was the Aztec Calendar the same sort of astrological record only flat?
I suppose all calenders are flat astronomical records

Are there examples of the astrolab in the Egyptian or South American cultures? I should have a look for that.
I don't know about portable astrolabes.
The Indian style observatories just need a tower and an angle scale marked on the ground, so aren't difficult to build. To get more accuracy just make a bigger circle! Astrolabes are harder to make since you need to be able to mark a small accurate scale.

The egyptians certainly had a device like a roman Groma, you just need a wooden cross with 4 strings and you can use the stars to find north. This was used to align pyramids and presumably anything else you want aligned.
baywax
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Aug21-08, 11:09 AM
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Quote Quote by mgb_phys View Post
I suppose all calenders are flat astronomical records


I don't know about portable astrolabes.
The Indian style observatories just need a tower and an angle scale marked on the ground, so aren't difficult to build. To get more accuracy just make a bigger circle! Astrolabes are harder to make since you need to be able to mark a small accurate scale.

The egyptians certainly had a device like a roman Groma, you just need a wooden cross with 4 strings and you can use the stars to find north. This was used to align pyramids and presumably anything else you want aligned.
Sorry, that should read "Mayan" calendar.

Very interesting stuff.


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