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The IEP entry on Anaximander has:

The astronomy of neighboring peoples, such as the Babylonians and the Egyptians, consists mainly of observations...In contrast, there exists only one report of an observation made by Anaximander...for Anaximander’s merits do not lie in the field of observational astronomy, unlike the Babylonians and the Egyptians, but in that of speculative astronomy.

We may discern three of his astronomical speculations:

(1) that the celestial bodies make full circles and pass also beneath the earth,

(2) that the earth floats free and unsupported in space, and

(3) that the celestial bodies lie behind one another.

Notwithstanding their rather primitive outlook, these three propositions, which make up the core of Anaximander’s astronomy, meant a tremendous jump forward and constitute the origin of our Western concept of the universe.

The idea that the celestial bodies, in their daily course, make full circles and thus pass also beneath the earth – from Anaximander’s viewpoint – is so self-evident to us that it is hard to understand how daring its introduction was. That the celestial bodies make full circles is not something he could have observed, but a conclusion he must have drawn

What catches my attention is the discussion of the Egyptian Solar God Ra who was established as a major deity by the time of the fifth dynasty circa 2400 BC. He is said to travel on two solar boats:

called the Mandjet (the Boat of Millions of Years), or morning boat and the Mesektet, or evening boat. These boats took him on his journey through the sky and the Duat, the literal underworld of Egypt

In this mythological picture, Ra sails through the sky from the West to the East on the morning boat and then through the underworld, that is under-the-world on the evening boat from the East to reappear in the West. Although it is not described as a circle it is at least a continuous circuit so is topologically a circle. Ra himself is preserved through the circuit. He goes above & under the world.

The parallel with the first statement that the IEP makes and finds so daring I find quite startling. Given the possibility of one parallel, are there not likely to be more?

Are there standard works that explore connections between Babylonian & Egyptian cultures and the Presocratic tradition?

Notably there aren't myths of either Helios or Apollo that can have the same parallel that Ra does here. (Helios crosses the sky in a Chariot but sails back on the oceanus back to the East).

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This is touched on (but not at great length) in Thomas McEvilley's The Shape of Ancient Thought.

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    It appears to be mentioned in greater length in Martins Bernals Black Athena. Its going to be a while before I get a chance to look at McEvilleys book, does he reference Black Athena? Mar 8, 2013 at 5:04
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    It's listed in McEvilley's bibliography, but I don't recall any extended reference to it. I read Bernal's volume 1 when it came out, and had mixed feelings-- it was quite speculative. Mar 8, 2013 at 13:28
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The best example I can think of, is Pythagoras, for a variety of reasons.

While there is no concrete empirical evidence that Pythagoras ever traveled to Egypt, it has been speculated over the centuries that Pythagoras-(who was a native of the widely traveled Aegean sea region), was a fairly sophisticated traveler for his time. Commentaries have suggested that Pythagoras traveled to the Middle East, India, as well as Egypt.

Pythagoras' famed right triangle Theorem, in all likelihood, was greatly influenced-by (or perhaps "borrowed") from early Egyptian Civil Engineers-(specifically, Egyptian Pyramid Designers). The famous Giza Pyramids were designed around 2500 BC/ BCE, approximately 2000 years before Pythagoras' time. If Pythagoras traveled to Egypt, he would have almost certainly visited the Giza Pyramids and would have probably been awestruck by their beautiful symmetry-(and mystical significance).

It would be overly simplistic to say that Pythagoras initially learned Mathematics from Egyptian Civil Engineers and Priests when touring the Pyramids of Giza. In all likelihood, Pythagoras' natural flair for Mathematics, was probably greatly improved and enhanced when walking through the Pyramids of Giza and learning about its fine craftsmanship from the Egyptian intelligentsia.

Of course Pythagoras' philosophy was not merely confined to his famous Right Triangle theorem; his philosophy was far more comprehensive and interconnected whereby, the (Egyptian influenced) Right Triangle Theorem, played an important role...though not necessarily, a Central role in his overall thought. His transmigration of the soul, as well as his love for all animals and apparent vegetarianism, appears to have significant Indian/Hindu influences-(most likely from his alleged travels to India).

Nevertheless, it is Pythagoras' likely travels to Egypt and encounters with Egypt's mathematical elites that helped him co-devise the foundations of Western Geometry and Trigonometry....a Mathematical system that was probably established on the partial borrowings from early Egyptian Civil Engineers.

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