Byrd Wrote:
-------------------------------------------------------
> Well, some spelling and grammar mistakes
> ("Babylonian's" for "Babylonians" - as someone
> with a degree in English, the use of an apostrophe
> to incorrectly indicate a plural noun is always
> grating) - and frankly the evidence isn't terribly
> convincing.
>

Hi Byrd,

Thanks for providing feedback. This example is quite an easy fix.


> You are using tertiary (or even further removed)
> sources that say calculating the stars was
> something that the ancient Egyptians did well --

Could you clarify your concern here - I am making no claim in this paper that the Egyptians did develop models of the planetary phenomena. For full transparency, I was making a claim around the development of models for the planetary phenomena in a prior paper. I have set aside those claims as I work on this paper. The claim I am making is that they applied a zig zag function (one of the building blocks of the Babylonian System B planetary models
) to the hours of nighttime. Returning to the tertiary sources, I'm presenting those sources in context and the section where they are presented concludes with the view of modern scholars such as Neugebauer and van der Waerden. These examples are presented because there is some confusion around them, including the possible clues as to dating specific types of knowledge. This situation is elegantly discussed by Neugebauer in the referenced paper.


>
> The math, likewise doesn't carry through. You can
> learn the principles of addition but this doesn't
> mean you will be applying the use of addition (to
> count your sheep and goats) to predicting the
> amount of harvest from the annual Nile Flood (in
> other words, a level of 10 feet meant that your
> fields would yield 30 bushels per acre.)
>

Here again, I am unsure what your concern is. If you look at the development of Babylonian mathematics and Babylonian mathematical astronomy, there is a 1,300 year gap between the development of an advanced mathematics and the development of mathematical models for astronomy. The primary concern for astronomy, according to Neugebauer, is whether the basic properties of the arithmetic and geometric sequences are known. The evidence is unambiguous that the Egyptians knew of arithmetic progressions, there are examples presented in my paper from the Rhind Mathematical Papyrus. Gillings was of the opinion that the RMP indicates knowledge of the sum to n terms of an arithmetic progression.


> The "zig zag" function also doesn't imply that the
> Egyptians were using it or invented it -- they
> were in contact with the Babylonians and it's
> quite possible that they simply copied a clock
> from something that was a gift to the king and
> then modified it to fit their own needs. This
> could be done by simple observation and not by
> independent calculations.
>
The application of a zig zag function to model the variability in the timing of the synodic phenomena and the variability in the positions appears approximately 400BCE. We don't know how the Babylonian astronomers developed their models as they appear fully formed around that time. However, the Karnak clock example of a zig zag function modelling the variability in the length of night time hours throughout the year is 1,000 years older. In other words, the Karnak clock uses the same technique to model a different process. We know it is modelled because of the systemic differences between the model and actual observations would yield, something which the later water clocks attempted to correct. I would refer you to Clagget starting p70 for additional details.



Edited 1 time(s). Last edit at 09/08/2022 03:06AM by engbren.