engbren Wrote:
-------------------------------------------------------
> > 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 scholars, a "primary source" is a quote from the people of that time about something they're doing. Merer's diary, for instance, is a primary source for building the Giza pyramids since he was there at the time and was recording what he was doing. Rhind Mathematical Papyrus is a primary source.

A secondary source is someone quoting what someone else said... Plato is actually a secondary source for Socrates (we treat his recording of what Socrates said as true...but we actually don't know if those exact words are what Socrates said or if Plato is putting words in his mouth.)

Tertiary sources would be a summary; e.g. "Plato said that Socrates told a long story about a continent called Atlantis." We have a claim by someone who claims to be summarizing Plato.

A worse source is the type you give where (to quote exactly from your paper) you use “The Egyptian men of old who had faithfully studied the heavenly bodies and had learned the motions of the seven gods...(etc)" -- Although we know the author of that quote, we don't know who he means by "Egyptian men of old who had faithfully studied..." and what time period. Did he mean the ones at the Library of Alexandria? Was he relying on old legends? Did one of the Giza guides tell him that bit of data?

It would be a great primary source if you were discussing "what the Greeks and Romans of 1st-4th century AD thought of the Egyptians" because it's indeed one of these individuals talking about their beliefs in what the Egyptians knew. But as a source for what the Egyptians actually knew, it's a terrible data point.


> 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.

Right. And you're lacking any primary or secondary sources.

> 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.

(acknowledged)

> 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,

I did note this. But this doesn't mean that they used it for time-telling.

> 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.

Again, knowledge and application are two different things. You might know how to make a wheel (the Egyptians did) but applying it to pottery and to transportation are two different things. The Egyptians didn't develop wheeled vehicles though it would have been possible since they were one of the very first civilizations to have a wheel (which they used for pottery).


> >
> 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.

And since they were interested in math and astronomy (where this kind of function would be useful) it's more likely that this developed in Babylon.

> 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.

I would disagree here. We have good evidence that the Babylonians got as far as the earliest elements of calculus (https://www.space.com/31765-ancient-babylonians-tracked-jupiter-with-math.html).

But Clagett himself says (p. 68) that the calculations are wrong and that the clock was copied from somewhere else (because the day lengths are not correct for the season). This would mean that they did NOT know how to do a function to divide the hours up properly but were simply copying it from somewhere else. IF they had the calculations, they would have used that at the time of the clock's creation; not something that was correct over 100 years prior but was now out of sync.

-- Byrd
Moderator, Hall of Ma'at