Byrd Wrote:

>
> 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?
>
That quote is directly from van der Waerden per footnote 11 in my paper. I am using it as it appears to confirm some ancient knowledge but when considered in full context, it, along with many other similar quotes do not actually confirm that knowledge. This is dealt with by Neugebauer:

Neugebauer, O. (1942). Egyptian planetary texts. Transactions of the American Philosophical Society, 32(2), 209-250.

> > 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.
>
Here I will point you to Clagett pp 68-69:

"... when the clock was built in Amenhotep III's time it was already out of date, since the assignment of its shortest scale to the tenth month was not valid for the period of Amenhotep III but rather for that of Amenhotep I more than one hundred years earlier (see Fig. III.37) when a certain official named Amenemhet describes having constructed such a clock and dedicated it to Amenhotep I..."

So here is a secondary source in Clagett telling us there exists an inscription claiming to create a water clock similar to that of the Karnak clock. Further on p 70 there is a discussion of the inscription in Amenemhet's tomb:

““While reading in all the books of the divine word” (i.e., the whole of Egyptian literature) he found “[the (longest) night of wintertime to be 14 [hours long] when the [shortest] night of the summertime is 12 hours [long]” and that the hour lengths from month to month increase and then decrease.”

This quote from Clagett also appears in pp5-6 of my paper. Clagett on p70 discusses the fit of Amenemhet's tomb inscription with the design of the Karnak water clock.

Separately, Jens Hoyrup, an expert in Babylonian mathematics published a review of Clagett's book. You can access Hoyrup's paper here: [www.academia.edu]
Hoyrup's review actually extends beyond a mere review and provides additional colour and detail on the Karnak clock and the Amenemhet inscriptions on pp17-18. In this discussion, Hoyrup states:

"The Karnak clock assumes the change of the length of night to be uniform from solstice to solstice – in the idiom used to discuss Babylonian astronomy, it constitutes a zigzag-function (which should
not be taken as evidence of a borrowing, cf. note 25).."

Given both Clagett and Hoyrup are referenced in my paper, I am unclear why you think I am lacking any primary or secondary sources.


> > 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.
>

Refer to Hoyrup p18 as above.


> > >
> > 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.
>
Hoyrup's footnote 25 related to the quote I presented above appears on p19:

"That is, they follow a zigzag function, and the positions themselves thus the summation of such a functions; there is hence no need whatsoever to ascribe the use of second-order approximations in the Hellenistic water clocks to Mesopotamian inspiration"


> > 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).
>
There is good evidence that the Babylonians developed an advanced mathematics in many ways. Allowing Egyptian modelling of a process with a zig zag function, which is after all, the simplest possible way to model a time varying process, does not take away from the Babylonian achievements.

> 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.
I think this objection is dealt with by reading Clagett in full context as I presented above.