The Astronomical Basis of Egyptian Chronology of the Second Millennium BC

Egyptian dates are widely used for fixing the chronologies of surrounding countries in the Ancient Near East. But the astronomical basis of Egyptian chronology is shakier than generally assumed. The moon dates of the Middle and New Kingdom are here re-examined with the help of experiences gained from Babylonian astronomical observations. The astronomical basis of the chronology of the New Kingdom is at best ambiguous. The conventional date of Thutmose III’s year 1 in 1479 BC agrees with the raw moon dates, but it has been argued by several Egyptologists that those dates should be amended by one day, and then the unique match is 1504 BC. The widely accepted identification of a moon date in year 52 of Ramesses II, which leads to an accession of Ramesses II in 1279 BC, is by no means certain. In my opinion that accession year remains nothing more than one of several possibilities. If one opts for a shortened Horemhab reign, dating Ramesses II to 1290 BC gives a better compromise chronology. But the most convincing astronomical chronology is a long one: Ramesses II in 1315 BC, Thutmose III in 1504 BC. It is favored by Amarna-Hittite synchronisms and a solar eclipse in the time of Muršili II. The main counter-argument is that this chronology is at least 10–15 years higher than what one calculates from the Assyrian King List and the Kassite synchronisms. For the Middle Kingdom on the other hand, among the disputed dates of Sesostris III and Amenemhet III one combination turns out to be reasonably secure: Sesostris III’s year 1 in 1873/72 BC and Amenemhet III’s 30 years later.

A multivariate distribution for sub-images

A new method for obtaining multivariate distributions for sub-images of natural images is described. The information in each sub-image is summarized by a measurement vector in a measurement space. The dimension of the measurement space is reduced by applying a random projection to the truncated output of the discrete cosine transforms of the sub-images. The measurement space is then reparametrized, such that a Gaussian distribution is a good model for the measurement vectors in the reparametrized space. An Ornstein–Uhlenbeck process, associated with the Gaussian distribution, is used to model the differences between measurement vectors obtained from matching sub-images. The probability of a false alarm and the probability of accepting a correct match are calculated. The accuracy of the resulting statistical model for matching sub-images is tested using images from the Middlebury stereo database with promising results. In particular, if the probability of accepting a correct match is relatively large, then there is good agreement between the calculated and the experimental probabilities of obtaining a unique match that is also a correct match.

Modelling the Rayleigh match

We use the photopigment template of Baylor et al. (1987) to define the set of Rayleigh matches that would be satisfied by a photopigment having a given wavelength of peak sensitivity (λmax) and a given optical density (OD). For an observer with two photopigments in the region of the Rayleigh primaries, the observer's unique match is defined by the intersection of the sets of matches that satisfy the individual pigments. The use of a template allows us to illustrate the general behavior of Rayleigh matches as the absorption spectra of the underlying spectra are altered. In a plot of the Y setting against the red–green ratio (R), both an increase in λmax and an increase in optical density lead to an anticlockwise rotation of the locus of the matches satisfied by a given pigment. Since both these factors affect the match, it is not possible to reverse the analysis and define uniquely the photopigments corresponding to a specific Rayleigh match. However, a way to constrain the set of candidate photopigments would be to determine the trajectory of the change of match as the effective optical density is altered (by, say, bleaching or field size).