18 Nov 2011

The historical use of non-decimal counting bases


When we think of other cultures with alternative number bases, that is, counting systems other than the decimal system of one to ten that we've arbitrarily become accustomed to in the modern world, many will recall the examples of Sumerian's base-60 system (sexagesimal) or the Mayan base-20 system (vigesimal). A professor of anthropology at Humboldt State University, Victor Golla, describes some other interesting systems on page 220 of California Indian Languages (2011) under the heading 4.10.3 Quaternary and Octonary Systems:
"A small residue of counting schemes that cannot be classed as quinary, decimal, or vigesimal are found in Northern Yukian, Salinan, and Chumash (Appendix D: 3, 9, 6, and 7). In all three language groups the count is by fours, either straighforwardly quaternary (based on four, in Salinan and Chumash) or octonary (based on eight, in Northern Yukian). Counting by fours apparently had its origin in an old practice, attested ethnographically among the Yuki (Kroeber 1925:878-879), of counting sticks held between the fingers rather than counting the fingers themselves."

12 Nov 2011

A matter of the Egyptian heart


The Egyptians placed a lot of importance on the heart and it was believed to be the seat of the mind and the soul. In the English-speaking world, we usually treat "heart" as a symbolism of the feelings but for ancient peoples around the Mediterranean, it was instead the seat of reason and essence. They didn't realize yet the significance of the brain in that regard and of the bodily organs that Egyptian mummifiers traditionally preserved in their sacred rites, the brain wasn't one of them.

Considering how central the heart was to the ancient Egyptian perception of the soul, one would think we'd know how to pronounce the word by now. In hieroglyphs, it's represented only in consonants and we write this in standard orthography as ỉb. This unfortunately gives the false impression that we should just assume a pronunciation of /ib/. Indeed, Antonio Loprieno does reconstruct */jib/ and compares it directly with Semitic *libb- assuming in turn an Afro-Asiatic reconstruction of *lib (see Ancient Egyptian: A linguistic reconstruction [1995], page 31). So isn't that our answer?

I'm beginning to think it isn't. For one thing, this reconstruction could only work for the earliest stage of Egyptian before all instances of word-initial *y- were nullified in the language. Since the reed leaf symbol came to represent a glottal stop as a result, by the time of Middle Egyptian, we could only have had *ib at best. So isn't this our answer then?

To be honest something still seems off. The related Cushitic branch seems to instead point to *lub- with a rounded back vowel. If we derived an expectation of the Egyptian form from that piece of external data, we'd arrive at *ub, not *ib! Adding to the difficulty is that Coptic has replaced the word for "heart" with a completely different word, hēt (from ḥȝty). No clues there.

So what can we rely on to decide the matter? I finally came across the Hebraicized name Ḥophraˁ, the name of a pharaoh of the sixth century BCE. The original Egyptian form is represented in hieroglyphic writing as wȝḥ-ỉb-rˁ. It suggests that ỉb was at that point pronounced like the -oph- in Ḥophraˁ, causing me to want to side with the Cushitic reconstruction. Therefore *ub seems far more sensible than Loprieno's *(y)ib.

I'm curious about this word lately and want to get it right because of the parallel Proto-Berber form reconstructed as *ulβ. I wonder then if this might suggest that Proto-Berber had coloured the prothetic vowel with the original quality of the root vowel now lost between the two surviving consonants. If so, I have no clue how to account for the *i in Semitic *libb- however. The Semitic vocalism of the root now becomes the outlier.