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."

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.

The reconstruction of the Pre-Egyptian case system

Antonio Loprieno states something confusing to me on page 55 of Ancient Egyptian: A linguistic introduction (1995):

"Also, the ending *-u is still preserved, although functionally reinterpreted, in the forms of some singular patterns as well: when the original stem ended in a vowel, for example *u in *ḥāruw '(the god) Horus,' *-a in *ḫupraw 'form,' or *-i in *masḏiw 'enemy,' the ending was maintained as a glide, often written in good orthography as <-w> in the case of *-aw as opposed to <-ø> in the case of *-iw or *-uw: <ḫprw> =: *ḫupraw 'form,' <ḥfȝw> =: *ḥaf3aw 'snake.'"

Stated more directly, he's claiming that the *w in *ḫupraw was written by scribes according to "good orthography" while strangely ignored in *masḏiw and *ḥāruw despite being present in all these words. It's hard to understand why that would be so. It's rather as if we have *ḫupraw with *w but *masḏi and *ḥāru without. But then this would be inconsistent with what he's stated on the development of the case system from Pre-Egyptian into Old Egyptian.

So it seems that either I'm missing something here or his theory needs a few tweaks. If I ventured an attempt at revisal, perhaps we could try Pre-Egyptian nominatives *ḫaprúwu, *másḏiyu and *ḥārawu. After reduction of unstressed vowels, this becomes *ḫaprūwa /xəpʰˈɾəwə/, *masḏi /'masɟi/ and *ḥāru /'ħaːɾu/ before the case ending was omitted altogether: *ḫaprū, *masḏi and *ḥāru. I contend that only the first word ever motivated writing w. I question its existence altogether in the pronunciation of the second. In the third, 'hawk', I suspect the word was built on the notion of 'that which is above', consisting of *ḥar 'above, upon' and an ancient masculine suffix *-aw, becoming therefore *-u. As such, it couldn't have consonantal w during literate times either since we have only a short vowel. This then explains Loprieno's "good orthography" which now reflects a transparent, underlying reality. No more arcane scribal rules on whether or not to write the trailing semivowel. No more wildcard symbols either, as I've shook my fist at beforehand.

Socrates' debate with Gorgias and others

I'll get to Egyptian tomorrow, but for now please take a look at Plato's Gorgias on Perseus, which may be read both in its original Greek and also in English translation. It's then discussed on Youtube by an interesting online lecturer.




As I finally got around to reading Gorgias, I immediately appreciated how much it relates to the modern age. The seething anger of a growing number of people towards an insolent plutocracy is just beginning to boil over as the markets show increasing instability and as yet more responsible homeowners are being put out to the streets. To add insult to injury, these same victims are doubly left crippled in utter joblessness as politicians flutter about feigning stupidity. Democracy? Only in word, not in deed.

Socrates' words spoken more than two thousand years ago ring true as he rejects feel-good Rhetoric for the greater virtues of Truth. He proceeds to tear apart in laborious detail and unceasing wit all the ridiculous arguments put to him in favour of "might makes right" and in favour of childish selfishness at the expense of society. In effect, he establishes the beginnings of a logical morality, not based on cultish dogma or religious superstitions but only on pure reason. As the lecturer briefly notes, Socrates treats Truth in a quasi-religious way, being in keeping with the Apollonian traditions of his time (ie. the likening of justice and truth to a kind of illumination by the all-seeing sun god Apollo). Yet Socrates' public process of inquiry is anything but religious. Quite the opposite, it's defiantly anti-religious as he challenges the validity of all idle beliefs that do only harm to humankind. As then, we still have trouble heeding his insights and to our own peril.

Changes in Pre-Egyptian vocalism

Lately I've been reflecting on what Loprieno says about the early Egyptian vowel system on page 55 of Ancient Egyptian: A linguistic introduction (1995):

"In our discussion of phonology (section 3.4.3), we saw that one of the major features of Egyptian in its early stages was the presence of a strong expiratory stress, which eventually caused a reduction to /ø/ of short vowels in open syllables in posttonic position, with the resulting change from the Dreisilbengesetz to the Zweisilbengesetz (**saḏimat > *saḏmat 'she who hears')."

While Loprieno speaks of reduction to zero, I've long been thinking more along the lines of a Pre-Egyptian system of *a, *i and *u being reduced to *schwa* wholesale in all unstressed positions. To begin with, long vowels were only to be found in stressed positions in Pre-Egyptian, at least if the comparison with Proto-Semitic is trustworthy, and this length contrast in stressed positions clearly remained in Egyptian, as still evidenced by Coptic. I therefore choose to write all of these reduced, unstressed monophthongs of Pre-Egyptian as *a (to be implicitly understood as [ə]). Furthermore diphthongs *Vy and *Vw (*V = any vowel) then become *i [əj] and *u [əw] respectively. This has worked very well for me for a while now. The result is an Egyptian vowel system that still looks on the surface much like Proto-Semitic with long vowels restricted to stressed syllables and unstressed positions having only short *a, *i and *u. Yet since the system has been notably altered, we find a curious incongruence nonetheless between the vowels of Proto-Semitic and those of Egyptian.

We can also avoid a lot of the wildcard symbols Loprieno and others occasionally use in the unstressed syllables this way since my theory makes this pointless: Only *a can exist in these positions unless accompanied by a written semivowel y or w in which case the appropriate short high vowel is selected. It appears that the matter of whatever the original vocalism may be is an issue for Pre-Egyptian reconstruction, not Egyptian proper. Loprieno's */'ri:ʕuw/ (> */'ri:ʕə/) 'sun' becomes my *rīˁa.

There are further reasons why I'm dwelling on this, but I've divided it up into subsequent posts.

Theft is big business

BBC News informs us of the frustratingly inevitable plundering that occurred in yet another country in arms: Libya's historic treasures survive the revolution.

One may start suspecting a regular, enduring theme of events given Egypt's looting under the watch of Zahi Hawass (who was unsettlingly connected with the Mubarak regime at home, mind you) and Iraq's looting of Babylonian artifacts during the Iraq war. Regardless of why it keeps occurring lately, the world loses one more piece of its soul as we stand by and simply allow our collective history to be sold for a cheap buck.