Adversus Marcionem

It occurred to me that I might be accused of cosmic dualism, of a Christian sort. In what follows, I refer to H Clifton Ward "Marcion and his Critics". Ward was asked to present the present-year consensus on Christianity's most earnest early Platonist.

Bear with me as I remind y'all that we all rely upon Marcion's enemies. We have little Marcion directly. We may have his prologues to certain Pauline epistles in Latin - I am presuming "vetus", that is pre-Jerome. (CALLED IT 7/15/21: For the NT, Jerome did only the Gospels, leaving the rest to the Pelagians.) But otherwise we are stuck with Tertullian and others like him.

For Ward, Marcion's thought derives from a fellow Anatolian Greek, one Numenius of Apamea. I must disclose that I have not so far read Numenius directly. Ward presents Numenius as proposing a great Platonic ideal of goodness, to which ideal other gods aspire. So far so Bagestan.

Marcion judged the Old Testament God so imperfect that Marcion could not serve Him. In His stead Marcion proposed that Jesus had dropped in on us from a superior god, the "Father". In this respect Jesus acts like the Serpent in Eden, which later or parallel "gnostic" sects made explicit.

Marcion, perhaps, reified Numenius' ideal of goodness as a god itself. I have not done this directly; but I do admit that, in my schema, the "demiurge" Who created this universe has not reached the Divine ideal Himself. In an uncountable multiverse, other gods are likely ahead of Him. And again, Marcion's enemies might not be being fair to his thought.

This daring supposition, Marcion could not prove from the four Gospels we got - which are all thoroughly Jewish. Instead Marcion acquired some version of Luke's Gospel. The anti-Marcionite Church Fathers, in what they quote, certainly make it look bad for Marcion's text. However that text might not be Marcion's own. Since - once more - we rely on Marcion's enemies, it is possible those enemies had taken genuinely-distorted recensions; by Marcion's more-zealous disciples, perhaps. (Hippolytus similarly owned an expansion of "Gospel of Thomas" ch. 4 perhaps via tafsir. Ditto, what John Damascene would make of the Quran's Camel of God.) Also many variants are shared with known manuscripts of Luke, not otherwise Marcionite.

It happens that Luke in any version relies on Mark. Tertullian (Ward points out) marvels that Marcion's Jesus appears in Capernaum out of nowhere and starts preaching in synagogues. A nonJew may certainly enter a Bet Midrash and observe the services therein; but he won't be ascending the pulpit to preach. Marcion's text has a subtext, at the very least; that Jesus appeared in the semblance of a mature rabbi.

I would further question that the God of Torah was all that bad. Certainly the Jews and Samaritans never thought so; it only takes a cursory reading of Dennis Prager to learn how Israel has wrestled with God and decided to submit to Him. If nothing else, the God of the Good Book created us and loves us: He is the God we know and grew up with. If the Old Testament God is good-enough, there is no need to posit a better one. I go further: given all the horrors that inhabit the Far Realm, the chances that any other god is trustworthy drop to the infinitesimal.

Marcion, writing in the early second century, had little warrant to argue that Jesus himself had posited some other god. In that gospel anterior to Luke - both ours and Marcion's - Jesus would not even renounce Judaism. The most Mark's Jesus did, was to argue points of halakhah, and here and there to assert Messianic privilege for himself.

I can best sum up Marcion's thought as - nice try, dude.

Genesis 1.5

In the Quran, and also in Late Antique Christian mythology, Eden wasn't the first place God allowed in chaos... and faced a rebellion.

I have here laid out a case that the Eden episode was not even a rebellion. God had allowed free-will to enter His creation from the start; Eve and Adam simply expressed it. It follows, those two hadn't failed God's test. They passed it. As of Late Antiquity, various "gnostic" movements and, also, the challenge of Sasanian Iran had laid out the inadequacy of the Genesis legend to underpin a postJudaic state.

So late-antique Miaphysite Christendom, and then Islam, proposed a parallel Sündenfall: free-will exists in Heaven as well. The Satan, before Genesis Two, had expressed free-will there. In this parallel, God was wholly unequivocal: the râjim Accuser sinned, and himself was murjim.

One could explain this as God making a mistake, learning from that, and then running an experiment under the more-controlled environment of the Paradise. This blog's theology does allow for a god that learns. But from a story-structure perspective this looks repetitive.

I counter-propose: that the Biblical God, who has free-will by nature, grew into godhood in the same amniotic plane as did several other prospective gods. A mithal in our spiral arm of the galaxy is the planetary nebula, with a star and its planets. The star does not create the planets but it does constrain their growth.

Lucifer, by the way, is associated with the Morning Star which we call "Venus". It looks brilliant like the Moon, but like the Moon it reflects only what the Sun gives it.

Also by the way, the Bible and the Quran teach lessons for the betterment of humankind, and not Stone-Age humankind but civilised humankind.

Back to the empyrean: some of those Brown Dwarf Demigods accepted a subordinate role as God's agents - Greeks experience them as "angels". Other protogods perhaps escaped but they shan't detain us here.

The lesson the postBiblical tales of Lucifer the Angel would teach is that this one had stayed on to accept a role subordinate to God. Lucifer could not accept a role subordinate to man.

Misanthropy is certainly a believable motive. I note here that ParaCatholic popular cinema has other free-willed angels, later, following Lucifer's path: Dogma, for instance, and more daringly The Prophecy. But free will is free will. Any free willed entity under God is going to chafe against God eventually.

No god's realm can bear an angelic court for long. When those of us who deserve to meet the Biblical God, meet that God; said God shall entertain us as honoured guests. But this God shall, still, allow us our free-will. And we shall be parted: for better or for worse.

The Biblical God and human free will

I have been attempting this weekend to read from Genesis Two only what I find in Genesis Two.

Here I propose a solution, to defend Israel's and - now - Christians' maintenance of this text: God let the Serpent in, on purpose. Call it a missing verse in Genesis Two.

The Serpent - as Interloper - is not under God's control. The Serpent either came from the outer Chaos directly, or else was one of those protogods whom YHWH defeated. We haven't gotten into "Lucifer" doesn't matter; this hypothesis works equally for Nyarlathotep or Cronos.

I also don't claim supreme power for God. I do claim He knows what transpires in this universe, let alone in that (much less complex) walled garden which was Eden. So if the Serpent got into God's own greenhouse, He let it in.

In fact, God let it in at the start. When He explained to Adam and Eve how the Garden worked - "if you figure out this hack, which is RIGHT THERE IN THAT TREE OVER THERE, this Garden is going to collapse" - that command only makes sense after he had imbued Adam and Eve with the ability to make that choice.

The ability to make that choice, independently of God's will, is exactly Chaos. It is the Serpent.

After it was all done, Adam and Eve would name their third child Set. The Egyptians named their god who defeated the chaos-snake Apophis, also, Set. Possible coincidence. Possible not.

UPDATE 7/29: I've discussed Lucifer. He's still irrelevant.

Why a snake?

The next question I ask of Genesis Two: why a serpent in particular.

Many other animals have enjoyed a reputation for dangerous cunning, in the long tradition of Old World human animism. The jackal; the hyena. The owl. The bear to an extent. Certainly the ferret. The crocodile, the scorpion. But Genesis Two went with the snake.

I'd look at Near Eastern post-animism, first. The Epic of Gilgamesh brought in a motif, of a snake eating the flower of immortality. That the snake speaks to Eve first, hints at a sexual subtext.

Fertility actually pervades Genesis Two. Woman is created at the start; at the end, woman is doomed to bear children, which she did not in Eden.

The "knowledge of good and evil" which the serpent brought was, exactly, the Neolithic Revolution. Man and women learnt agriculture and animal-domestication. (Perhaps excepting the dog.)

The interloping serpent

Stephen King, in his short-story "The Gunslinger", had the titular character enter a small decadent town at the edge of a desert. A female preacher controlled this town "Tull", and sought to rile up the Tullfolk against the gunslinger. This she did by a reading of Genesis Two (among others): the serpent in Eden was no natural beast, said she; but an alien from outside.

Such derives from Christianity and maybe even more from Islam, whose Quran nowhere relates the form which al-Shaytan took - unless it were fire.

Genesis Two does, I agree, hint in Stephen King's direction. Especially as an Israelite Torah, God built Eden for the incubation of man, those creatures most resembling Him. God didn't build it for dogs or giraffes or beetles. If some non-human entity was sentient in the Garden, that wasn't part of God's plan. Either the serpent shouldn't be there at all or else something else was speaking through it. Either way: an Interloper.

Sündenfall

The Genesis Two story presents a reasonable illustration of how God has guided us. This story potentially addresses other philosophies: that we should be like gods ourselves, and contrariwise that superhuman guidance has already harmed us. Genesis Two provides some nuance against both.

Genesis Two introduces into hunter-gatherer Eden, other animals with some sentience. Among these was a tetrapod serpent. This ancestral dragon - in the myth - believed that he had become wiser than man, although Genesis does not detail how he had come by his wisdom. Out of whatever motive, this yuan-ti advised man - rather, woman - how she might exit the Lower Palaeolithic.

Well... so we did. And the yuan-ti changed too: his seed were doomed to crawl on their bellies, forever. So the myth teaches.

Genesis Two (and the Bible generally) plays loose with this world's chronology, and there never was a talking ophidian race outside Clark Ashton Smith books. The Bible did, however, get a lot right. It even intuited that snakes were upon-a-time more like lizards and crocodiles, with four feet.

Genesis Two introduces that degeneracy is possible. For that, the dragon (besides its other uses for this tale) is an object lesson: the tetrapodophis might have evolved into a reptile with usable hands or even wings, like certain dinosaurs did; but it didn't. In our world, the Australian Aborigine started out in Sahul as not so different from the cunning New Guineans beloved by Jared Diamond. What shipcraft the aborigine had used to settle Sahul, he lost in the Southland. The Tasmanians, they tell us, were worse; they even lost fire and had to institute taboo to share fire to their veriest enemies. And all Europe remembers at least one Dark Age and, in the Balkans, perhaps intuits two more.

Genesis Two at the same time, if not calling us degenerate, is of two minds about the direction of our progress. It moots that progress isn't good for its own sake.

To that, our ethnography proposes other directions of progress. To return to New Holland, the Aborigines might have developed a certain agriculture, like their cousins in the New World: through turning the landscape into a game-park. In effect: the Aborigines, Amazonians, and many North Americans re-created Eden as Dreamtime. In our day Richard Manning has argued we had been better off to stay in such environments and to have left harsher climes to the Neanders.

As for which side the Bible takes: Genesis Two belongs to that larger Book. However we subdivide (or re-edit) this overarching book, as the Christian Bible, as the Samaritan Bible, or even as "J": we have in Genesis Two but Ephrem's foretaste of a world like those in which gods live. Our Eden was metastable; it could not survive much scrutiny. As Tasman and Van Diemen found the Australians, so the serpent found us.

But the Bible gives us hope. Its god didn't choose the Aborigines to guide mankind. He chose Israel. Who was already wandering an urban, Neolithic world. In fact, a literate Bronze Age world: through Moses, later, was divulged Israel's Law.

In Genesis Two the serpent had no interest in bettering us. The Torah, as a whole, presents a better Guide for us, who desires our betterment.

The stakes of Eden

Theists want a loving god. Such a god will prefer his own theists.

If there be no such god, we are secular-humanists at best. We can perceive something better and we can aspire to it. Some humanists even dwell on the Right - in some cases, far to the Right. Still, secular humanists share that they believe themselves never to have experienced a fall and a return - or, if they did, it doesn't matter. We are as gods, to co-opt Genesis Two. To the extent theists disassociate themselves from secular humanists, they will be seeking out myths of the Fall.

Genesis Two belongs to a larger Book. That Book placed this story, not toward the narrow ancestors of the Jews, but immediately after Creation. It must apply to all mankind.

To avoid fundamentalism, the Garden of Eden myth which Genesis Two relates must be read as parable.

Dennis Prager teaches that the Bible's stories elsewhere react to ambient early-Semitic and Egyptian texts. Like The Peloponnesian War, the Bible - where it does not tell its own, southern Canaani stories - is revisionist.

Genesis Two is vital to all the Israelidic religions. If Christians don't understand it, they don't understand Christianity. Likewise, I hazard, for Jews and Samaritans. Muslims, whose Quran cites this story, need to return to reread it as well.

Witness to Tocharia

Razib Khan writes: Yamnaya DNA found in the Tian Mountains. Razib h/t's Eurogenes which is where I too had found it first, but Razib hosts the most-comprehensive summary.

Yamnaya is the north Pontic and Ukrainian culture of the Bronze Age. Since David Anthony's 2007 The Horse, The Wheel, And Language and really since Mallory 1987 and if we're being honest since Gimbutas before all of them, that culture is assumed ancestral to all the IndoEuropean languages.

This includes the "Tocharian" languages... clustering on the Chinese side of those Mountains Of Heaven. As of last April we own documents in three Tocharian languages. All Tocharian texts are Common-Era in date, by which time the Tocharian-speaking peoples had already gone Buddhist and at least one language - Agnean - had already died out.

As for how Tocharian should have started in the eastern Balkans to end up in western China... well, that's been a good question, for the last thirty years or more. There's an ancient third-millennium Bronze Age site at Siberian Afanasievo (Latin orthographies differ); very Yamnaya in culture, and also in DNA. But Afanasievo wasn't literate, so we don't know what language its people spoke. Except that it probably wasn't Aryan: their male DNA is R1b, like mine; and not R1a, like the Andronovo culture to its south by consensus deemed ancestral to Iran and northwest India.

But a lot can happen in two or three thousand years. Maybe Afanasievo got hit by Mongols or Avars. Maybe the winters got bad. Maybe they got the plague - in fact, we know they did catch septicaemic plague, because we've dug up their plague-ridden corpses. So although we have a clear track from Yamnaya to Afanasievo, and some circumstantial evidence of DNA and linguistics from the 400 AD Tarim; we're lacking much in between.

We are now being introduced to Shirenzigou, decidedly on the Han side of the Tian range. The site is Iron Age - which has some meaning in a Chinese context, because China proper never quite had an Age of Iron, since the united Chinese civilisation allowed for a thriving bronze trade well into the gunpowder age which, of course, China invented itself. The approximate century of these not-Chinese mountaineers is 200 BC.

Shirenzigou DNA is a mix - partly east Asian, as we'd expect. [UPDATE 7/28: Eurogenes thinks they're Huns.] But it's also partly Yamnaya. And the male line is R1b - there's no R1a, which means it isn't Aryan.

The conclusion is that Shirenzigou's Yamnaya half is Afanasievo. So, by 200 BC, an Afanasievo-descent population should have made itself even more powerful over the west of the Tarim Basin.

One wonders what the Achaemenids or Alexander's diadochoi would have made of this people. Or if the Qin or the First Han regimes ever encountered them. They were literate on both sides; and Agnean was assuredly a spoken language before it became written-only. We may be discovering live Agnean texts in our lifetimes, as we've discovered Tocharian C.

BEFORE ALL THAT 10/28/21: Junggar. But for this post we don't care; we're at the Qin era and beyond.

The nerds in the Neander brain

Neander Vale Man and Magnon Cave Man have been known for over a century, with the Magnon Man recognisably us. They and we overlapped. Our genes show evidence for that overlap - but not much.

(Here I shall lay out my usual fine-tunings of Cro-Magnon itself. Cro-Magnon 1 is a Black Death era victim - oopsie. The others are now classed Aurignacian, living after that Campanian Ignimbrite eruption; no-one living after 37kBC ever met 50%+ Neanders. In turn Aurignacian DNA - which survived to the Magdalenian era - didn't weather the Neolithic turnovers any better than the Neanders had weathered that eruption. Nobody anymore talks "Cro-Magnon" in an ancestry context, because they're close to a dead end. They talk of "Early Modern Humans".)

Up to the late 2000s of our era, most of us assumed that the Neanders were simply wiped out. We just didn't know how: that volcano was one of many suspects, or perhaps conspirators. Some authors counter-surmised that the Neanders interbred with us; but this debate went more in the popular press. Larry Gonick with his Cartoon History was most influential to my generation, and then Gregory Cochran's and Henry Harpending's 10000 Year Leap. The scholars doing peer-review felt limited by the evidence, and well into our millennium even the DNA was not showing mixture, even at low levels.

A classic clash between Bayesian common-sense on the one side, and inductive Popperian reasoning on the other.

As of 2010ish our DNA extraction got good enough to find traces at the 3% level or less. The plebs had won this one against the nerds: Neanders live amongst us. Soon after that we found in the Siberian Denisova cave (a Frenchman might call it, "Cro-Denis") another population. This caveman was descendate from the same Pleistocene out-of-Africa movement which led to Neander; but - by the time of the remains - already itself very different from Neander. And we've conjectured further offshoots from Cro-Denis' post-Neander ancestor; these contributed disproportionately to Melanesian DNA. Human populations remain haunted by other ghosts besides. Some ghosts entered some African genomes.

For our purposes here: before modern humans mixed with Asians, those modern humans had already mixed with Neanders, presumably in the Near East. Everyone from the Outer Hebrides to Tasmania to Greenland shares in the Neander legacy...

... slightly. One reason it took so long to find any admixture at all in modern peoples, is that said people's ancestry had become more African and less Neander as the generations progressed. Some of the balancing is accounted for by a great return of now-hybrid Europeans back to north and east Africa, on the occasion of the Ice Age ~15kBC. We are absolutely talking whole tribes, with the women: U5 mitochondria show up in the Maghreb, and N1 in Somalia. More important was a dilution in Eurasia: a "basal Eurasian" population, xenophobic enough to avoid contact with Neanders, finally relented so far as to surrender to now-hybrid tribes. A third factor, which we're getting into, was modern-human selection against Neander DNA although, of course, these stretches would cluster where it mattered and not over the "junk" stretches.

Cochran and Harpending further surmised that Neander DNA revolutionised the non-African brain. The African brains and - by then - the Eurasian brains had each reached its equilibrium by, oh, 100kBC. Even that early, there was some outflow from this population to that. Cro-Denis itself was part Neander, and early modern humans had bumped into Neanders - early modern women, specifically. Just not on the scale of the great out-of-Africa 70kBCish. And the sporadic fluid-swapping didn't change anyone's Palaeolithic way of life. Those 70kBC revolutionary changes - so claimed C&H - demanded a Neander-human hybrid, of 70kBC Eurasian proportions. The hybrid could develop in directions Neanders, and Africans, could not on their own.

It turns out Neander DNA stretches - and the various Denisovans' - do have gene-expression to affect the brain. We were told last year that scientists have grown Neander neurons in the lab. Neander grey looks different from African grey at the cellular level. And from our grey. Which pointed away from Neander influence on us, and from C&H.

We may, at last, have our DNA evidence - in that direction (h/t hbdchick). Natalie Telis, Robin Aguilar, and Kelley Harris have posted "Selection against archaic DNA in human regulatory regions". Those regions affect muscle... and the brain. In our ancestors Eurasian muscle was allowed to deteriorate, which means that tools and (necessarily) skills had got better; so the real action was happening on the brain. Bluntly, Neander DNA wasn't good for the head; and the less of it there was, the better our toolset got. Which would "severely constrain", as is politely put, Cochran and Harpending.

Neanders and most Denisovan subgroups couldn't ever maintain much of a population size. The large heads, larger than ours, made breeding difficult. Also, the climate was harsh. (Razib points to southeast Asia being different, but there you run into other problems - like the volcanoes, and in our 100k year time-scales interglacial global warming flooding the shores and leaving behind islands.) Lower populations, and isolated populations, induced inbreeding and genetic drift. Some of those genes caused the Neander traits to drift. In the case of the brain, badly.

Thomas Wynn thought in 2012 that the Neander brain would become ultraconservative, fixed into patterns to survive in their isolated refugia. We today call such tendencies OCD or even autism.

But Cochran and Harpending would say, that's what our Eurasian ancestors needed, was some instinct to stay in the valley we know, even in winter. It led to time-preference. If Neander neurons didn't last amongst our ancestors, perhaps they lasted long enough to protect our developing brains over that last Ice Age.

UPDATE 7/27 11:26 AM - to 7/25 you go.

UPDATE 9/9 - Consider not the brain but the skull. Perhaps the larger Neander cranium allowed modern human brains to grow for longer...?

V'Hu Aḫer

As has been mentioned of Gamaliel, the Jews remembered (second-hand) the careers of hundreds of late Second Temple rabbis whom the gentiles remember, if at all, likewise secondarily. Let's talk about An Other One - Aḫer (Akher), in Hebrew.

I found out about Aḫer in Amir Aczel's book on The Mystery of Aleph. The second chapter hints at the Jewish mystic tradition as a bridge between the Pythagorean societies of the ancient Greeks, and mathematically-minded Christian theologians of High Mediaeval Europe. This chapter does not, unfortunately, make that case - nor any case. This chapter is (by far) the weakest in the book, and I am reliably informed it turns Christian readers away from the subsequent chapters, which are better. But anyway.

The Jews have a curse for those they dislike most: "may his name be erased". In olden times the Jews chose to distort the names of false gods: thus Syrian "Baal" became "Bosheth" and the Tyrian-Carthaginian "Molok" became "Molech". Later they (famously) renamed Jesus "Bar Panthera". "Aḫer" is another one of those heretics and/or apostates from Judaism - in this case, identified with Elisha Ben Abuyah.

Elisha is a name Biblical-enough; I am less certain of his patronymic, from Abuyah. I will assuredly find that someone has proposed a Hebrew etymology but, to me, it sounds Aramaeoid or Iranian. Syrian and early Islamic texts are full of names like Marduwayh, Shiroë, Babaë, maybe even Penkaye. Orthographies are not standard: Syriac and Persian are both long-running languages each with their own dialects in this place or at that time.

In Syriac, the "Jacobite" dialects underwent the so-called Canaanite Shift of long A to long O. My guess would be, some time between the 200s and 500s AD. After that, Jacobite communities entered the East, where lived Aramaeans who did not take this shift and refused the theology of Jacob Bar Addai. The Aramaic(s) which influenced the Qur'an, also, had not taken this shift (per Mingana: pdf). Jews, especially those still in the west, can be expected to turn Aramaic to that shift. So let us propose Elisha as a man from the Galilee.

Elisha earned a mention in Mishnah - one mention, Pirkei Avot 4:20. Up to the end of the second century AD, the Jews did not consider Elisha outside the mainstream - as contrast Bar Panthera. Jewish tradition has since become unclear about what "Aḫer" actually taught.

The story which Aczel relates comes from the two Talmuds, on the "Hagiga" tractate. Each quotes from the Gamara:

Ben Azzai glimpsed at the Divine Presence and died. And with regard to him the verse states: “Precious in the eyes of the Lord is the death of His pious ones” (Psalms 116:15). Ben Zoma glimpsed at the Divine Presence and was harmed, i.e., he lost his mind. And with regard to him the verse states: “Have you found honey? Eat as much as is sufficient for you, lest you become full from it and vomit it” (Proverbs 25:16). Aḥer chopped down the shoots of saplings. In other words, he became a heretic. Rabbi Akiva came out safely.

In the Iraqi Talmud (which is all Aczel knows), Aḫer's heresy was dualism. In those days, Iraqi Jews lived under Iranian government. The Iranians viewed their own "Zoroastrianism" as the Aryan religion, to be imposed on fellow Aryans, like in central Asia, and soon enough over Armenia. I don't read that the Magi molested the Semites in Iraq much, except to quash revolts. But then, in the 200s AD, came the Manichees. Those were always on the lookout to poach Christians (at least) for their own. It is not hard to imagine Manichees recruiting Jews too. Manichaeanism is, notoriously, dualist and gnostic.

The Palestinian Talmud proposes something wholly different: theodicy. Its Elisha observes that those who break the Torah often get away with it. The stated backdrop is the persecutions under Roman government; of whose emperors, Hadrian is named.

I cannot but think of Ibn Sayyad in Islam: a sort of bogeyman, an archetypal agent of the Satan on Earth whose heresies tempt the faithful. The content of the heresies shifts depending on the needs of the community. In Palestine, Jews worried about Roman brutality; in Iraq, they worried about Manichaean seductions. Each local ghetto constructed its Aḫer accordingly.

As for what Elisha taught in life: G-d knows best. It may just be that he was forgotten, except for his patronymic and that one line in the Pirkei Avot. The later rabbis, warning against heresies from within, needed famous names to attach to their moralising stories. For the archetype of the philosopher whose musings lead astray, they ran with Elisha.

The independent career of Matthew's pater-nostrum

That which we Latins call the "Pater Nostrum" is the version of "the Lord's Prayer" preserved in Matthew's Gospel. A fortnight back, Neil Godfrey at Vridar proposed an argument that the prayer's author cobbled the thing from earlier Christian formulae and texts - most of which survive to this day.

Says Godfrey: the prayer has authentic analogues to early Christian jargon, as we know it from Mark and from Paul. The first generation were prone to invoke "Abba / Father" as a Syro-Greek gloss; "Marana tha" is another early Aramaeism, "our Lord come". The Lord's Prayer conflates these, opening with, "our Father" (it becomes Abbana, in Aramaic). For the latter, the Lord's Prayer went with "thy kingdom come" (malkhûthâkha thâ...?).

Godfrey further notes that where the author changes the wording of these early Christian terms, he does it in accordance to how Matthew's Gospel does it elsewhere. Mark would have Jesus, walking amongst us like YHWH through Genesis Two, forgive sin. Matthew instead presents Jesus as the human Christ, walad begotten of Yoseph in the line of (all too) human King David. This messiah hasn't authority to forgive sin... but he can forgive debt, if only we'll crown him. (Michael Hudson, proponent of Jubilee in our day, prefers Matthew.)

Godfrey concludes that Matthew had the means, motive, and opportunity to compose a communal prayer in tune with his own reading of Mark... and that it wasn't Jesus who taught him. It was not even "Q": Luke's parallel in the "sermon on the plain", Godfrey says, is stripped down from Matthew's.

A commenter Steven Watson on 5 July asked, what about the Didache. Since Godfrey hasn't got 'round to it, I'll give that a shot here :

Emran El-Badawi noted in his book The Qur'an and the Aramaic Gospel Traditions that the Edessene "Syriac" tradition contains Syriac adaptations of the New Testament, which weren't always perfect translations. The Beatitudes, for instance, rhyme: El-Badawi, 90-1. The "Pater Nostrum" is similarly pithy and loaded in rhyme: 107-8. "Our Father" is "Abbûn" in this version rather than the "Abban(a)" I expected, although that may be Osrhonene dialect. A more-drastic change is tîthê malkhûthâkh. This is there to rhyme with nêtqdash shmâkh. This has to be secondary to early Aramaean Christendom.

This strategy of rhyme looks like the memré genre in Edessene Syriac and, soon enough, the saj' rhetoric in the Qur'an. Matthew composed and the Edessenes re-composed. And the latter did it without reference to earlier Aramaean Christians.

Pericopae like this probably went out as qeryâné first, independently of a full official translation. (It went similar in Old Latin, before Jerome.) When the Edessenes hammered out their "Peshitta" translation, wherever they feared a fight with those Christians accustomed to the older readings, they just copied those readings right in there, fixing only what was at worst deviance from the Greek at the time. (Again: similar in Jerome. And with King James, with respect to the translations before him.)

Even in Greek a lot of the "New Testament" scraps come to us through Greek lectionaries. These, too, often stubbornly held to older readings which the Byzantine official text had revised.

To answer Steven Watson: the Lord's Prayer is composed exactly to be memorised and spoken in a group. It was Matthew's full intent that it escape "into the wild", as it were; to enter liturgy even in places like Edessa where the full Gospel was not yet translated. It is no marvel that the Prayer drifted into Greek liturgies too, even such as weren't yet ready to accept a Jesus biography as Scripture - or, if they already had one, like Mark's, and weren't ready to replace it. It would be more of a marvel if the Didache had resisted this prayer.

The Jubilee of the Mu'minin

The Islamic dating system is today called "Hijri". But in the earliest Arabic-invasion documents known to us, we read nothing to do with Hijra; we just read "the year of the Arabs". But sometimes, when they mark the year, it is sanat qaḍāʾi 'l-muʾminīn; as vocalised Shaddel a sana ago.

Shaddel's reading of qaḍāʾ here was Madinan, with reference to the Revolution's Year One. For Hoyland that qaḍāʾ was semi-famously "the dispensation of the believers". That reading even in the early 2000s struck me as more Schofield - Darby than Muhammad - 'Umar. It seemed more in line with modern Anglo-Protestant universities' theological theories than with anything that might make sense to the average Late Antique Syrian.

Mathieu Tillier and Naïm Vanthieghem are on this case now. They've been looking at Fusṭāṭ, that fossatum near modern Cairo. Here, that "SQM" notation appears only in the dates for debt notices.

As for how Islamic finance worked (and works) outside Egypt, let's not delve into that in scope of this blog-post. I will note, here, that religious reformations have, in Biblical contexts, proposed a Jubilee, to forgive all debts public and private. Certainly the Arabs' takeover of Egypt commenced a stark religious shift. My Muslim readers should recall, also, that no Muslim as of the 20s / 640s could agree upon one Quran; 'Uthman's collection would come 30 / 650. All the Arabs had to go on, was what the Egyptians had to go on: the Bible.

Tillier and Vanthieghem do not utter the word "jubilee" in their article. So let's do it right here and now: the sanat qaḍāʾi 'l-muʾminīn was the year after the Zero-Year of accounts being settled. It was the year after the Arabs proclaimed the Jubilee. Where and when they conquered, their subjects canceled what they owed to their prior (Greek and Persian) creditors.

P ≠ NP

In 2000 were mooted seven Problems for a "Millennium Prize", to succeed (and in parts include) Hilbert's twenty-three.

I have mentioned the Continuum Hypothesis, which was one of Hilbert's; a new set theory is still outstanding, but the mathematicians have demoted that from the top six.

We are not counting Henri Poincaré in this six because his Conjecture is a Theorem now - it has been solved. The whole Geometrisation Conjecture has been solved; although mathematicians didn't buy Perelman's proof at the time (2003) they did iron it out eventually (2007). Any four-dimensional manifold must exist in any one of eight geometries. Given that our universe is an instance of one of those 4-D manifolds (probably), this matters to future studies of local physics. And to theologians, perhaps.

Of the six remaining Problems, perhaps the hottest Problem is P Or Not To P. To whit: whether a nonpolynomial problem, like an expansion into factorial or otherwise-exponential (that is, f(x)= 2^x) possibilities, may be solved by a polynomial-step method - by such a f(x)= x² "algorithm", as the Arabs call it. The traveling salesman's eternal question of how to get his route to multiple houses done shortest (or, fastest) is the classic instance of "NP complete".

I have had an interest in this since I first did Comp Sci in college. All programmers know P v NP; it is a matter of survival. If our boss demands a quick solution to some NP problem, once we have found out that it is in fact NP, we tell our boss LOLGF - we can't do it. 'Tis one of those problems. They shoot horses don't they?

I am not here to solve P v NP formally. I'm sorry, HAL; but I can't do that. I will, here, lay down my marker that P ≠ NP.

The Inductive Method is the algorithm which proves functions true, or not, within a given infinite-but-countable set. Georg Cantor found stuff which the inductive method doesn't find. The stuff which Cantor flagged as unreachable to an inductive algorithm is exactly an exponential function. f(x)= 2^x. Plus or minus four.

Algebraic numbers are countable; they are subject to induction. Those are the numbers accessible to polynomial functions. Transcendental numbers aren't so accessible; among which is the natural logarithm of "one". There is no polynomial function that can net you a transcendental number like e (or pi). I posit there is no polynomial-time algorithm that can solve a problem with e-to-the-power-that-time variables.

Again : I am not calling this highschool-level blog post OMGz PROOF P ≠ NP. I will, however, declare it as sufficient as intuition. Nobody is going to find a polynomial-time solution to a nonpolynomial problem in my lifetime. Or in yours.

Luke's sources for Paul's early biography

There's talk that Luke took Paul's dictation.

Luke's use of the Gospel of Mark (wholesale) hints that, before Paul, Luke didn't have firsthand access to Jesus' first generation of followers, nor even second. The Apostolic era is later, so those generations were accessible to Luke. But here, too, he could find documents - not least, letters attributable to Paul. Luke was not a muhaddith like Papias; Luke had a bias to written texts over oral tradition.

Paul did on occasion speak of his own past: such as in Galatians 1:13f, and in a (probable) "severe letter" now preserved 2 Corinthians 10-13 [UPDATE 12/12/23: I now think the Lachrymose was different so not preserved]. Some of these episodes end up in Luke's Acts. Let's talk Gamaliel as a test-case.

The Christian historian Luke holds Gamaliel as an important rabbi among the Pharisees; tending to moderation. This is in accord with the Jewish memory, as preserved (mainly) by Gamaliel's students. Luke also claims that saint Paul né Saul of Tarsus held himself out as a devotee of Gamaliel. THAT, I don't know.

Gamaliel's name is nowhere uttered in Paul's epistles - even in the disputed epistles. It also seems strange that on the one hand, Luke has Saul as a persecutor of Christians; and on the other, as a Gamalielite. Wouldn't such a one be a moderate? I mean, it is possible that Saul vacillated over his career in Judaism, before converting, but . . .

Pauline epistles survive in which the narrator declares himself an ex-persecutor; Galatians is the most important. If Luke had access to such, and to letters of Paul (or to Paul) as mentioned Saul's training as a Jew, he could reconstruct the events as he had.

But that doesn't mean we must. Can we trust such letters, not preserved to us, were authentic? 1 Timothy is not taken seriously by Paul's biographers; its narrator's self-image famously contradicts 2 Corinthians'. Pauline apocrypha went out early: also dismissed are 2 Thessalonians and Colossians.

Gamaliel, in retrospect

Gamaliel comes across in Christian literature as the mentor of Saul of Tarsus, even as a convert alongside him. The Copts were particularly prone to this. Much derives from Saint Luke's book of Acts, itself (I think) from now-lost early Christian writings. Which writings Luke had taken by faith.

Elsewhere in the first-to-second centuries' Judaism, we rarely find contemporary attestation of any rabbi, whose fame (or infamy) later Jews would remember. In such Jewish literature, Gamaliel is typical. In Christendom Luke will note our man in Acts; but nowhere names him in his Gospel.

We do have considerable attestation of first-century Judaean politics, at least. Roman-ruled Judaea hosted a Sanhedrin of Jews from various factions who met to arrange Jewish orthodoxy. The Sadducees from the Temple dominated this synod. To the extent Pharisees contributed to Sanhedrin, which I concede 30s AD Judaean politics could have forced; the Sadducees preferred Shammai's party.

I propose that Gamaliel did exist in the 30s-50s AD; but that he was on the outs, like the Essenes... and like the Christians. It was later, after the Ninth Of Av, that Gamaliel's successors raised his profile. Luke was among those who heard of Gamaliel.

Not so sure about Paul.

UPDATE 7/13: Luke's Quellenfrage belong in a Luke essay. The core of it was commented on 7/11 anyway... elsewhere.

Bull from the sea

2600 BC, during the Bronze Age, the Greek-Armenian ancestors had not yet embarked upon the wine-dark sea. Far south in the Cyclades, the islands were still populated by who-knows. Semites? Egyptians? Anatolians?

Some islanders from the Syra-Keros Culture found a small outcrop off the latter; it's its own island now, "Dhaskalio". They thought it was a grand place for a monument. So they quarried Naxian marble - a lot of marble. And they remade Dhaskalio into a fitting platform for a pyramid.

The researchers report to The Independent that the top of the pyramid was empty, at first. Also, they found 1,000 ritually broken religious marble figurines (mainly depicting women in symbolic form), again brought there [to Naxos] from all over the Cyclades archipelago. The figurines were from all over the Aegean; there's also obsidian tools and "blades" from Melos.

I think, here, is the Threshing-Floor rife in protohistoric Bronze Age farming-culture. Syra-Keros harvested (emmer) wheat, which they needed to thresh. 2600 BC is too early for horses, and I doubt they ever had much of a horse-culture in Keros or even Naxos. The animals in these islands tend small, like the sheep. But the Aegean shores did, by then, have cattle (even if they weren't retaining water so well). So the threshers were oxen.

Further, I am scenting the iron tang of sacrifices in the area. In the preliterate Near East, it was common for symbolic figurines be taken to the site of trade. There, mediators smashed the figurines in such a way as could only be deliberate. There the defaced images remained, to confirm receipt of the cargo. If the figurines were humanoid ...

Later, the pious locals contented themselves with smashing figurines in effigy.

The view from Tblisi

The Christian monastery at "Mount Sinai" might not be at the Israelites' Sinai, but it has earned its own importance in Christian history. Because the Roman Christians unilaterally stuck the name "Sinai" onto the site, and because it was, well, kind of dry and out of the way; it preserved a lot of manuscripts not preserved elsewhere. In 2005, a set of MSS rediscovered 1975 were published. Many MSS were in Iberian Kartuli, sometimes called "Georgian" today; Stig Simeon R. Frøyshov in 2012 published a summary.

I am sure that followers of Robert Hoyland's work - and of Stephen Rapp's - were hoping that there might be some Islam As Others Saw It in there. Well there wasn't. It's mostly eastern Christian liturgy. The base content isn't interesting to Muslims and it's not much more interesting to us Latins, influenced by Charlemagne as we are. But what it does give us, is a snapshot of the liturgies of early Iberia. Also of the Kartuli language still spoken there. And, it happens, of the Christian liturgies of the Late Antique Near East.

Christianity didn't start from the Caucasus; it started from Roman-occupied southwestern Syria. When the Iberian nation accepted Christianity, they had to learn how do Christianity. The Laz on the Pontic coast were beholden to the Greeks, and the Hayots of Armenia accepted much from northeastern Syria; but the Iberians over the hills chose to bypass it all, and to take it from the source. Then just prior to the Crusades, Iberian monks in Muslim-ruled Palestine moved their libraries to Sinai: some from Jerusalem, some from the laura of Mar / Saint / Agios Saba. The Iberians saved pretty much all of it, with few losses. As a result, there's a lot of early Jerusalem Christian practice in Kartuli, which later Christian reforms subsequently changed in Iberia as much as in Palestine; which stayed the same in Kartuli at Sinai.

Although Kartuli-language Christianity in Palestine (before the move) stayed Palestinian, Frøyshov points out that back home in Iberia the locals were drawing from further east. The Kura River flows to the Caspian, remember. Via Heinzgerd Brakmann, the ordination prayers in the MS "Tbilisi NCM A-86", had taken on additional prayers from Mahoze / Madain. These Iraqi prayers got to Iberia at some point after the Testamentum Domini, of the 300s AD; and before the MS's transcription circa 1000 AD. There's also a "Ninevite fast", by which we must read early Islamic Mosul.

I expect that non-Hellenophone Melkites all along that post-Byzantine frontier from Jerusalem to Tblisi (they say თბილისი means "warm" but, consider "theo-polis"...) never did close the door against the Nestorians. Under Islamic rule came several Christian attempts at rapprochement between communions - All In This Together, You Know.

There's even a Kartuli rite of marriage at Sinai! For Latins these days this is of interest, in that we're now being told that our sacrament derives from the Synod of Diren in the 670s AD. That one is "Nestorian" but for those early days, I never could much extricate Nestorian doctrine from post-Toledo filioque Catholicism. I'd love to see what relationship the Jerusalem(?) rite has with the Nestorian sacrament.

UPDATE 7/13 10:45 PM - This noonish post can just go to 7/9 because, why not.

Our side of the mithaq

Back in the late 1990s, some Chomskyite Zappa-fan entered a competition on topic of whether God existed or not. His tack was to run for the office. He conceded he'd already lost the competition on account of begging the question. But he laid out his platform, at least; and compared that with the Biblical god's platform. He didn't win the competition, and based on Trump's own secular election he sure didn't get himself elected to that more elevated position; but he did get himself interviewed on the radio. Got hisself linked on the Secular Web too.

I harbour no interest in running for such office (especially not now). But in that spirit, I propose a constituency, for any prospective deities over this universe. Assuming they want my vote.

And I am not begging the question as hard as he did. I already know that there are gods out in the multiverse (for the gamers: "astral plane", "limbo", "far realm"...), likely an infinity of gods. I also know that we're not infesting the body of any of them, dead or alive. The only options are that we're inhabiting some god's creation or else we're drifting in an amniotic (self-created) bubble. Either way, the gods are out there, on the outside. That discussion is settled.

What I want is a god worth the following. Some gods aren't worth it. Most gods aren't. I have read my Lovecraft as diligently as that other guy had read his Chomsky.

I request that the god keep his promises. Since he is Lawful, I don't demand that the god be infinitely wise and powerful; I know that is impossible, in a being of Law.

The god should, whether or not he created this universe of Law, at least respect its Lawful nature and intervene only to protect us. Mainly from Nyarlathotep, but also on occasion from our own most grievous mistakes.

The god should have some patience and mercy for us the humans. As a limited being (by Law), the god is capable of being flawed. I count mercy despite our deserts as a slight infusion of Chaos.

The god's doctrines should promote human life. They should, also, scale in accordance with humankind's ability to understand this universe. I expect that the god, as concerned with his own preservation, will not suffer a witch to live; "disgusting quislings" as I recall Lewis calling such. I can accept that; but, since we've already conceded the point, I request further exceptions to counter anti-human humans: exceptions for just-war and for lawful executions.

If the god didn't create this universe, I want one with at least so much sentimentality as to adopt it.

COMMENTARY 7/13: I'd had this in my mind for decades; only figured how to organise it all, this afternoon. So I'm backdating it to some day this week closer my other theologic musings.

How philosophers encounter the universe

Almut Hintze researching Zoroastrianism concluded that the Gathas imagined our universe as the body of a living god, infected with evil [summary here]. There's a lot of that in modern "environmentalism".

Gnostic Christianity believed that this universe is a Created Prison. Catholicism dresses it up better but, at base, agrees.

Atheists assume that our universe has no purpose, or (if you're a Lovecraftian) that we shouldn't follow whatever purpose the gods have laid out for it. So atheists don't care how we all came into being - with one exception.

The secular-humanists, with whom I hung out in the late 1990s, are an optimistic bunch. Humanists assume we inhabit an amniotic spacetime. That Seth MacFarlane joke about the pre-whisky Irish, riffing on "converting our bodies to pure energy"? An actual humanist thing.

Those atheists who aren't humanist, deep down, don't really think that the gods never existed. They suspect that the gods were here, once upon a time; but that they have abandoned us since.

Classification of universes

Such universes as can exist, exist in any one of these essential definitions:

• Amniotic fields in progress
• Discarded amniotic fields, which their gods had exited (not necessarily "abandoned" - see below)
• The bodies of living gods
• The bodies or fragments of dead gods
• Creations of gods

From the gods' perspective, universes have these purposes:

• The bodies of living gods
• Prisons
• None

Biography of a young god

In the utterchaos of the multiverse, wherein "time" and "space" have no meaning, shreds of the chaos conjoin and make meaning. Some of these form enough of a shell that said bubble can maintain something like the time-dimension in our universe. In these shells, dwell the gods.

Such bubbles in the multiverse - Dungeons and Dragons calls them, "planes" - are able to contain entities with intelligence, and to retain them. Let's call these bubbles "amniotic".

Within their amniotes, newly-formed self-created gods will be like newly-formed babes, without even the sense of instinct. But, since they have time on their side (so to speak), they can grow mentally.

Some intelligences take over their plane and use it, like our brains use our bodies. Others find ways to exit their birth-plane and to become free-floating planes of their own. Whether they subsumed their amniotic plane or else budded off from it, free-floating sentient planes are gods - absolute despots of their own selves.

Here is, per universe-bubble, where the first ethical choice was made. Did one sentient destroy all its rivals in its own amniotic plane, on the way to godhood? did certain sentients collaborate amongst themselves? did they merge, or spin off descendants?

Once freed of the amniotes, gods float through the multiverse with the memories of what they did there. Friendships and animosities were made, and qualities like "mercy" and "judgement".

In victory, some gods spared the sentients who lost these struggles; the latter souls are incarcerated in special planes, which planes they cannot (easily) escape or subsume. The Greeks named this concept "Tartaros". Here the cycle begins again. Maybe its "titans" can make a better effort this time.

So, the cosmology of the Bagestan: countless planes and - from them - countless gods. Each mindless plane and each mindful god contains internal logic and some analogue of "time". Concepts of order, mercy, life, and death exist outside Divine definition. Some planes are amniotic, that is self-created; of these, some have an internal order which its inhabitants set out before they became gods. The other planes, the gods created secondarily.

There is a Heaven - one Heaven. No god lives there. All the gods a human would want to worship, are trying to get there.

Upload #180: by grace of the throne

In the last six weeks, I have had cause to rethink my online presence; but I have assuredly not recanted my stance on the history of Islam. I have only collected more facts.

As usual, the last project in is the first project fixed, so: "Promised Egypt" is cleaned up... a lot. For one thing I deleted that appendix, which content you've already read in The Arabs.

I'd gone through Arthur Jeffery's Foreign Vocabulary again, so: "Blasting the Sultan" and "Against Jihad" have more Syriana. In other Jeffery news I found in Materials a variant of Q. 20:98 on the "lord of the throne" so, "The Ararat Tax" takes that into account. I also overhauled its 'Noah and the Prophets' subsection, in the light of Marijn van Putten, "The Grace of God", now published in BSOAS 82.1.

I re-read Sadeghi and Bergmann, "The Codex of a Companion of the Prophet and the Qur’an of the Prophet". This affected "Running Over The Sabbath" on sura 62 and especially "The Spenders in Hypocrisy" on sura 63, which hadn't been touched since 2016. The sura 63 links further touched on the reception of sura 76 so, "The Test of Man".

"Monks, Muslims, and Sura 57" takes on another 5>57 link I'd found in Neal Robinson's classic "Hands Outstretched" article. "God’s Path Leads through the Caliph" wrestles with Q. 59:2's clenching against the believers. "Donning the Mantle" (which was too short) has an additional 20>74 link.

Most of the altered projects were altered because I'd misspelled "Qur'an" in the title of a Boullata book; having misspelled "Boullata" earlier. @#$%! Anything else, I don't remember.

Madrassa.

Thoughts on induction

Georg Cantor's theory on infinities flow from the inductive method. That's the method by which you say if some function of "i" is true for i=1, and if you can show that where the function for "i" is true then f(i+1) is also true, then the thesis is true for the whole {i} field.

The inductive method gave rise to Karl Popper's metaphysic. Not all philosophers approve induction.

Cantor never challenged induction as such. What Cantor had done was to define and to find some "j" which doesn't exist in the inductive field of countable numbers. His "j" was 2^∞-4. He'd shown up induction's mathematical limits.

Bertrand Russell famously proposed another limit to inductive reasoning, as applied to the natural world:

We know that all these rather crude expectations of uniformity are liable to be misleading. The man who has fed the chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken.

Russell suggests that the chicken was unaware of the general fate of the domesticated junglefowl, and of the applications of "Bayes' Theorem" - or if you like of Bayes-Price-Laplace. You might think you're in an average day of your life. But are you in the average day of your species' life?

Induction, then, is a Platonic ideal, or a Pythagorean one; best applicable to the mathematics of the possible. For the real world, you need B-P-L.

Why it's bad to lose your Gellar field

Everything possible depends on mathematics. The concrete reality of "everything possible", we can call "the multiverse".

The multiverse is utterly mindless and chaotic. The Near Eastern imagination could explain it only through the metaphor of a stormy ocean. It is, in that famed Semitic rhyme, Tohu ve-Bohu.

Our universe on the other hand is not chaotic. It has a geometry: three spatial dimensions of no particular direction, and one further dimension which goes in one direction. By that alone, anything in our universe can instinctively grasp concepts like "cause and effect".

Our universe also follows rules of physics. Relevant to geometry: you can't blip from one spot to another spot, without taking time, that time being constrained by the speed of light. In effect the speed of light is the ratio of distance over time.

To bend these rules of our universe may or may not be possible through the means we own within this universe. But if we do that, we're leaving the universe. We're entering what may well be chaos. Pending some revelation from some multiversal alien, it near-certainly is chaos, given that chaos is uncountable and we're not. And I'd not be quick to trust that alien, either.

Set theory

During my sixth form, or the junior/senior years for Colonials, I got interested in the nature of infinities and the singularity. What if we treated "Two Divided By Zero" as an actual number, like pi. I raised this to my math teacher / tutor; he recommended I rethink my presuppositions. He recommended Georg Cantor. Not in the original German; in an English-language summary.

Georg Cantor back in 1870s had run a thought-experiment: let's list through all the positive integers in binary-notation. Nerds call these, the natural numbers. First, there's 1. And then 2 - "10". And "11", and "100" (for 3). And so on. Next, pretend you're a Semite and start reading them from top-right.

So, you got this:

0..0001
0..0010
0..0011
0..0100
0..0101

Now: consider the number when you pick digits, diagonally:

0..00001
0..00010
0..00011
0..00100
0..00101

Cantor said: suppose we flip those digits. By definition, it's not 1. It's not 2. It's not 3 ("011") - and moreover, that third digit has flipped boolean to "true", so we know it's greater than 3. As you go down row x, the function of x becomes 4, 12, 28, 60...

By this, Cantor had formally defined (Two to the Power of x, Minus One) Minus Three, with x -> Infinity. He'd defined a new theory: a theory of sets. The natural numbers map one-to-one with these rows of binary digits. And, they can never count to 2^∞-4. Not as in, it would take too long. As in: the unbounded set of the natural numbers does not contain this number.

More: any function you can think of to "hash" the integers, any deterministically-driven list of binary-digit sequences: once you've defined them and listed them, Cantor - that devil - can ruin your day by subsequently doing his diabolical diagonal.

It further turns out that if you stick a decimal in front of these binary digits, that the Continuum of real numbers [0,1] - which include pi-3 - isn't countable, either.

This forced mathematicians to take stock of which sort of numbers can be mapped to countability. They got as far as the algebraic numbers, like 5 and -12 and 3.6 and even root-2 and even even those x solutions in the complex plane for finite polynomials including famously-insoluble x⁵ - x + 1. They also found a way to count two-dimensional space: so, the imaginary / complex algebraic numbers were countable. But they (literally) couldn't square the circle: pi wasn't algebraic. Above all, take e - whose natural logarithm is equal to one. The logarithm function is the inverse of the exponential function.

Infinities and their inverted twins, the infinitesimals, are the bane of mathematics; but this inductive method of Cantor is the same method used in, for a start, calculus. Cantor's incipient set theory did run into "Russell's Paradox" but that paradox was swiftly corrected by the rigourous Zermelo–Fraenkel theory. There's also Cantor's hypothesis on whether there exists some infinity between countable numbers and the uncountable Continuum, which unfortunately Zermelo-Fraenkel's theory couldn't - and can't - address. Or so the Internets tell me. I never got this far.

I got far enough to figure out that no serious mathematician has disproven Zermelo–Fraenkel. So Cantor's discovery of uncountable infinities must stand.

Somali women as European expats

Via Eurogenes: Gravettiana. [UPDATE 5/5/22 moar]

Gravettis are the Europeans after the Neanders were done wit': from 30kBCish, through to the latest Ice Age blast. Gravettiana still inhabits the Palaeolithic; but they have moved on from "Cro-Magnon Man". The general time-frame is the domestication of the dog.

This paper is headed up by one E. Andrew Bennett. They note that the Gravettis have the N1 mitochondrion - that's the female line. This is not the N of the modern Euro "Daughters of Eve", who descend (mainly) from N's basal daughter R.

Most interesting here is that the Gravetti N1 line is on its way to N1b. N1b today is Ashkenaz (10% are N1b1b)... and Somali (N1b2).

One thought is the Viking / Islamic slave-trade in those proverbially-beautiful women of the Caucasus. But I'd not think to see them cluster in Somalia in that case; I'd expect larger populations in richer regions of the Islamic world, like Basra. Also N1b seems early, to be a base. Doesn't look late-antique.

I'm thinking more, the mass-migrations of that Ice Age. We already have (from Karen Bojs) the U clades of western Europe streaming into western North Africa. Seems to me that N1b from eastern Europe might take a different route.

The rise of a Philistine nation

After about 1200 BC, the southwestern corner of the Mediterranean coast came under New Management. It had been Canaanite, ruled by Egyptians. Suddenly the cities, foodstuffs, and placenames changed. The Egyptians were still around-about, but now they were building fortresses to hem in the changelings.

I was on a dig in Ashqelon / Ascalan some decades ago. By then the neutron-activation method had come into its own; proving that a lot of Mycenaean "III-C" ware was produced on-site. The genetics are now in, and they're showing that the locals were heavily southern-European.

The wording of the research leans away from southern coastal Anatolia: whence the late "Hittite" states of Carchemish, and whence the Lycians. Ashqelonian DNA looks more like Caphtor / Crete.

We could propose that various Sea Peoples took over the region, each with its own language. Ashqelon - it's now all but proven - got the Greeks. Other nearby cities got the Valistinians (Ilya Yakubovich, "Phoenician and Luwian in Early Iron Age Cilicia"), speaking Anatolian. Maybe there were "Sherden" cities speaking old Sardinian. Maybe even Etruscans got involved, here as at contemporary Lemnos.

Etruscans, Archaic-era Greeks, and Carians did make themselves heard around the Eastern Med; they have certainly got themselves read, in their graffiti. But from 1200 to 800 BC, if you wanted to make a living in the Eastern Med, you had to learn Canaanite.

Once the Bible gets good and started, the Med coast is culturally "Philistine", but everyone there is already speaking "Hebrew". From a 1100 BC perspective, it's more like the "Philistines" are speaking the same foreign language which leftovers from the dead Egyptian empire were having to speak: Canaanite. 1100 BC sure wasn't 300 BC and it wasn't even 700 BC. The Bible's probably right.