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 threetwo 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. MORE LIKE "TOCHARIAN F" 5/28/25: Well that's a bummer, "Tocharian C" loans seem just Bactrian.

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 Scofield - 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.