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‘Rise above yourself and grasp the world’ Archimedes – attribution

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women and warfare, part 2: humans, bonobos, coalitions and care

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bonobos, or how to be good (without gods)

Shortly before I started writing the first part of this article, I read a sad and disturbing piece in a recent New Scientist, about an Iron Age citadel in modern Iran, called Hasanlu. Its tragic fate reminded me of the smaller scale tragedies that Goodall and others recount in chimpanzee societies, in which one group can systematically slaughter another.

Hasanlu was brutally attacked and destroyed at the end of the ninth century BCE, and amazingly, the massacred people at the site remained untouched until uncovered by archeologists only a few decades ago. One archeologist, Mary Voigt, who worked the site in 1970, has described her reaction:

I come from a long line line of undertakers. Dead people are not scary to me. But when I dug that site I had screaming nightmares.

Voigt’s first discovery was of a small child ‘just lying on the pavement’, with a spear point and an empty quiver lying nearby. In her words:

The unusual thing about the site is all this action is going on and you can read it directly: somebody runs across the courtyard, kills the little kid, dumps their quiver because it’s out of ammunition. If you keep going, there are arrow points embedded in the wall.

Voigt soon found more bodies, all women, on the collapsed roof of a stable:

They were in an elite part of the city yet none of them had any jewellery. Maybe they had been stripped or maybe they were servants. Who knows? But they were certainly herded back there and systematically killed. Its very vivid. Too vivid.

Subsequent studies found that they died from cranial trauma, their skulls smashed by a blunt instrument. And research found many other atrocities at the site. Headless or handless skeletons, skeletons grasping abdomens or necks, a child’s skull with a blade sticking out of it. All providing proof of a frenzy of violence against the inhabitants. There is still much uncertainty as to the perpetrators, but for our purposes, it’s the old story; one group or clan, perhaps cruelly powerful in the past, being ‘over-killed’, in an attempt at obliteration, by a newly powerful, equally cruel group or clan.

Interestingly, while writing this on January 4 2019, I also read about another massacre, exactly ten years ago, on January 4-5 2009. The densely populated district of Zeitoun in Gaza City was attacked by Israeli forces and 48 people, mostly members of the same family, and mostly women, children and the elderly, were killed, and a number of homes were razed to the ground. This was part of the 2008-9 ‘Gaza War’, known by the Arab population as the Gaza Massacre, and by the Israelis as Operation Cast Lead. The whole conflict resulted in approximately 1200-1400 Palestinian deaths. Thirteen Israelis died, four by friendly fire. And of course I could pick out dozens of other pieces of sickening brutality going on in various benighted parts of the world today.

Attempts by one group of people to obliterate another, whether through careful planning or the frenzy of the moment, have been a part of human history, and they’re ongoing. They are traceable as far back, at least, as the ancestry we share with chimpanzees.

But we’re not chimps, or bonobos. A fascinating documentary about those apes has highlighted many similarities between them and us, some not noted before, but also some essential differences. They can hunt with spears, they can use water as a tool, they can copy humans, and collaborate with them, to solve problems. Yet they’re generally much more impulsive creatures than humans – they easily forget what they’ve learned, and they don’t pass on information or knowledge to each other in any systematic way. Some chimp or bonobo communities learn some tricks while others learn other completely different tricks – and not all members of the community learn them. Humans learn from each other instinctively and largely ‘uncomprehendingly’, as in the learning of language. They just do it, and everyone does it, barring genetic defects or other disabilities.

So it’s possible, just maybe, that we can learn from bonobos, and kick the bad habits we share with chimps, despite the long ancestry of our brutality.

Frans De Waal is probably the most high-profile and respected bonobo researcher. Here’s some of what he has to say:

The species is best characterized as female-centered and egalitarian and as one that substitutes sex for aggression. Whereas in most other species sexual behavior is a fairly distinct category, in the bonobo it is part and parcel of social relations–and not just between males and females. Bonobos engage in sex in virtually every partner combination (although such contact among close family members may be suppressed). And sexual interactions occur more often among bonobos than among other primates. Despite the frequency of sex, the bonobos rate of reproduction in the wild is about the same as that of the chimpanzee. A female gives birth to a single infant at intervals of between five and six years. So bonobos share at least one very important characteristic with our own species, namely, a partial separation between sex and reproduction.

Bonobo sex and society, Scientific American, 2006.

Now, I’m a bit reluctant to emphasise sex too much here (though I’m all for it myself), but there appears to be a direct relationship in bonobo society between sexual behaviour and many positives, including one-on-one bonding, coalitions and care and concern for more or less all members of the group. My reluctance is probably due to the fact that sexual repression is far more common in human societies worldwide than sexual permissiveness, or promiscuity – terms that are generally used pejoratively. And maybe I still have a hankering for a Freudian theory I learned about in my youth – that sexual sublimation is the basis of human creativity. You can’t paint too many masterpieces or come up with too many brilliant scientific theories when you’re constantly bonking or mutually masturbating. Having said that, we’re currently living in societies where the arts and sciences are flourishing like never before, while a large chunk of our internet time (though far from the 70% occasionally claimed) is spent watching porn. Maybe some people can walk, or rather wank, and chew over a few ideas at the same (and for some it amounts to the same thing).

So what I do want to emphasise is ‘female-centredness’ (rather than ‘matriarchy’ which is too narrow a term). I do think that a more female-centred society would be more sensual – women are more touchy-feely. I often see my female students walking arm in arm in their friendship, which rarely happens with the males, no matter their country of origin (I teach international students). Women are highly represented in the caring professions – though the fact that we no longer think of the ‘default’ nurse as female is a positive – and they tend to come together well for the best purposes, as for example the Women Wage Peace movement which brings Israeli and Palestinian women together in a more or less apolitical push to promote greater accord in their brutalised region.

October 2017 – Palestinian and Israeli women march for peace near the Dead Sea, and demand representation is any future talks

Women’s tendency to ‘get along’ and work in teams needs to be harnessed and empowered. There are, of course, obstructionist elements to be overcome – in particular some of the major religions, such as Catholic Christianity, Islam, Hinduism and Buddhism, all of which date back centuries or millennia and tend to congeal or ‘eternalise’ the patriarchal social mores and power structures of those distant times. However, there’s no doubt that Christianity, as the most western religion, is in permanent decline, and other religions will continue to feel the heat of our spectacular scientific developments – including our better understanding of other species and their evolved and unwritten moral codes.

The major religions tend to take male supremacy for granted as the natural order of things, but Melvin Konner, in his book Women after all, has summarised an impressive array of bird and mammal species which turn the tables on our assumptions about male hunters and female nurturers. Jacanas, hyenas, cassowaries, montane voles, El Abra pygmy swordtails (a species of fish) and rats, these are just a few of the creatures that clearly defy patriarchal stereotypes. In many fish and bird species, the females physically outweigh the males, and there’s no sense that, in the overwhelming majority of bird species – whose recently-discovered smarts I’ve written about and will continue to write about – one gender bosses the other.

Turning back to human societies, there are essentially three types of relations for continuing the species – monogamy, polyandry and polygyny. One might think that polyandry – where women can have a harem of males to bed with – would be the optimum arrangement for a female-centred society, but in fact all three arrangements can be turned to (or against) the advantage of females. Unsurprisingly, polygyny (polyandry’s opposite) is more commonly practiced in human society, both historically and at present, but in such societies, women often have a ‘career open to talents’, where they and their offspring may have high status due to their manipulative (in the best sense of the word) smarts. In any case, what I envisage for the future is a fluidity of relations, in which children are cared for by males and females regardless of parentage. This brings me back to bonobos, who develop female coalitions to keep the larger males in line. Males are uncertain of who their offspring is in a polyamorous community, but unlike in a chimp community, they can’t get away with infanticide, because the females are in control in a variety of ways. In fact, evolution has worked its magic in bonobo society in such a way that the males are more concerned to nurture offspring than to attack them. And it’s notable that, in modern human societies, this has also become the trend. The ‘feminine’ side of males is increasingly extolled, and the deference shown to females is increasing, despite the occasional throwback like Trump-Putin. It will take a long time, even in ‘advanced’ western societies, but I think the trend is clear. We will, or should, become more like bonobos, because we need to. We don’t need to use sex necessarily, because we have something that bonobos lack – language. And women are very good at language, at least so has been my experience. Talk is a valuable tool against aggression and dysfunction; think of the talking cure, peace talks, being talked down from somewhere or talked out of something. Talk is often beyond cheap, it can be priceless in its benefits. We need to empower the voices of women more and more.

This not a ‘fatalism lite’ argument; there’s nothing natural or evolutionarily binding about this trend. We have to make it happen. This includes, perhaps first off, fighting against the argument that patriarchy is in some sense a better, or more natural system. That involves examining the evidence. Konner has done a great job of attempting to summarise evidence from human societies around the world and throughout history – in a sense carrying on from Aristotle thousands of years ago when he tried to gather together the constitutions of the Greek city-states, to see which might be most effective, and so to better shape the Athenian constitution. A small-scale, synchronic plan by our standards, but by the standards of the time a breath-taking step forward in the attempt not just to understand his world, but to improve it.


Melvin Konner, Women after all, 2015

New Scientist, ‘The horror of Hasanlu’ September 15 2018

Max Blumenthal, Goliath, 2013–09)

Written by stewart henderson

January 11, 2019 at 11:25 am

Archimedes, the Mathematikos and the birth of science

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Rise above yourself and grasp the world.

Archimedes (attributed: inscribed on the Fields Medal)

One of Archimedes’ most spectacular inventions, the gravity-defying spiral-in-a-cylinder, or screw – still effective

Canto: So we spent some time at the Waikato museum in Hamilton, braving the school holiday crowd to view an exhibition celebrating the work of Archimedes (c 287-212 BCE) and his fellow mathematikos, and noting how it inspired the likes of Leonardo some 1800 years later. So let’s talk about their breakthroughs and about why there was such a gap between their clever contrivances and the maths on which they were based, and the scientific revolutionaries of the sixteenth and seventeenth centuries.

Jacinta: These are intriguing and vital questions. Many modern scientists have been dismissive of the science of the ancient Greeks because they think of Aristotle as representative. I think it was Lawrence Krauss I heard complaining of Aristotle’s belief that women had less teeth than men – apparently he never thought to count them! But the fact is that, though Aristotle is sometimes known as the father of empiricism, he probably doesn’t deserve that title except in respect of ethics, and politics, which he based on what actually works for societies and city-states, which is why he collected and analysed their constitutions. The mathematikos, on the other hand, eschewed ethical issues in favour of mathematics – geometry in particular (think Euclid). And, especially in the work of Archimedes, they enjoyed phenomenal success in many practical areas.

Canto: Especially warfare apparently. It seems Archimedes in particular was called on more than once to defend his city, Syracuse, with war machines. In the blurb to the exhibition, they mention ‘torsion ballistae’. Can you please explain?

Jacinta: Well, I’ll tell you about the torsion siege engine. It replaced the earlier tension siege engine, possibly invented in Syracuse in the time of Dionysius the Elder (c 432-367 BCE) – so the engineering of weapons of war was already a big thing at the time. It was basically a massive catapult. The first torsion device of this kind is generally dated to the time of Philip II of Macedon, Alexander’s dad, circa 340 BCE. The first extant evidence of its use comes from a list of items in the arsenal of the Acropolis in Athens dating to 338-326 BCE. So what is torsion? It’s the energy created by winding something up, like a spring. In earlier times, human hair, horsehair and animal sinews were used for this purpose.

Canto: So plats give you energy?

Jacinta: Torsion basically means twisting. The Greeks apparently used specially cured sinew combined with human or animal hair to create a ‘torsion bundle’ – we don’t know what the exact recipe was – which was fixed to a wooden frame and could be twisted and released regularly via levers without breaking. But the key development was the mathematics of these devices. This military website describes:

The critical dimension was the diameter of the sinew “spring” or torsion bundle. For a bolt shooter, the ideal diameter was one-ninth the length of the bolt. For a rock thrower the ratio was more complex; the diameter (d) of the bundle in dactyls (about 3/4 inch) should equal 1.1 times the cube root of 100 times the mass of the ball (m) in minas (about a pound). Saddled with a numerical notation system even more awkward than Roman numerals, the Greeks developed sophisticated geometric methods to compute cube roots.

Canto: So how were these maths – these geometric methods – derived. Euclid was the great geometer of the time, wasn’t he?

Jacinta: Actually, though the exact time-frame of Euclid’s life isn’t known, his Elements came out after this invention, but before the work of Archimedes. Clearly it must’ve been drawn from earlier mathematikos, such as Eudoxus, who worked out, via an early version of integral calculus, that areas of circles relate to squares of their radii, and volumes of spheres relate to the cubes of their radii, and various other relations between volumes and dimensions of pyramids, cylinders, cones etc, which obviously had practical applications as described above.

Canto: Okay, so tell us about Archimedes’ particular contributions, and about why the great work of the mathematikos was apparently discontinued after Archimedes. Considering that the Roman Empire didn’t become christianised until some 500 years after Archimedes’ death, we can’t really blame the Christians – can we?

Jacinta: Well, I mentioned that early version of integral calculus. It was called the method of exhaustion, a kind of geometric calculus which Archimedes took further than anyone before him, both in theoretical terms and via practical applications. Now I’m far from being a mathematician, but I’ve come to appreciate the essentiality of maths in understanding our universe – so much so that I perhaps regret my lack of mathematical expertise more than I regret anything else in my old life. This is by way of saying that I won’t try to explain Archimedes’ maths – but an understanding of maths is essential to understanding the magnitude of his achievement.

Canto: Okay, so what about his inventions?

Jacinta: Well the key is the application of complex and what might have seemed pointlessly abstract maths about the relations of ‘perfect’ shapes such as spheres, cones and cylinders to real world problems and their solutions. The lever is a good example. Archimedes didn’t invent levers but he was clearly fascinated by them. And it shouldn’t take long to realise that they have immense practical applications. Doors are levers, as are nail clippers, nutcrackers and see-saws. Archimedes wrote what we now call a treatise, On the equilibrium of planes, to explain the maths behind them. But the best illustration of Archimedes’ combination of theory and practice is probably what is known as Archimedes’ principle, which essentially launched the field of fluid dynamics, or fluid mechanics:

the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid.

It comes from another treatise of his, On floating bodies. Now let me see if I can explain this. Take an object, any object. The downward force exerted on it is its weight. Immerse it in water. It will float or it will sink, and even if it floats it’ll be partially submersed. The principle doesn’t apply to objects that sink, which will have a density of anything over and above a certain level which permits it to float – I think.

Canto: But that principle, though it comes from a treatise about floating bodies, doesn’t distinguish between floating and sinking. It says ‘fully or partially submerged’…

Jacinta: But an object can be fully submerged and still float. To sink means to continue in a downward direction.

Canto: I’ve found that an object that floats – I’m thinking of water as the fluid, and perhaps I shouldn’t – always seems to have a certain proportion above the water level. Think of icebergs, and human bodies. But I think I get it – the force that keeps you up and floating will be equal to the weight of the water your body displaces… So if I was ten kilos heavier, I would still float but the upward force acting on me would be greater, but not by ten kilos, rather by the larger volume of water my larger body displaces measured in kilos, or by some measure of force…

Jacinta: I don’t think that’s wrong, but I’m not sure if it’s right. The problem for me is that the principle as stated doesn’t specify a floating body, only a body immersed – partially or fully in a fluid. Think of a stone dropped in water. It sinks. To the bottom.

Canto: And if the fluid is bottomless will it just keep on sinking? It’s as if there’s no upward force acting on it at all, or very little. I’m imagining a bottomless column of still water here, not an ocean with its currents…

Jacinta: Ha, I was thinking of a bathtub, but with a bottomless well, it will depend on the density of the stone. I think at some point it’ll slow down and be suspended. I’m sure water pressure will play a role, and density – of the water. And density is somehow related to pressure, and I’m getting lost…

Canto: We may need to do a Khan academy course. But getting back to Archimedes and the mathematikos, why was so little of their work built upon, until Galileo and others became inspired so many many centuries later?

Jacinta: That’s possibly too long a story to go into here, not that I’m much equipped to tell it. It no doubt relates to the gradual decline of the increasingly dispersed Greek culture of the Hellenistic and post-Hellenistic era. I wouldn’t want to say Christianity was a major cause but it certainly didn’t help. By the time the Roman Empire became Christianised, the culture that created figures like Archimedes had long passed. Roman culture was a lot more militaristic and less speculative. Blue sky research wasn’t in vogue. Of course, why all this happened I wouldn’t venture to say without many years of research into the cultural changes then occurring. But the slowness of the scientific recovery, that I would attribute to Christianity, and later to the conservative turn in Islam that still prevents original science from being practiced in those countries where it holds sway.

Written by stewart henderson

May 2, 2018 at 9:13 pm