A mathematical approach to the demise of the Neanderthals.

Pure mathematics is, in its way, the poetry of logical ideas. Albert Einstein.

I have never been proficient at mathematics. But that doesn’t mean that I am not fascinated by the field of maths.

Hold that in your thoughts as I mention the name of blogger: Patrice Ayme.  It’s a non-de-plume but so what!  What blows me away, to use the vernacular, is the depth of thought expressed through the keyboard of Mr. Ayme (even the gender is an assumption).  The sub-heading on the home page of his blog is “Intelligence at the core of humanism“.  Just run your eye down the list of Recent Posts to the right-hand side of the home page to get a feel for the topics covered in the last few months.  Impressive is an understatement!

Anyway, five days ago Patrice published a post proposing how the Neanderthals were outbred, under the title of Math Extinguished Neanderthals.  It fascinated me and Patrice was gracious in allowing me permission to republish it on Learning from Dogs.


Math Extinguished Neanderthals


Zillions of theories about the “disappearance” of Neanderthals. The latest one, from Oxford University, claims that Neanderthals’ big, beautiful eyes, and their big muscles caused their demise. They were too busy looking at things, and flexing their muscles. The idea is that significantly larger eyes would have crowded the Neanderthal brain out, making them relatively stupid. In particular it made them incapable of having social groups as large as those of Homo Sapiens Sapiens.

Big Eyes Do Not Kill

Big Eyes Do Not Kill

Sapiens girl on the left, Neanderthal girl on the right (reconstitution published in Science Magazine a few years ago).

I have long argued that the strength of democracy came from having many brains working in parallel. There is little doubt that larger social groups bring a higher cultural intelligence, hence higher individual intelligence. So I agree about that bit of logic. Yet, ironically, to reach the conclusion that Neanderthals’ social group were less numerous, the simple fact that Neanderthals were bigger, is enough. There is no need for hazardous demeaning allegations about Neanderthals’ brains.

That big eyes made Neanderthals stupid contradicts some facts that were thought to be established:

1) Sapiens Neanderthalis’ brains were significantly larger to start with. See Wikipedia.

2) Many very clever Homo Sapiens Sapiens have small brains. Famously Anatole France, an intellectual, had only a 1,000 cubic centimeters brain. Homo Floresiensis, the “hobbit” species living on the island of Flores, Indonesia, until it was wiped out recently, was extremely intellectually capable, although it had really small (and completely different) brains.

3) In the Middle East, Neanderthals and Sapiens went back and forth through the same large caves over 50,000 years. So whatever happened, it was not in evidence for 50,000 years.

So, of course, I have my own theory. That’s what philosophy is all about: trying to guess what really matters most, and how that most significant data logically articulate. Then scientists, politicians and writers can swoop, figure out the details, and attribute themselves the glory.

What could have happened by around 28,000 years ago that caused the demise of Neanderthals? At the time, the last fierce glaciation was gaining ground. (It reached its maximum 25,000 years ago.) Some have argued, absurdly, that the Neanderthals could not take it. That’s beyond silly, as Neanderthals had evolved, from half a million years ago, precisely to handle extreme cold.

Neanderthals were stocky, powerful, and they had thrived through hundreds thousands years of glaciation, mostly on a meat diet, hunting big game. But they also knew how to cook plants, and eat them.

50,000 years ago, Neanderthals exterminated Cave Bears, a huge animal who lived in caves, prime real estate Neanderthals craved for. Could the disappearance of Cave Bears be logically linked to the disappearance of Neanderthals? Yes. That’s a consequence of my theory. More advanced technology played a direct role.

How did Neanderthals kill Cave Bears? With technology. We do not know exactly what weapons Neanderthals had at their disposal. However, technology had improved, and kept improving. Recently it was found that Sapiens Sapiens (Homo SS; I hope one gets the joke) in Africa had invented bows and arrows 80,000 Before Present (BP).  (About 60,000 years earlier than previously thought!) Before bows and arrows, the propeller had been invented, and was used in Europe. The propeller took advantage of angular momentum to send a sort of mini lance further and stronger than by hand.

Why did the Neanderthals and Denisovans (another human species from Central Eurasia) lose their edge? Advancing technology is the obvious answer. When technology of clothing and weapons was sufficiently advanced, the physiological advantage that the Neanderthals genetically had, disappeared. Homo Sapiens Sapiens could thrive just as well through winter.

At that point, Homo Sapiens Sapiens from Africa could be as successful as the Neanderthals through the freezing wastelands of Europe. OK.

But the Homo SS outbred the Neanderthals, so they became genetically more successful. How do I explain that?

Simple. However, the explanation involves the exponential function, the same function found all over, and that the mathematician Rudin called “the most important function in mathematics”. The exponential also explains the plutocratic phenomenon, and that is why it’s so dangerous. The exponential always rules extinction events, that’s why one day a species is all over, like the American Pigeon, or the Tasmanian Tiger, and the next day, it’s gone.

So visualize this. Neanderthals were bigger than Homo SS, just like the Polar Bear is bigger than the Black Bear. Bigness is an adaptation to cold. Southern Europe’s Brown Bears are smaller than those found in Kamchatka, or Alaska (also known as Grizzlies: the Grizzly is an emigrated European Brown Bear!) Bigger makes warmer inside. That’s why the most massive animal that ever was, the Blue Rorqual, at up to 180 tons, is nearly twice the mass of the largest dinosaur (it’s not just that it’s floating, but also that water is cooler than Jurassic air, I hold).

To simplify, let’s use a bit of exaggeration (that’s reasoning by exaggeration, one of my preferred tactic of thought; the one humor exploits, and why joking helps thinking). Let’s assume Neanderthals were twice more massive than Homo SS.

Now let’s consider an habitat where Homo SS and Neanderthal bands roamed. They will tend not to mix, for obvious racist reasons. The racial hatred between Neanderthals and Homo SS has got to have been colossal. People who look too different are not even sexually attracted to each other (and where Neanderthals and Homo SS were in contact in the Middle East, for 50,000 years, there is no evolution of an interbred species, an indirect proof that there was no love lost there!)

The density of human mass is going to be roughly the same all over, because that density depends only upon the resources available (mostly meat on the hoof, and fur in burrows in glaciating conditions).

Thus, there would have been apartheid. But the Homo SS would have been twice more numerous, where they reigned (from my assumption of twice the mass). So now graft on this a catastrophe; a drought, a flood, a very tough winter, a volcanic super disaster, whatever. The climate was highly variable, starting about 40,000 years ago, just when Homo SS appeared. Some have stupidly argued that Neanderthals were too stupid to adapt to this changing circumstances. Like this paralyzing stupidity struck them just when Homo SS were around. My explanation is more subtle.

After a catastrophe in said habitat, say one of these numerous habitat in Europe isolated by glacial mountain ranges, or seas and lakes, most of the human population would be wiped out, Homo SS, just as Neanderthals. There would tend to be always a small remaining population, because the greatest limit on man is man himself: as a population gets wiped out, resources rebound, and life of the survivors tend to get much easier (that’s what happened in Europe after the Black Death of 1348 CE; if nothing else, survivors could ask for higher salaries from their plutocratic masters, and they did).

So say 90% of the population of the habitat was wiped out. As suddenly resources are now not limited, the human population will rebound exponentially. The equation is: N(t) = N(0) exp(Rt). “R” is the “Malthusian” parameter, the rate of growth. Now it’s going to require twice the resources to feed a Neanderthal to sexual maturation (under our outrageously simplifying assumption that Neanderthals are twice the mass). Thus one may assume that R(Homo SS)/R(Neanderthal) is 2. The end result is that the quotient:

Number Homo SS/ Number Neanderthal = A exp(2t). (Where A is the ratio of the populations H SS/Neanderthal after the catastrophe.)

Thus the population of H SS would exponentially grow relative to that of the Neanderthals, resulting in a quick extinction. And in no way this is happening because Homo SS were superior. Just because they were more gracile.

Hence the mystery of the evolution of contemporary man is smoothly explained. Just a bit of math. QED.

Europeans & Asians: Not Just African

Europeans & Asians: Not Just African


Patrice Ayme


Note 1: what of the mentally deliquescent and racist article in the Proceedings of the Royal Society? First, they sank so low as tousing orbit size as a proxy, that Neanderthals had larger visual systems than contemporary AMH [Anatomically Modern Humans]. That’s about as intelligent as saying that, because special forces use night vision goggles, they have got to have bigger visual systems.

The main woman author also found the same physiological feature, bigger eyes, in the past, about people presently living at high latitude. She contentedly asserted that, because light levels are lower in the north, people living in the north (40,000 years at least for Homo SS) have bigger eyes. Amusingly, she did not draw, in that case the conclusion that Norwegians and the English are therefore more stupid. Somehow, though, in her lack of smarts, she applies that controversial reasoning to Neanderthals. Does she have giant eyes?

Seriously the Oxford study rests on a central fact that contradicts one of established facts about Neanderthals. Indeed it claims Neanderthals’ brains were not any larger than Homo SS.


Note 2; what catastrophes am I talking about? Well the climate fluctuated wildly, to start with. Second, A Campanian ignimbritevolcanic super-eruption around 40,000 years ago, followed by a second one a few thousand years later, certainly crashed Neanderthal populations (based on logic, and evidence fromMezmaiskaya cave in the Caucasus. Mitochondrial DNA analysis of a specimen there is C14 dated 29,000 years BP, one of the latest living pure Neanderthals). After such a catastrophe, the exponential rebounds of populations would have advantaged Homo SS, as explained above.


Note 3: OK, I exaggerated with the mass ratio. (Mathematicians often do this, considering an exaggerated case to understand the mean, through the tails.) But the real mass ratio would be aggravated because, Neanderthal was built in such a way, relative to gracile Homo SS, that they consumed more calories per day (some paleontologists have come up with 300). So there is no doubt that the effect above will play a role, even if the mass ratios were not as bad. Notice the mechanism above would tend to extinguish the Neanderthal traits that were most characteristic of the subspecies.


Note 4: A preferred trick of Neanderthals’ haters is to exhibitArchaic Neanderthals‘skulls, and compare them to those of modern men. The skull of an Archaic Neanderthal of 400,000 years ago should not be compared to a modern human, less than 40,000 year old! All the more since Neanderthals’ brain size augmented faster than the brain size of Homo Sapiens Sapiens.


Note 5: Part of the mechanism above generalizes for other species in competition. It provides with a disappearance mechanism after ecological turbulence, according to species’ ecological footprint.


So hope that others shared my pleasure at reading the essay.

Going to close with another quotation from Mr. Albert Einstein: “As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.”

22 thoughts on “A mathematical approach to the demise of the Neanderthals.

  1. Neanderthals were never stupid, they are known to have used music and done cave painting.

    Cave bears were around long after the Neanderthals vanished, as proven by their claw marks over cave paintings made by homo sapiens at Chauvet.

    Neanderthals were the product of their times, they fell to the same climate change as did the mammoth, dire wolves and sabre-toothed cats.


    1. Alex: It’s not clear to me how old Chauvet is (most frequent quoted age is 32 K BP). I did not know there were claw marks over the paintings there. What I do know is that in official science at this point the Cave Bear disappeared by 27,500 years ago, and pure Neanderthals were still found by 29,000 BP.

      Pure Neanderthals’ disappearance preceded that of the last mammoth by more than 20,000 years. There were mammoths on Wrangel island until historical times, definitively proving that mammoths did not disappear because it got cold. To claim species adapted to cold for more than half a million years disappeared because it got cold does not look cool to me.


      1. With regards to climate change in the Ice Age the food was abundant so size and power was the attribute of many of the animals. Size means there is a need for more energy to sustain life. When climate changed the food sources slowly got less, the herbivores such as the mammoth was impacted, that rolled into the impacts on all the carnivores, including the Neanderthals. The mammoths of Wrangle island survived so long because they evolved into a smaller size, thus less energy was needed to survive. The new era required speed and a smaller size, the large size and slowness of the Neanderthal doomed them. Climate change can be a slow process which means extinctions follow in a slow process over tens of thousands of years.


    2. Hi Alex. Did you see any of the Andrew Marr’s History of the [Human] World programmes on the BBC last Autumn? In the first epsiode (i.e. covering 70k to 7k years BP) Andrew Marr clearly implied that he accepts the consensus view that Homo Sapiens triumphed over Neanderthals in the same way that the American grey squirrel is out-competing the British red squirrel. However, PA’s post adds a layer of complexity that is not obvious from such simplistic analogies as the grey-versus-red-squirrel.


      1. Thanks Martin!
        I find the sentence of Alex: “in the Ice Age the food was abundant so size and power was the attribute of many of the animals” rather curious. There was more than one ice age, first of all, and tundra is no cornucopia…


  2. There is some controversy whether the neandethal actually did out at all. I believe one year ago or somoething like that, there was a scientific research which showed that most non-africans have a few percent of neanderthal DNA in their genome. This suggests that the neanderthals did not die out, but assimilated with modern humans almost completely through interbreeding (some scientists believe that blue eyes and blond hair in northern europeans is actually inherited from neanderthals). This phenomen is known as pseudo-extinction.


    1. I am unaware of any research suggesting Neanderthals have a connection to Africa. The Berbers who moved across to North Africa are likely to have Neanderthal genes along with their light skin, blue eyes and fair hair.

      The Neanderthal ranged from Britain to Israel to India. The last stronghold of the Neanderthal was Spain. The Basque have 1% Cro-Magnon DNA, which is a species of human resulting from a mix of Neanderthal and Home Sapien DNA.


      1. To my knowledge, the Cro Magnon, the species living in France during and after the last huge glaciation are view as pure Homo Sapiens Sapiens. The percentage of Neanderthal DNA is hotly debated. some recent research (2012) claimed to have found plenty of Neanderthal genes in North Africa.

        Besides the genes, as I mentioned in comments on my site, typical Neanderthal tools, Mousterian axes, for example, were found in North Africa. It’s not clear to me that Chauvet is not mousterian (that is, Neanderthal).


      1. Here I am! (Finally! ;-)!) Thanks for publishing this on LfD. The extinction mechanism I propose can be applied to many other species (for example, it could have helped in the Cave Bear’s demise, as human pressure would have advantaged European Brown bears, exponentially).


    2. The mechanism I propose would have favored the exponential disappearance of heavy (the grossest) Neanderthal traits.Thus, an hybrid population would have returned progressively to the appearance of Homo Sapiens Sapiens (even if significant Neanderthal genes lay just below apearances).

      The first discovery of 1% to 4% Nenaderthal DNA is from Pääbo of the MAX PLANCK in 2009.


      1. Hi Patrice, I am sorry I missed this on your blog but, hope you will forgive me if I respond here instead… As it happens, another anonymous blogger called “Duncan” posted a comment on my blog yesterday, to which I have completely coincidentally just responded as follows:

        You are quite right to allude to Jevons’ Paradox, as indeed I have done in the past: Increased efficiency in the manufacturing process of any product will always be exceeded by a consequential increase in demand for the product; leading to accelerating rates of resource consumption. Thus, all Jevons did was translate into an industrial context the assertion of one Rev. Thomas Malthus regarding population – that the ability of humans to produce food would be exceeded by the number of people needing to be fed. In both cases, technological optimists continue to insist that both men were merely pessimists or lacking in imagination. I think we shall soon find out who is wrong.

        With the benefit of the Historians’ Fallacy (also known as hindsight), the insight of your post – that a larger body needs more food resulting in a lower ecological carrying capacity for that species – seems obvious. However, it is no more obvious than many of the other facts of our current predicament that so many refuse to admit… Sadly, civil disorder now seems inevitable because:
        — We now inhabit a World where economic growth is near impossible due to a global debt crisis; and
        — Anthropogenic climate disruption (a.k.a. ‘global weirding’) is now leading to higher food prices.

        Perhaps the crisis in Cyprus will be a wake-up call to the EU. I hope so because I do not want to imagine what would happen if the banks refused to open in Greece, Spain, Italy, Portugal, or Ireland…


  3. Thanks Martin. What I am also saying is that:

    1) it is hard to transform a near extinction event into total eradication (see the Black Plague of 1348 CE). Indeed, the more the extinction, the easier it gets for the survivors, as resources rebound (this is similar to the famous lynx-rabbit oscillation).

    2) However, larger animals (Neanderthals, dinosaurs), or animals with a higher metabolic load (Neanderthals) are going to be to be left behind exponentially, during the rebound phase.

    In the case of Neanderthals the periodic catastrophes could have been of climatic origins (waves of cooling, warming and unstable climate as the earth underwent various tipping points, one way or another, into the occasionally severely glaciated period between 60 K and 11 K BP. A severe volcanic catastrophe or two would have added near extinctions episodes.

    In the case of dinosaurs, the massive Deccan eruptions, over millions of years, culminated with the most acute episode, more or less contemporaneously with a massive asteroid impact (!). According to the exponential extinction theory, the back and forth of near extinctions would have put a severe extinction pressure on the dinosaurs and the like, as smaller, more efficiently active mammals and birds would have put huge pressure on dinosaurs and flying reptiles (same in the sea). By eating their eggs to start with, as mammal and bird population would have exploded very fast back up at any relief.

    See: http://patriceayme.wordpress.com/2009/11/21/trapped-by-super-traps/

    Speaking, indeed, of extinction events, I will adress Cyprus next. A hint: European taxpayers ought not to finance Russian mobsters.


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