Middle Woodland: the Hopewell culture

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When I associated bows and arrows to the origin of autism and color blindness, I did not know much about native Northamerican culture, except some fragmented knowledge I acquired while looking at Nostratic language theory some 15 years ago. Then I started to google about the history of bows and arrows in North America, and it actually fits the autism/square-root-law narrative quite well. The advantage of looking at North American civilization is that USA is far more advanced in the study of archaeology, and also, by the time the European arrived at the New World, we already have advanced written records. So, while hunter-gatherer society might be harder to study in the Old World because writing and scientific discipline came much later, in the New World we have a frozen time capsule, and the hunter-gatherer history is much more recent: the research material is much more fresh.

From what I have been able to read, bows and arrows was transformational in the late Middle Woodland period, characterized by the Hopewell culture with their burial mounds. The Hopewell culture did not invent the bow: it was introduced to them from the Athabaskan culture (which in turn might have learned about bows and arrows from later contacts with Asia). Hopewell culture was more or less harmonious, and long-distance trade was common. All that ended when bows and arrows came to the scene. So, it was a perfect case study for the transition from hunter-gatherer society into agricultural society. Also, metallurgy never made its way into American Northeast. So, we have a very clean case of the emergence of large-scale agriculture.

https://en.wikipedia.org/wiki/Woodland_period#Middle_Woodland_period_(200_BCE%E2%80%93500_CE)

(Plenty more materials if you google for "Hopewell culture")

In Hopewell culture, they already used pottery/ceramics. They did not invent bows and arrows: those weapons arrived later. The societal size arguably might have been larger to the comparable case of the Old World. The question would then be: would that have any impact on the rate of color blindness and autism?

If the square-root law holds, we would predict that the prevalence rates of color blindness and autism must both be lower in the Hispanic population, as compared to people of European and Asian descend.

Low prevalence rate of autism in Hispanic population in the USA has long been known. But then, here is also a more-or-less recent study in Mexico. It puts the number at 1 in 115: much lower than the 1 in 68 figure quoted for the general autism prevalence rate in the USA.

https://www.autismspeaks.org/science/science-news/first-estimate-autism-prevalence-mexico-pegs-number-1-115

Similarly, for color blindness, the prevalence rate of the Hispanic population in the USA is 2.6% in boys, much lower than the ~4% typically quoted for the general male population.

https://iristech.co/statistics/

See? The prevalence rates of color blindness and autism in Hispanic population lends support to the validity of the square-root law. It's a bit like the case of Down Syndrome. When I first linked Down Syndrome to the Iron Age and emergence of empires, I had no idea about archaeological finding. You'd think Down Syndrome, at the prevalence rate of 1 in 600, should have a lot of skeletons/skulls found already. But no. The earliest skeleton stands only at 1,500 years ago, in Medieval France.

So, linking bows and arrows to the emergence of color blindness and autism is not just some random comment. It provides direction on specific things to look into in anthropology/archaeology. And that's the power of having a theory and a model: it allows you to look into things that no one has ever thought about before.

https://www.researchgate.net/publication/18627757_Visual_Acuity_and_Color_Blindness_Among_Brazilian_Cayapo_Indians
https://webcache.googleusercontent.com/search?q=cache:Q4HpxDi1rZcJ:https://www.researchgate.net/profile/Francisco_Salzano/publication/18627757_Visual_Acuity_and_Color_Blindness_Among_Brazilian_Cayapo_Indians/links/58a1c93aa6fdccf5e97102c3/Visual-Acuity-and-Color-Blindness-Among-Brazilian-Cayapo-Indians.pdf

Published 46 years ago (in 1972).

...Recently severa! papers have stressed the importance of the study of color vision and visual acuity in an evolutionary context [2, 8, 10, 14, 15]. It was pointed out, for instance, that the much lower frequency of defective color vision in primitive as compared to civilized peoples could be explained at least in part by a relaxation of selection against individuais with this condition in agricultura! as contrasted with hunting-and-gathering societies. NEEL and PosT [10] suggested in addition the possibility of a transitory 'positive' selection for color blindness during the transitional period when hunting and gathering was being replaced by agriculture and pastoralism. Color-blind individuais would have been among the first to turn to other pursuits besides hunting and since these would be less hazardous a positive selection could have resulted. They further pointed out that color blindness provides the only clear example of a simple inherited defect whose frequency seems to have significantly increased with the advent of civilization; therefore, a considerable effort should be directed toward the testing of the correctness of these and other hypotheses .

So, considering the articles referenced therein, about 50 years researchers already were looking into the hunter-gatherer-to-agricultural shift as the precise period when color blindness entered human race. (Their explanation of "relaxation of selection" differs from the newer explanation of combat advantage of seeing through camouflage.)

A more recent review (year 2016) re-affirms these findings. (Check references 51-55 therein, too.)

http://revista.fmrp.usp.br/2016/vol49n3/REV2-Ocular-Health-of-Brazilian-Indigenous-Populations.pdf

Color vision has been studied in some investigations [51-55] in addition to those already cited. The Ishihara pseudoisochromatic table was used in most studies, [53,54,55] with the results indicating a very low frequency of color vision deficiency among Indian males and no case among Indian females. When the Terena ethnic group was evaluated using the Hardy, Rand and Rittler (HRR) pseudoisochromatic test in Mato Grosso do Sul, no case was detected among males. [51] Females were not evaluated in that study.

All these researchers had no idea about the square-root law. On my side and independently, I simply applied the math of the square-root law, and arrived exactly at the same conclusion.

Combined results of Brazilian Indians with the result mentioned previously about the low prevalence rate of color blindness in Hispanic population in the USA, plus the key role of bows and arrows in the transition of Hopewell culture from hunter-gatherer society to fully agricultural society, the evidence is compelling that indeed in the Old World, the bow was responsible for the introduction of color blindness genes into the human race, via the "(un)natural selection by wars." Yeap, ever after the introduction of the bow and the arrival of agriculture, the only natural predators of humans are... other humans! Wars dictated the genetic shift in human race ever since. (Plus some new diseases.)
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Could you say in ten words what your idea is? You lost me.

Lost me, too. What exactly is the square root law? I did not see that explained.

To be fair though, it's Friday, I'm exhausted from taking postsurgical care of a family member after outpatient surgery, and I'm only on my 3rd cup of (weak) coffee.

https://en.wikipedia.org/wiki/Penrose_square_root_law ? It's about voting force, isn't it? How did you connect it to autism and color blindness?
Color blindness prevalence vary depending on ethnicity.
No really good data about autism because diagnostic criteria are still under developement, no simple, objective tests have been invented yet. Differences may be due to underdiagnosing and underreporting as well as real prevalence variation. Too little data to formulate solid conclusions.

Not that one. The square-root law I am talking about is this one.

On square-root law and Central Limit Theorem:
https://www.britannica.com/science/probability-theory/The-central-limit-theorem
... The equation also illustrates clearly the square root law: the accuracy of X̄n as an estimator of μ is inversely proportional to the square root of the sample size n.

Basically, given a sample of size N, the natural fluctuation (standard deviation) is of size sqrt(N). It's often used to discriminate between whether subgroups should be considered as normal fluctuations, or outliers/anomalies.

The folk-style example of the square-root law is the famous "Birthday Problem." At what size of a group of students, is the probability of finding two people with the same birthday greater than 0.5? This is taught in high schools and colleges all over the world, when students learn about probability and statistics.

A lot of people would guess it's around 180 people, because that's half of 365 days. But that is wrong. The correct answer is actually 23 students, which is closer to 19.1, the square root of 365.

Last edited by eikonabridge on 27 Apr 2018, 11:36 am, edited 2 times in total.

I've been talking about all this for over a year. Frankly, to understand what I am saying, you really need to track all the links and references that I have provided. See my reply above. I have provided reference in the predecessor of this thread. This is not a new thread. This is a follow-up discussion.

Bows and arrows caused color blindness and autism.

That's 8 words. Anybody that reads those 8 words would think that's nuts. That is until you comb through all the previous studies on related subjects. Then you realize so many researchers have looked into similar subjects.

From Hopewell culture we see clear evidence that bows and arrows caused hunter-gatherers to become farmers (agriculture). That is undisputed.

From color blindness study across different races (including native Australians, natives of Americas, Africans, etc.) one sees clearly that hunter-gatherer societies had low prevalence rate of color blindness. So the color blindness entered human race when agriculture came. That is not new: it was known already 50 years ago. You need to explain that. I have an explanation.

Similarly I have an explanation when autism first entered human race (based on mathematics alone). And from there combined with the case of color blindness, I traced it to bows and arrows as the ultimate cause why color blindness genes and autism genes entered human race. (Autism entered first in the form of BAP.) I didn't just stop at color blindness and autism. My article last year also explains schizophrenia and Down syndrome.

- - -

If you want the implication of all this, here it is. AUTISM IS NOT A DISORDER. Autism is intended by Mother Nature. Same with color blindness. Both color blindness and autism have been with us for over 10,000 years. They serve a purpose. Autism and color blindness are part of what's normal. They are not anomalies.

So people should stop seeking TREATMENT for autism. There is nothing to treat. What autistic children need is DEVELOPMENT, not TREATMENT. They are perfectly fine the way they are. There is zero problem with them. The problem is on the other side. Our society is sick and in need of treatment. We've been treating the wrong patients.

That is the message.

Reminds me of something I learned in college. "The angle of the dangle is inversely proportional to the heat of the meat."

^ sorry - my chuckle for the day.

OK, a mechanism for selection in favor of colorblindness was suggested (camouflage, turning to activities that were less hazardous). Do you propose a mechanism why autism would be advantageous?

I have to add, it seems to me that severe, Kanner style autism may still be a disorder. Like, sickle-cell anemia confers some advantage against malaria, hence it persists, but it is still definitely a disorder.

https://consumer.healthday.com/eye-care ... 86437.html
Are you implying that Asians have been hunter-gatherer societes for significantly longer than Europeans?

Statistics varies depending on study.

https://www.ncbi.nlm.nih.gov/pubmed/22472762
Large random population surveys show that the prevalence of deficiency in European Caucasians is about 8% in men and about 0.4% in women and between 4% and 6.5% in men of Chinese and Japanese ethnicity.Mar 1, 2012

8% and 6.5% are really not that different, when you compare to results from, say, Brazilian native Indians. In the paper above on Cayapo Indians, the result was 1 in 120 males, or 0.8%. That gives you perspective of scale.

As far as clan size, it does vary. Modern clan size basically is the population size of a country. And from https://en.wikipedia.org/wiki/List_of_countries_by_population_(United_Nations) we see that Finland's population size 5.5 million people sits at the median value, but the log-standard-deviation is roughly one decade up or down. (A more correct log-average procedure for all countries actually returns 2.8 million people). So, clan sizes do vary, from place to place.

That being said, the case of Hopewell culture offers also a possible scenario. Namely, that in Asia a supplementary agriculture might have happened alongside the hunter-gatherer lifestyle, like the case of the Hopewell culture. Remember Hopewell culture already had pottery. They had long-distance trade networks. Generally speaking, there was no war, no violence in the Hopewell culture, before the arrival of the bow. All this meant they had relatively larger clan size. If arrow was invented, say in the Fertile Crescent and then later imported to East Asia, that may explain the smaller prevalence rate of color blindness there. So, it's not that there was a big change in timeline, it's just the environmental factors (and therefore lifestyles) were different.

(Japanese Jōmon era pottery happened very early, around 14,500 BCE. See
https://en.wikipedia.org/wiki/J%C5%8Dmon_period#Earliest_pottery. So, in all likeliness, even though the main lifestyle there was still hunter-gatherer society, supplementary, casual agriculture was in place.)

- - -

I was reading on polydactyly. That is, having more than 5 fingers or 5 toes. See this article:

http://www.dailymail.co.uk/news/article-4973342/Brazilian-family-12-fingers-toes-each.html


This incidence rate is 1 in 1,339 newborns among the Caucasian according to a study. If we take 2.8 million as typical clan size today, then sqrt(2,800,000) ~ 1,673. Namely, polydactyly falls on the fringe of what's normal.

Humans share 50% of DNA with bananas. We and bananas came from a common ancestor. Mother Nature is constantly seeking new ideas. She plays a game known as the "multi-armed bandit." https://en.wikipedia.org/wiki/Multi-armed_bandit. The main questions are: How much to exploit? How much to explore? There is a balance between exploitation and exploration. The square-root law gives a guidance as what should be considered as exploitation (what's normal) and what should be considered as exploration (what's anomalous).

So I went ahead and wrote a simple two-armed bandit program, using the "epsilon-decreasing" approach. If square-root law is any good, we would allocate f=sqrt(T) trials for exploration, and the rest for exploitation, where T is the total number of trials. For simplicity, I use only two arms, where one arm has winning probability 0.15, and the other one 0.45. (I have also tried 0.15 vs. 0.30.) It is a simple exercise to show that the value of the "decreasing epsilon" as function of the index of trial t is

epsilon(t) = d f / d t = 1/[2*sqrt(t)]

In general, if we use a power law with power exponent p such that 0<p<1, then

f = t^p
epsilon(t) = d f / d t = p/[t^(1-p)]

From there, we run the two-armed bandit Monte Carlo simulation, and obtain the return (total rate of winning). Running enough times and taking the average value for each index of trial t, I got the following plot (vertical axis is the expected total win rate up to the trial "t", horizontal axis is trial index "t"):



And guess what? Within the power-law family of exploration sizes, the square-root law p=0.5 is indeed the optimal solution!! ! (I've extended T to 2,000 and p=0.5 is still the optimal strategy.) It means the square-root law is the optimal way of playing the two-armed bandit (within the power-law family a la "epsilon-decreasing"). Mother Nature has been playing the multi-armed bandit game for a long time, so we would expect her to follow some behavior close to the square-root law, so to optimize the survival game of each species, or clan within a species.

Now, in layman's terms, what does this mean? It means that there is validity to expect that Mother Nature indeed operates according to the square-root law. Namely, given a sample N, it reserves a small sub-sample of size sqrt(N) for exploration, while uses the rest for exploitation.

- - -

I was also thinking about the "synchronization" of the square-root law of clan population size with the genetic condition's prevalence rate. How come the prevalence rate of say, color blindness, is "synchronized" perfectly with the prevailing clan size at the moment of the introduction of arrows in early (full) agriculture societies? I think this is what is going on:

(a) because color blindness offers increased odd of survival (especially against ambushes) for clans, gradually the color blindness prevalence rate will be increasing. Those clans with lower prevalence rate gradually are eliminated.

(b) clans with prevalence rates lower than dictated by the square-root law do not have stability. Remember: Mother Nature uses anything below sqrt(N) for exploration, not for exploitation. This means that such clans are in danger of running out of color-blind people due to natural fluctuations. And once there is lack of color-blind people, they run the danger of extinction due to wars.

(c) The only way of guaranteeing stable supply of color-blind people is to make sure the prevalence rate of this condition surpasses the sqrt(N) threshold. At that moment, color blindness becomes part of exploitation instead of exploration.

(d) Population of the winning clans would increase. But the food production areal density (and also Dunbar-like considerations of intra-clan affinity) eventually causes clans to splinter. The splintered groups share similar familiar-cultural background and technology know-how, so likelihood of wars dramatically reduces between the splintered clans. These clans expand radially, dominating over other clans with lower prevalence rate of color blindness, until it is met with other clans with similar ratios of color blindness. But, now, the color blindness rate given by square-root law introduces "numerical supremacy" that makes further wars irrelevant to major change in color blindness rate. Due to the lack of transportation and other technology, further wars were unlikely to alter the prevalence rate. That is, the prevalence rate "decouples" from other evolutionary factors, and stays stable. This is a bit like why the cosmic microwave background (CMB) radiation has a stable temperature around 2.7 degrees Kelvin, yet we are not frozen to death here on earth. We don't feel cold, because CMB photons have decoupled from the world of matter. (For "decoupling", see https://en.wikipedia.org/wiki/Decoupling_(cosmology)). Saying it another way, the simplified version is this: while clans compete in ever increasing prevalence rate of color blindness, the first clan to reach the sqrt(N) threshold expands rapidly and defeats all other clans and fill up entire regions (separated by natural geographic boundaries). So, in the limit of rapid expansion (reminds me of cosmological inflation, ha!), it is certainly true that the color blindness rate would be frozen, forever. Sure, this is an approximation. In reality wars would still happen, but because fraternal clans have similar (stable) genetics and technology know how, there is no clear winner. The prevalence rate is already over the threshold of exploitation, so it's stable, and the changes slow down.

Soon afterwards, other technologies (domestication of animals, wheels, bronze, writing, iron, etc.) became determinant (instead of arrows), and clan sizes became increasingly larger. Color blindness no longer played any significant role in the survival of a clan

With each significant advance in technology, new genetic conditions entered human race in a similar way. For instance, clinical-level autism happened in all likeliness due to domestication of animals. (This would explain why black people have typical prevalence rate of autism, but low color blindness rate. Sub-Sahara Africa, unlike other parts of the world, stands out because cattle domestication happened long before agriculture.) Bronze Age brought us schizophrenia, and Iron Age gave us Down Syndrome. Throughout it all, the mathematics of the square-root law operated behind the scene.

- - -

And who says math is boring? Ha!

I disagree.

Bows and arrows caused color blindness and autism.

Dude ...that is....too FEW words.
Your saying "A caused Z" when there is no obvious connection between A and Z.

You need to expand it just a little. Make it into a story. So that folks know what you're trying to prove.

For example

If you had said "the invention of archery made our ancestors into such good hunters that they depleted the game, and then that forced us into domestication and agriculture, which in turn enabled color blind folks to survive". then than would give us all a handle WTF you're talking about.

I don't know if the above IS what you're saying, or not ( I don't claim to understand what you're saying). Just giving that as an example.