Dunbar's Number: an Analytic Expression

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Recently I combined the application of IHI (Inverse of Herfindahl Index) and the Square Root Law to the normal distribution, and was startled to find that the result gave an analytic expression for the Dunbar's Number. As far as I know, this is the first time someone has ever derived an analytic expression for Dunbar's Number. Here is a short summary:



That is, D=erf(sqrt(pi/2))/erfc(sqrt(pi/2))^2. See, the world doesn't stop moving forward, while people sleep. Ha ha. (If you have a Google Chrome browser, you can paste in the formula and it will return the numerical value 158.581934551. Yep, Chrome also works as a good calculator.)

People by now knows I use mathematics and physics to raise my kids. Sure, it all sounds surreal, but somehow it all works. Ha ha. For instance, here is the Quora article I wrote on Renormalization.

https://www.quora.com/Can-you-explain-renormalization-in-physics-in-simple-words/answer/Jason-Lu-179

So what does Dunbar's number have to do with autism? Well, it's just another proof that Mother Nature really does operate with the Square Root Law. Also, this is the thing. Dunbar's Number is often interpreted as the maximum number of friends one can possibly have. This picture from Internet is succinct in summarizing it:



Dunbar's number has also be used to estimate the size of neolithic hunter-gatherer tribe size. I guess, to me personally, the most important consequence of Dunbar's number and the Square Root Law is, from their application to the prevalence rate of atypical genetic conditions, we can derive that (a) autism, (b) color-blindness, and (c) bipolar disorder, all entered human race right after the invention of bow and arrows and the arrival of agriculture. I first wrote about it last year on WrongPlanet. https://wrongplanet.net/forums/viewtopic.php?t=362747. As always and as expected, no one understood the importance of this link. Ha ha. That's the price you pay for being the first person in the world to say something. But that's OK, Galileo had it worse.

I mean, there are plenty of clues. We know both color-blindness and autism are male-dominated. With color-blindness more so than autism. I mean, Mother Nature is telling us so clearly that this is because both conditions are related to military advantage, since in the old days, boys did the fighting. Yet, somehow our society has been so deaf and blind to Mother Nature's message. Instead, we look for chemicals, vaccines, you name it, as causes of autism. You type in "X is linked to autism," and you'll find some research studies. E.g. X could be: air pollution, mother obesity, alcohol, smoking, etc. I mean, why look for all these esoteric causes, instead of considering autism as something meant by Mother Nature, all along? People always come to me and tell me that, autism not only has social-behavioral manifestations, but that many on the spectrum also have physical co-morbidity, like seizure. They show all that as ultimate proof that autism is a medical disorder. And I just have to laugh. Com'on, if you were physically fit, what would happen to you in the neolithic agricultural era? You would be drafted into labor, or defense. Relative physical weakness is precisely what has enabled autistic people to be exempt from physical labor, and contribute with their brain power instead. That is, relative physical weakness is not a bug, but a feature. Why not look at Leonardo Da Vinci. He had seizure, but he has also invented so many innovated military weapons. Nahh, the disorder view is simply incompatible with the Square Root Law, we should have known that from a start. The problem is, we think we are smarter than Mother Nature, but we are not. Mother Nature has had 4 billion years to do evolution. Color-blindness, Autism, Bipolarity, Schizophrenia, all have evolutionary explanations. They all helped human tribes survive, after the arrival of civilization and its wars. Tribes without these genetic traces have largely been wiped out: they couldn't compete.