Anthropology Friday: Numbers and the Making of Us, by Caleb Everett pt. 4

Yes, but which 25% of us is grape?

Welcome to our final post on Numbers and the Making of Us: Counting and the Course of Human Cultures, by Caleb Everett. Today I just want to highlight a few interesting passages.


For example, there is about 25% overlap between the human genome and that of grapes. (And we have fewer genes than grapes!) So some caution should be exercised before reading too much into percentages of genomic correspondence across species. I doubt, after all that you consider yourself one-quarter grape. … canine and bovine species generally exhibit about an 85% rate of genomic correspondence with humans. … small changes in genetic makeup can, among other influences, lead to large changes in brain size.

On the development of numbers:

Babylonian math homework

After all, for the vast majority of our species’ existence, we lived as hunters and gatherers in Africa … A reasonable interpretation of the contemporary distribution of cultural and number-system types, then, is that humans did not rely on complex number system for the bulk of their history. We can also reasonably conclude that transitions to larger, more sedentary, and more trade-based cultures helped pressure various groups to develop more involved numerical technologies. … Written numerals, and writing more generally, were developed first in the Fertile Crescent after the agricultural revolution began there. … These pressures ultimately resulted in numerals and other written symbols, such as the clay-token based numerals … The numerals then enabled new forms of agriculture and trade that required the exact discrimination and representation of quantities. The ancient Mesopotamian case is suggestive, then, of the motivation for the present-day correlation between subsistence and number types: larger agricultural and trade-based economies require numerical elaboration to function. …

Intriguingly, though, the same maybe true of Chinese writing, the earliest samples of which date to the Shang Dynasty and are 3,000 years old. The most ancient of these samples are oracle bones. These bones were inscribed with nuemerals quantifying such items as enemy prisoners, birds and animals hunted, and sacrificed animals. … Ancient writing around the world is numerically focused.

Changes in the Jungle as population growth makes competition for resources more intense and forces people out of their traditional livelihoods:

Consider the case of one of my good friends, a member of an indigenous group known as the Karitiana. … Paulo spent the majority of his childhood, in the 1980s and 1990s in the largest village of his people’s reservation. … While some Karitiana sought to make a living in nearby Porto Velho, many strived to maintain their traditional way of life on their reservation. At the time this was feasible, and their traditional subsistence strategies of hunting, gathering, and horticulture could be realistically practiced. Recently, however, maintaining their conventional way of life has become a less tenable proposition. … many Karitiana feel they have little choice but to seek employment in the local Brazilian economy… This is certainly true of Paulo. He has been enrolled in Brazilian schools for some time, has received some higher education, and is currently employed by a governmental organization. To do these things, of course, Paulo had to learn Portuguese grammar and writing. And he had to learn numbers and math, also. In short, the socioeconomic pressures he has felt to acquire the numbers of another culture are intense.

Everett cites a statistic that >90% of the world’s approximately 7,000 languages are endangered.

They are endangered primarily because people like Paulo are being conscripted into larger nation-states, gaining fluency in more economically viable languages. … From New Guinea to Australia to Amazonia and elsewhere, the mathematizing of people is happening.

On the advantages of different number systems:

Recent research also suggests that the complexity of some non-linguistic number systems have been under appreciated. Many counting boards and abaci that have been used, and are still in use across the world’s culture, present clear advantages to those using them … the abacus presents some cognitive advantages. That is because, research now suggests, children who are raised using the abacus develop a “mental abacus” with time. … According to recent cross-cultural findings, practitioners of abacus-based mathematical strategies outperform those unfamiliar with such strategies,a t least in some mathematical tasks. The use of the Soroban abacus has, not coincidentally, now been adopted in many schools throughout Asia.

The zero is a dot in the middle of the photo–earliest known zero, Cambodia

I suspect these higher math scores are more due to the mental abilities of the people using the abacus than the abacus itself. I have also just ordered an abacus.

… in 2015 the world’s oldest known unambiguous inscription of a circular zero was rediscovered in Cambodia. The zero in question, really a large dot, serves as a placeholder in the ancient Khmer numeral for 605. It is inscribed on a stone tablet, dating to 683 CE, that was found only kilometers from the faces of Bayon and other ruins of Angkor Wat and Angkor Thom. … the Maya also developed a written form for zero, and the Inca encoded the concept in their Quipu.

In 1202, Fibonacci wrote the Book of Calculation, which promoted the use of the superior Arabic (yes Hindu) numerals (zero included) over the old Roman ones. Just as the introduction of writing jump-started the Cherokee publishing industry, so the introduction of superior numerals probably helped jump-start the Renaissance.

Cities and the rise of organized religion:

…although creation myths, animistic practices, and other forms of spiritualism are universal or nearly universal, large-scale hierarchical religions are restricted to relatively few cultural lineages. Furthermore, these religions… developed only after people began living in larger groups and settlements because of their agricultural lifestyles. … A phalanx of scholars has recently suggested that the development of major hierarchical religions, like the development of hierarchical governments, resulted from the agglomeration of people in such places. …

Organized religious beliefs, with moral-enforcing deities and priest case, were a by-product of the need for large groups of people to cooperate via shared morals and altruism. As the populations of cultures grew after the advent of agricultural centers… individuals were forced to rely on shared trust with many more individuals, including non-kin, than was or is the case in smaller groups like bands or tribes. … Since natural selection is predicated on the protection of one’s genes, in-group altruism and sacrifice are easier to make sense of in bands and tribes. But why would humans in much larger populations–humans who have no discernible genetic relationship… cooperate with these other individuals in their own culture? … some social mechanism had to evolve so that larger cultures would not disintegrate due to competition among individuals and so that many people would not freeload off the work of others. One social mechanism that foster prosocial and cooperative behavior is an organized religion based on shared morals and omniscient deities capable of keeping track of the violation of such morals. …

When Moses descended from Mt. Sinai with his stone tablets, they were inscribed with ten divine moral imperatives. … Why ten? … Here is an eleventh commandment that could likely be uncontroversially adopted by many people: “thou shalt not torture.” … But then the list would appear to lose some of its rhetorical heft. “eleven commandments’ almost hints of a satirical deity.

Technically there are 613 commandments, but that’s not nearly as catchy as the Ten Commandments–inadvertently proving Everett’s point.

Overall, I found this book frustrating and repetitive, but there were some good parts. I’ve left out most of the discussion of the Piraha and similar cultures, and the rather fascinating case of Nicaraguan homesigners (“homesigners” are deaf people who were never taught a formal sign language but made up their own.) If you’d like to learn more about them, you might want to look up the book at your local library.


11 thoughts on “Anthropology Friday: Numbers and the Making of Us, by Caleb Everett pt. 4

  1. The suggestion of a commandment against torture is ridiculous. The commandment against murdering those within your tribe is fair enough, it’s not uncommon to be annoyed enough to kill people. Actually wanting to torture people within your tribe is such a strange deviation it wouldn’t be known in the ancient world. And torturing those outside your tribe is obviously fine.


  2. I’m not surprised that you found it frustrating and repetitive, I find many modern books to be such. It seems as if even good modern writers, writing about interesting subjects they know a lot about. are incapable of writing clear, clean, interesting prose. I stead we get endless digressions on tangential matters, piles of verbal padding, constant genuflections to the current dogmas of Racism, Sexism, and Homophobia, and nasty little swipes at our ancestors for not being as wonderful as us. Even as good as writer as Stephen Pinker does it, never mind lesser lights.

    With hindsight, there’s no doubt that the high noon of good, clear popular science writing was sometime between 1950 and about 1970. There are still some good s.cience writers around, but they are mostly older, and in the minority


    • I think part of it is that publishers just like to publish books of a certain length. People like to think they’re getting their money’s worth, and a book that’s 150 pages therefore probably sells better than one that’s 50 pages. So I think most authors feel compelled to pad their manuscripts.


  3. My favorite abacus is the Russian “schoty”, with ten beads per wire. The two middle beads are a darker color to more easily distinguish 4, 5, 6, and 7. It’s faster than a soroban because any digit can be changed to any other digit by pushing only one bead, and simpler because everything is ten’s complement, never five’s complement. Nonetheless, any book of soroban algorithms works just as well on the schoty.

    I came up with additional hacks like lifting the multiplicand off the baseline as a reminder that its digits are to be replaced, not added to (Japanese avoid this problem by subtracting one from the multiplier). I built abacuses of over 50 digits using a table saw, plywood, thick nylon cord, and hundreds of cheap plastic “pony beads”. Deep notches not only guide the cord but also hold wooden pegs, as it’s easy to lose one’s place on such a vast board. Be sure to shave off pips with a sharp blade before stringing the beads.

    I calculate left-to-right with my left index finger pointing to the current digit and a dull steak knife in my right hand pushing beads up and down. For children, I write the digits of the multiplier or divisor on a slip of paper and move it as needed to show where partial products must now be added or subtracted (“Q” means “put the next digit of the quotient here”)

    I was surprised to learn that computing a square root is only slightly more complicated than long division (Kato Fukutaro’s method). Cube roots are hard, though. In all cases the abacus is much faster than pencil and paper, but requires greater concentration because it’s harder to back up if you make a mistake.


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