Favorite Things Redux: Beringian DNA

Map of gene-flow in and out of Beringia, from 25,000 years ago to present

Scientists have long believed that the first humans made it to the Americas by crossing from now-Russia to now-Alaska. When and how they did it–by boat or by foot–remain matters of contentious debate. Did people move quickly through Alaska and into the rest of North America, or did they hover–as the “Bering standstill” hypothesis suggests–in Beringia (or the Aleutian Islands) for thousands of years?

Archaeologists working at the Upward Sun River site (approximately in the middle of Alaska) recently uncovered the burials of three children: a cremated three year old, and beneath it, a 6-12 week old infant and a 30 week, possibly premature or stillborn fetus. The three year old has been dubbed “Upward Sun River Mouth Child,” and the 6 week old “Sun-Rise Girl Child.” Since these aren’t really names, I’m going to dub them Sunny (3 yrs old), Rosy (6 weeks), and Hope (fetus).

They died around 11,500 years ago, making them the oldest burials so far from northern North America. Rosy and Hope were probably girls; cremation rendered Sunny’s gender a mystery. Rosy and Hope were covered in red ocher and buried together, accompanied by four decorated antler rods, two dart points and two stone axes. (Here’s an illustration of their burial.) The site where the children were buried was abandoned soon after Sunny’s death–perhaps their parents were too sad to stay, or perhaps the location was just too harsh.

Rosy and Hope were well enough preserved to yield DNA.

Surprisingly, they weren’t sisters. Rosy’s mother’s mtDNA hailed from haplogroup C1b, which is found only in the Americas (though its ancestral clade, haplogroup C, is found throughout Siberia.) Hope’s mtDNA is from haplogroup B2, which is also only found in the Americas. Oddly, B2’s parent clade, (B), isn’t common in Siberia–it’s much more common in places like Vietnam, Laos, the Philippines, and Saipan. It’s not entirely absent from Siberia, but it got to Alaska without leaving a larger trail remains a mystery.

Since they are found in the Americans but not Asia, we know these lineages most likely evolved over here; the main questions are when and where. If the Bering Standstill hypothesis is correct and the Indians spent 10-20,000 years stranded in Beringia, they would have had plenty of time to evolve new lineages while still in Alaska. By contrast, if they crossed relatively quickly and then dispersed, these new lineages would have had much less time to emerge, and we would expect them to show up as people moved south.

Source: Ancient Beringians: A Discovery Changing Early Native American Hisotry

Or there could have been multiple migration waves, with different haplogroups arriving in different waves. (There were multiple migration waves, but the others occurred well after Sunny and the others were buried.)

In fact, there are five mtDNA lineages found only in the Americas (A2, B2, C1, D1, and X2a.) With Hope and Rosy, we have now identified all five mtDNA lineages in North American burials over 8,000 years old, lending support to the Beringian Standstill hypothesis.

But were the Upward Sun River children’s families ancestral to today’s Native Americans? Not quite.

It looks like Sunny’s tribe split off from the rest of the Beringians (or perhaps the others split off from them) around 22-18,000 years ago. Most of the others headed south, while Sunny’s people stayed in Alaska and disappeared (perhaps because all of their children died.) So Sunny’s tribe was less “grandparent” to today’s Indians and more “great aunt and uncle,” but they still hailed from the same, even older ancestors who first set out from Siberia.

I have previously favored the Aleutian or at least a much more rapid Beringian route, but it looks like I was wrong. I find the idea of the Bering Standstill difficult to believe, but that may just be my own biases. Perhaps people really did get stuck there for thousands of years, waiting for the ice to clear. What amazing people they must have been to survive for so long in so harsh an environment.


Cathedral Round-Up #29: Pinker, Truth, and Liars

Steven Pinker recently gave a short speech at Harvard (where he works) on how hearing certain facts without accompanying leftist counter-arguments causes people to become “infected” with right-wing thoughts:

The Left responded in its usual, thoughtful, reasonable fashion, eg “If you ever doubted that Steven Pinker’s sympathies lie with the alt-right…” The author of the piece also called Pinker a “lying right-wing shitweasel” on twitter.

Of course this is nonsense; as Why Evolution is True has pointed out, Pinker is one of Harvard’s most generous donors to the Democratic party.

The difference between Pinker and the Left is that Pinker is (trying) to be honest. Pinker believes in truth. He believes in believing true things and discussing true things. He believes that just because you believe a true thing doesn’t mean you have to go down this road to believing other, in his opinion untrue, things. You can believe more than one true thing. You can simultaneously believe “Blacks commit more homicide than whites” and believe “Blacks should not be discriminated against.”

By contrast, the Left is not trying to be honest. It is not looking for truth. It just wants to win. The Left does not want people to know that crime stats vary by race, that men and women vary in average interests and aptitudes, that communism is an atrociously bad economic system. Merely saying, “Hey, there are things you can’t say out loud without provoking a very loud controversy from the left,” has provoked… a very loud controversy from the left:

Link to the original conversation


The Left is abusing one of its own because merely saying these things out loud is seen as a betrayal of Leftist goals.


And yet he was in the right! They were wrong and he was right. And if all others accepted the lie which the Party imposed—if all records told the same tale—then the lie passed into history and became truth. ‘Who controls the past’ ran the Party slogan, ‘controls the future: who controls the present controls the past.’ —George Orwel, 1984


Anthropology Friday: Numbers and the Making of Us, part 2

Welcome to part 2 of my review of Caleb Everett’s Numbers and the Making of Us: Counting and the Course of Human Cultures.

I was really excited about this book when I picked it up at the library. It has the word “numbers” on the cover and a subtitle that implies a story about human cultural and cognitive evolution.

Regrettably, what could have been a great books has turned out to be kind of annoying. There’s some fascinating information in here–for example, there’s a really interesting part on pages 249-252–but you have to get through pages 1-248 to get there. (Unfortunately, sometimes authors put their most interesting bits at the end so that people looking to make trouble have gotten bored and wandered off by then.)

I shall try to discuss/quote some of the book’s more interesting bits, and leave aside my differences with the author (who keeps reiterating his position that mathematical ability is entirely dependent on the culture you’re raised in.) Everett nonetheless has a fascinating perspective, having actually spent much of his childhood in a remote Amazonian village belonging to the Piraha, who have no real words for numbers. (His parents were missionaries.)

Which languages contain number words? Which don’t? Everett gives a broad survey:

“…we can reach a few broad conclusions about numbers in speech. First, they are common to nearly all of the world’s languages. … this discussion has shown that number words, across unrelated language, tend to exhibit striking parallels, since most languages employ a biologically based body-part model evident in their number bases.”

That is, many languages have words that translate essentially to “One, Two, Three, Four, Hand, … Two hands, (10)… Two Feet, (20),” etc., and reflect this in their higher counting systems, which can end up containing a mix of base five, 10, and 20. (The Romans, for example, used both base five and ten in their written system.)

“Third, the linguistic evidence suggests not only that this body-part model has motivated the innovation of numebers throughout the world, but also that this body-part basis of number words stretches back historically as far as the linguistic data can take us. It is evident in reconstruction of ancestral languages, including Proto-Sino-Tibetan, Proto-Niger-Congo, Proto-Autronesian, and Proto-Indo-European, the languages whose descendant tongues are best represented in the world today.”

Note, though, that linguistics does not actually give us a very long time horizon. Proto-Indo-European was spoken about 4-6,000 years ago. Proto-Sino-Tibetan is not as well studied yet as PIE, but also appears to be at most 6,000 years old. Proto-Niger-Congo is probably about 5-6,000 years old. Proto-Austronesian (which, despite its name, is not associated with Australia,) is about 5,000 years old.

These ranges are not a coincidence: languages change as they age, and once they have changed too much, they become impossible to classify into language families. Older languages, like Basque or Ainu, are often simply described as isolates, because we can’t link them to their relatives. Since humanity itself is 200,000-300,000 years old, comparative linguistics only opens a very short window into the past. Various groups–like the Amazonian tribes Everett studies–split off from other groups of humans thousands 0r hundreds of thousands of years before anyone started speaking Proto-Indo-European. Even agriculture, which began about 10,000-15,000 years ago, is older than these proto-languages (and agriculture seems to have prompted the real development of math.)

I also note these language families are the world’s biggest because they successfully conquered speakers of the world’s other languages. Spanish, Portuguese, and English are now widely spoken in the Americas instead of Cherokee, Mayan, and Nheengatu because Indo-European language speakers conquered the speakers of those languages.

The guy with the better numbers doesn’t always conquer the guy with the worse numbers–the Mongol conquest of China is an obvious counter. But in these cases, the superior number system sticks around, because no one wants to replace good numbers with bad ones.

In general, though, better tech–which requires numbers–tends to conquer worse tech.

Which means that even though our most successful language families all have number words that appear to be about 4-6,000 years old, we shouldn’t assume this was the norm for most people throughout most of history. Current human numeracy may be a very recent phenomenon.

“The invention of number is attainable by the human mind but is attained through our fingers. Linguistic data, both historical and current, suggest that numbers in disparate cultures have arisen independently, on an indeterminate range of occasions, through the realization that hands can be used to name quantities like 5 and 10. … Words, our ultimate implements for abstract symbolization, can thankfully be enlisted to denote quantities. But they are usually enlisted only after people establish a more concrete embodied correspondence between their finger sand quantities.”

Some more on numbers in different languages:

“Rare number bases have been observed, for instance, in the quaternary (base-4) systems of Lainana languages of California, or in the senary (base-6) systems that are found in southern New Guinea. …

Several languages in Melanesia and Polynesia have or once had number system that vary in accordance with the type of object being counted. In the case of Old High Fijian, for instance, the word for 100 was Bola when people were counting canoes, but Kora when they were counting coconuts. …

some languages in northwest Amazonia base their numbers on kinship relationships. This is true of Daw and Hup two related language in the region. Speakers of the former languages use fingers complemented with words when counting from 4 to 10. The fingers signify the quantity of items being counted, but words are used to denote whether the quantity is odd or even. If the quantity is even, speakers say it “has a brother,” if it is odd they state it “has no brother.”

What about languages with no or very few words for numbers?

In one recent survey of limited number system, it was found that more than a dozen languages lack bases altogether, and several do not have words for exact quantities beyond 2 and, in some cases, beyond 1. Of course, such cases represent a miniscule fraction of the world’s languages, the bulk of which have number bases reflecting the body-part model. Furthermore, most of the extreme cases in question are restricted geographically to Amazonia. …

All of the extremely restricted languages, I believe, are used by people who are hunter-gatherers or horticulturalists, eg, the Munduruku. Hunter gatherers typically don’t have a lot of goods to keep track of or trade, fields to measure or taxes to pay, and so don’t need to use a lot of numbers. (Note, however, that the Inuit/Eskimo have a perfectly normal base-20 counting system. Their particularly harsh environment appears to have inspired both technological and cultural adaptations.) But why are Amazonian languages even less numeric than those of other hunter-gatherers from similar environments, like central African?

Famously, most of the languages of Australia have somewhat limited number system, and some linguists previously claimed that most Australian language slack precise terms for quantities beyond 2…. [however] many languages on that continent actually have native means of describing various quantities in precise ways, and their number words for small quantities can sometimes be combined to represent larger quantities via the additive and even multiplicative usage of bases. …

Of the nearly 200 Australian languages considered in the survey, all have words to denote 1 and 2. In about three-quarters of the languages, however, the highest number is 3 or 4. Still, may of the languages use a word for “two” as a base for other numbers. Several of the languages use a word for “five” as a base, an eight of the languages top out at a word for “ten.”

Everett then digresses into what initially seems like a tangent about grammatical number, but luckily I enjoy comparative linguistics.

In an incredibly comprehensive survey of 1,066 languages, linguist Matthew Dryer recently found that 98 of them are like Karitiana and lack a grammatical means of marking nouns of being plural. So it is not particularly rare to find languages in which numbers do not show plurality. … about 90% of them, have a grammatical means through which speakers can convey whether they are talking about one or more than one thing.

Mandarin is a major language that has limited expression of plurals. According to Wikipedia:

The grammar of Standard Chinese shares many features with other varieties of Chinese. The language almost entirely lacks inflection, so that words typically have only one grammatical form. Categories such as number (singular or plural) and verb tense are frequently not expressed by any grammatical means, although there are several particles that serve to express verbal aspect, and to some extent mood.

Some languages, such as modern Arabic and Proto-Indo-European also have a “dual” category distinct from singular or plural; an extremely small set of languages have a trial category.

Many languages also change their verbs depending on how many nouns are involved; in English we say “He runs; they run;” languages like Latin or Spanish have far more extensive systems.

In sum: the vast majority of languages distinguish between 1 and more than one; a few distinguish between one, two, and many, and a very few distinguish between one, two, three, and many.

From the endnotes:

… some controversial claims of quadral markers, used in restricted contexts, have been made for the Austronesian languages Tangga, Marshallese, and Sursurunga. .. As Corbett notes in his comprehensive survey, the forms are probably best considered quadral markers. In fact, his impressive survey did not uncover any cases of quadral marking in the world’s languages.

Everett tends to bury his point; his intention in this chapter is to marshal support for the idea that humans have an “innate number sense” that allows them to pretty much instantly realize if they are looking at 1, 2, or 3 objects, but does not allow for instant recognition of larger numbers, like 4. He posits a second, much vaguer number sense that lets us distinguish between “big” and “small” amounts of things, eg, 10 looks smaller than 100, even if you can’t count.

He does cite actual neuroscience on this point–he’s not just making it up. Even newborn humans appear to be able to distinguish between 1, 2, and 3 of something, but not larger numbers. They also seem to distinguish between some and a bunch of something. Anumeric peoples, like the Piraha, also appear to only distinguish between 1, 2, and 3 items with good accuracy, though they can tell “a little” “some” and “a lot” apart. Everett also cites data from animal studies that find, similarly, that animals can distinguish 1, 2, and 3, as well as “a little” and “a lot”. (I had been hoping for a discussion of cephalopod intelligence, but unfortunately, no.)

How then, Everett asks, do we wed our specific number sense (1, 2, and 3) with our general number sense (“some” vs “a lot”) to produce ideas like 6, 7, and a googol? He proposes that we have no innate idea of 6, nor ability to count to 10. Rather, we can count because we were taught to (just as some highly trained parrots and chimps can.) It is only the presence of number words in our languages that allows us to count past 3–after all, anumeric people cannot.

But I feel like Everett is railroading us to a particular conclusion. For example, he sites neurology studies that found one part of the brain does math–the intraparietal suclus (IPS)–but only one part? Surely there’s more than one part of the brain involved in math.

About 5 seconds of Googling got me “Neural Basis of Mathematical Cognition,” which states that:

The IPS turns out to be part of the extensive network of brain areas that support human arithmetic (Figure 1). Like all networks it is distributed, and it is clear that numerical cognition engages perceptual, motor, spatial and mnemonic functions, but the hub areas are the parietal lobes …

(By contrast, I’ve spent over half an hour searching and failing to figure out how high octopuses can count.)

Moreover, I question the idea that the specific and general number senses are actually separate. Rather, I suspect there is only one sense, but it is essentially logarithmic. For example, hearing is logarithmic (or perhaps exponential,) which is why decibels are also logarithmic. Vision is also logarithmic:

The eye senses brightness approximately logarithmically over a moderate range (but more like a power law over a wider range), and stellar magnitude is measured on a logarithmic scale.[14] This magnitude scale was invented by the ancient Greek astronomer Hipparchus in about 150 B.C. He ranked the stars he could see in terms of their brightness, with 1 representing the brightest down to 6 representing the faintest, though now the scale has been extended beyond these limits; an increase in 5 magnitudes corresponds to a decrease in brightness by a factor of 100.[14] Modern researchers have attempted to incorporate such perceptual effects into mathematical models of vision.[15][16]

So many experiments have revealed logarithmic responses to stimuli that someone has formulated a mathematical “law” on the matter:

Fechner’s law states that the subjective sensation is proportional to the logarithm of the stimulus intensity. According to this law, human perceptions of sight and sound work as follows: Perceived loudness/brightness is proportional to logarithm of the actual intensity measured with an accurate nonhuman instrument.[3]

p = k ln ⁡ S S 0 {\displaystyle p=k\ln {\frac {S}{S_{0}}}\,\!}

The relationship between stimulus and perception is logarithmic. This logarithmic relationship means that if a stimulus varies as a geometric progression (i.e., multiplied by a fixed factor), the corresponding perception is altered in an arithmetic progression (i.e., in additive constant amounts). For example, if a stimulus is tripled in strength (i.e., 3 x 1), the corresponding perception may be two times as strong as its original value (i.e., 1 + 1). If the stimulus is again tripled in strength (i.e., 3 x 3 x 3), the corresponding perception will be three times as strong as its original value (i.e., 1 + 1 + 1). Hence, for multiplications in stimulus strength, the strength of perception only adds. The mathematical derivations of the torques on a simple beam balance produce a description that is strictly compatible with Weber’s law.[6][7]

In any logarithmic scale, small quantities–like 1, 2, and 3–are easy to distinguish, while medium quantities–like 101, 102, and 103–get lumped together as “approximately the same.”

Of course, this still doesn’t answer the question of how people develop the ability to count past 3, but this is getting long, so we’ll continue our discussion next week.

The Social Signaling Problem

People like to signal. A LOT. And it is incredibly annoying.

It’s also pretty detrimental to the functioning of the country.

Take Prohibition. The majority of Americans never supported Prohibition, yet it wasn’t just a law passed by Congress or a handful of states, but an actual amendment to the Constitution, (the 18th) ratified by 46 states (only Rhode Island and Connecticut declined to ratify. I assume they had a large Irish population or depended on sales of imported alcohol.)

Incredibly, a coalition driven primarily by people who couldn’t even vote (women’s suffrage was granted in the 19th amendment) managed to secure what looks like near-unanimous support for a policy which the majority of people actually opposed!

Obviously a lot of people voted for Prohibition without understanding what it actually entailed. Most probably thought that other people’s intemperate drinking should be curbed, not their own, completely reasonable consumption. Once people understood what Prohibition actually entailed, they voted for its repeal.

But this is only part of the explanation, for people support many policies they don’t actually understand, but most of these don’t become disastrous Constitutional amendments.

What we have is a runaway case of social signaling. People did not actually want to get rid of all of the alcohol. People wanted to signal that they were against public drunkenness, Germans (this was right after WWI,) and maybe those Irish. Prohibition also had a very vocal group of people fighting for it, while the majority of people who were generally fine with people having the occasional beer weren’t out campaigning for the “occasional beer” party. It was therefore more profitable for a politician to signal allegiance to the pro-Prohibition voters than to the “occasional beer” voter.

Social signaling leads people to support laws because they like the idea of the law, rather than an appreciation for what the law actually entails, creating a mess of laws that aren’t very useful. For example, on Dec. 12, 2017, the Senate unanimously passed a bill “to help Holocaust survivors and the families of victims obtain restitution or the return of Holocaust-era assets.”

In the midst of increasing crime, an opioid epidemic, starving Yemenis, decimated inner cities, rising white death rates, economic malaise, homelessness, and children with cancer, is the return of assets stolen 75 years ago in a foreign country really our most pressing issue?

No, but do you want to be the guy who voted against the Justice for Holocaust survivors bill? What are you, some kind of Nazi? Do you want to vote in favor of drunken alcoholics? Criminals? Sex offenders? Murderers? Racists? Satanic Daycares?

Social signaling inspires a bunch of loud, incoherent arguing, intended more to prove “I am a good person” or “I belong to Group X” than to hash out good policy. Indeed, social signaling is diametrically opposed to good policy, as you can always prove that you are an even better person or better member of Group X by trashing good policies on the grounds that they do not signal hard enough.

The Left likes to do a lot of social signaling about racism, most recently exemplified in the tearing down of Civil War Era statues. I’m pretty sure those statues weren’t out shooting black people or denying them jobs, but nonetheless it suddenly became an incredibly pressing problem that they existed, taking up a few feet of space, and had to be torn down. Just breathe the word “racist” and otherwise sensible people’s brains shut down and they become gibbering idiots.

The Right likes to social signal about sex, which it hates so much it can’t shut up about it. Unless people are getting married at 15, they’re going to have extra-marital sex. If you want to live in an economy where people have to attend school into their mid-twenties in order to learn everything, then you either need to structure things so that people can get married and have kids while they are still in school or they will just have extra-marital sex while still in school.

Right and Left both like to signal about abortion, though my sense here is that the right is signaling harder.

The Right and Left both like to signal about Gun Control. Not five minutes after a mass shooting and you’ll have idiots on both sides Tweeting about how their favorite policy could have saved the day (or how the other guy’s policy wouldn’t have prevented it at all.) Now, I happen to favor more gun control (if you ignore the point of this entire post and write something mind-numbingly stupid in response to this I will ignore you,) but “more gun control” won’t solve the  problem of someone buying an already illegal gun and shooting people with it. If your first response to a shooting is “More gun control!” without first checking whether that would have actually prevented the shooting, you’re being an idiot. (By contrast, if you’re out there yelling “Gun control does nothing!” in a case where it could have saved lives, then you’re the one being an idiot.)

This doesn’t mean that people can’t have reasonable positions on these issues (even positions I disagree with.) But yelling “This is bad! I hate it very much!” makes it much harder to have a reasonable discussion about the best way to address the issues. If people can personally benefit by social signaling against every reasonable position, then they’ll be incentivised to do so–essentially defecting against good policy making.

So what can we do?

I previously discussed using anonymity to damp down signaling. It won’t stop people from yelling about their deeply held feelings, but it does remove the incentive to care about one’s reputation.

Simply being aware of the problem may help; acknowledge that people will signal and then try to recognize when you are doing it yourself.

In general, we can tell that people are merely signaling about an issue if they don’t take any active steps in their own personal lives to resolve it. A person who actually rides a bike to work because they want to fight global warming is serious; someone who merely talks a good talk while flying in a private jet is not.

“Anti-racists” who live in majority white neighborhoods “for the schools” are another example–they claim to love minorities but mysteriously do not live among them. Clearly someone else–maybe working class whites–should be forced to do it.

Signalers love force: force lets them show how SERIOUS they are about fighting the BAD ISSUE without doing anything themselves about it. The same is true for “anti-abortion” politicians, eg Kasich Signs Law Banning Abortions After Diagnosis of Down’s Syndrome. Of course Kasich will not be personally adopting or raising any babies with Down’s syndrome, nor giving money to their families to help with their medical bills. Kasich loves Down’s babies enough to force other people to raise them, but not enough to actually care for one himself.

Both sides engage in this kind of behavior, which looks like goodness on their own side but super hypocritical to the other.

The positions of anyone who will not (or cannot) put their money where their mouth is should be seen as suspect. If they want to force other people to do things they don’t or can’t, it automatically discredits them.

Communism, as in an entire country/economy run by force in order to achieve a vision of a “just society,” ranks as the highest expression of social signaling. Not only has communism failed miserably in every iterations, it has caused the deaths of an estimated 100 million people by starvation, purge, or direct bullets to the head. Yet communist ideology persists because of the strength of social signalling.

Local Optima, Diversity, and Patchwork

Local optima–or optimums, if you prefer–are an illusion created by distance. A man standing on the hilltop at (approximately) X=2 may see land sloping downward all around himself and think that he is at the highest point on the graph.

But hand him a telescope, and he discovers that the fellow standing on the hilltop at X=4 is even higher than he is. And hand the fellow at X=4 a telescope, and he’ll discover that X=6 is even higher.

A global optimum is the best possible way of doing something; a local optimum can look like a global optimum because all of the other, similar ways of doing the same thing are worse. To get from a local optimum to a global optimum, you might have to endure a significant trough of things going worse before you reach your destination. (Those troughs would be the points X=3.03 and X=5.02 on the graph.) If the troughs are short and shallow enough, people can accidentally power their way through. If long and deep enough, people get stuck.

The introduction of new technology, exposure to another culture’s solutions, or even random chance can expose a local optimum and propel a group to cross that trough.

For example, back in 1400, Europeans were perfectly happy to get their Chinese silks, spices, and porcelains via the overland Silk Road. But with the fall of Constantinople to the Turks in 1453, the Silk Road became more fragmented and difficult (ie dangerous, ie expensive) to travel. The increased cost of the normal road prompted Europeans to start exploring other, less immediately profitable trade routes–like the possibility of sailing clear around the world, via the ocean, to the other side of China.

Without the eastern trade routes first diminishing in profitability, it wouldn’t have been economically viable to explore and develop the western routes. (With the discovery of the Americas, in the process, a happy accident.)

West Hunter (Greg Cochran) writes frequently about local optima; here’s an excerpt on plant domestication:

The reason that a few crops account for the great preponderance of modern agriculture is that a bird in the hand – an already-domesticated, already- optimized crop – feeds your family/makes money right now, while a potentially useful yet undomesticated crop doesn’t. One successful domestication tends to inhibit others that could flourish in the same niche. Several crops were domesticated in the eastern United States, but with the advent of maize and beans ( from Mesoamerica) most were abandoned. Maybe if those Amerindians had continued to selectively breed sumpweed for a few thousand years, it could have been a contender: but nobody is quite that stubborn.

Teosinte was an unpromising weed: it’s hard to see why anyone bothered to try to domesticate it, and it took a long time to turn it into something like modern maize. If someone had brought wheat to Mexico six thousand years ago, likely the locals would have dropped maize like a hot potato. But maize ultimately had advantages: it’s a C4 plant, while wheat is C3: maize yields can be much higher.

Teosinte is the ancestor of modern corn. Cochran’s point is that in the domestication game, wheat is a local optimum; given the wild ancestors of wheat and corn, you’d develop a better, more nutritious variety of wheat first and probably just abandon the corn. But if you didn’t have wheat and you just had corn, you’d keep at the corn–and in the end, get an even better plant.

(Of course, corn is a success story; plenty of people domesticated plants that actually weren’t very good just because that’s what they happened to have.)

Japan in 1850 was a culturally rich, pre-industrial, feudal society with a strong isolationist stance. In 1853, the Japanese discovered that the rest of the world’s industrial, military technology was now sufficiently advanced to pose a serious threat to Japanese sovereignty. Things immediately degenerated, culminating in the Boshin War (civil war, 1868-9,) but with the Meiji Restoration Japan embarked on an industrialization crash-course. By 1895, Japan had kicked China’s butt in the First Sino-Japanese War and the Japanese population doubled–after holding steady for centuries–between 1873 and 1935. (From 35 to 70 million people.) By the 1930s, Japan was one of the world’s most formidable industrial powers, and today it remains an economic and technological powerhouse.

Clearly the Japanese people, in 1850, contained the untapped ability to build a much more complex and advanced society than the one they had, and it did not take much exposure to the outside world to precipitate a total economic and technological revolution.

Sequoyah’s syllabary, showing script and print forms

A similar case occurred in 1821 when Sequoyah, a Cherokee man, invented his own syllabary (syllable-based alphabet) after observing American soldiers reading letters. The Cherokee quickly adopted Sequoyah’s writing system–by 1825, the majority of Cherokee were literate and the Cherokee had their own printing industry. Interestingly, although some of the Cherokee letters look like Latin, Greek, or Cyrillic letters, there is no correspondence in sound, because Sequoyah could not read English. He developed his entire syllabary after simply being exposed to the idea of writing.

The idea of literacy has occurred independently only a few times in human history; the vast majority of people picked up alphabets from someone else. Our Alphabet comes from the Latins who got it from the Greeks who adopted it from the Phoenicians who got it from some proto-canaanite script writers, and even then literacy spread pretty slowly. The Cherokee, while not as technologically advanced as Europeans at the time, were already a nice agricultural society and clearly possessed the ability to become literate as soon as they were exposed to the idea.

When I walk around our cities, I often think about what their ruins will look like to explorers in a thousand years
We also pass a ruin of what once must have been a grand building. The walls are marked with logos from a Belgian University. This must have once been some scientific study centre of sorts.”

By contrast, there are many cases of people being exposed to or given a new technology but completely lacking the ability to functionally adopt, improve, or maintain it. The Democratic Republic of the Congo, for example, is full of ruined colonial-era buildings and roads built by outsiders that the locals haven’t maintained. Without the Belgians, the infrastructure has crumbled.

Likewise, contact between Europeans and groups like the Australian Aboriginees did not result in the Aboriginees adopting European technology nor a new and improved fusion of Aboriginee and European tech, but in total disaster for the Aboriginees. While the Japanese consistently top the charts in educational attainment, Aboriginee communities are still struggling with low literacy rates, high dropout rates, and low employment–the modern industrial economy, in short, has not been kind to them.

Along a completely different evolutionary pathway, cephalopods–squids, octopuses, and their tentacled ilk–are the world’s smartest invertebrates. This is pretty amazing, given that their nearest cousins are snails and clams. Yet cephalopod intelligence only goes so far. No one knows (yet) just how smart cephalopods are–squids in particular are difficult to work with in captivity because they are active hunter/swimmers and need a lot more space than the average aquarium can devote–but their brain power appears to be on the order of a dog’s.

After millions of years of evolution, cephalopods may represent the best nature can do–with an invertebrate. Throw in a backbone, and an animal can get a whole lot smarter.

And in chemistry, activation energy is the amount of energy you have to put into a chemical system before a reaction can begin. Stable chemical systems essentially exist at local optima, and it can require the input of quite a lot of energy before you get any action out of them. For atoms, iron is the global–should we say universal?–optimum, beyond which reactions are endothermic rather than exothermic. In other words, nuclear fusion at the core of the sun ends with iron; elements heavier than iron can only be produced when stars explode.

So what do local optima have to do with diversity?

The current vogue for diversity (“Diversity is our greatest strength”) suggests that we can reach global optima faster by simply smushing everyone together and letting them compare notes. Scroll back to the Japanese case. Edo Japan had a nice culture, but it was also beset by frequent famines. Meiji Japan doubled its population. Giving everyone, right now, the same technology and culture would bring everyone up to the same level.

But you can’t tell from within if you are at a local or global optimum. That’s how they work. The Indians likely would have never developed corn had they been exposed to wheat early on, and subsequently Europeans would have never gotten to adopt corn, either. Good ideas can take a long time to refine and develop. Cultures can improve rapidly–even dramatically–by adopting each other’s good ideas, but they also need their own space and time to pursue their own paths, so that good but slowly developing ideas aren’t lost.

Which gets us back to Patchwork.

Review: Numbers and the Making of Us, by Caleb Everett

I’m about halfway through Caleb Everett’s Numbers and the Making of Us: Counting and the Course of Human Cultures. Everett begins the book with a lengthy clarification that he thinks everyone in the world has equal math abilities, some of us just happen to have been exposed to more number ideas than others. Once that’s out of the way, the book gets interesting.

When did humans invent numbers? It’s hard to say. We have notched sticks from the Paleolithic, but no way to tell if these notches were meant to signify numbers or were just decorated.

The slightly more recent Ishango, Lebombo, and Wolf bones (30,000 YA, Czech Republic) seem more likely to indicate that someone was at least counting–if not keeping track–of something.

The Ishango bone (estimated 20,000 years old, found in the Democratic Republic of the Congo near the headwaters of the Nile,) has three sets of notches–two sets total to 60, the third to 48. Interestingly, the notches are grouped, with both sets of sixty composed of primes: 19 + 17 + 13 + 11 and 9 + 19 + 21 + 11. The set of 48 contains groups of 3, 6, 4, 8, 10, 5, 5, and 7. Aside from the stray seven, the sequence tantalizingly suggests that someone was doubling numbers.

Ishango Bone

The Ishango bone also has a quartz point set into the end, which perhaps allowed it to be used for scraping, drawing, or etching–or perhaps it just looked nice atop someone’s decorated bone.

The Lebombo bone, (estimated 43-44,2000 years old, found near the border between South Africa and Swaziland,) is quite similar to the Ishango bone, but only contains 29 notches (as far as we can tell–it’s broken.)

I’ve seen a lot of people proclaiming “Scientists think it was used to keep track of menstrual cycles. Menstruating African women were the first mathematicians!” so I’m just going to let you in on a little secret: scientists have no idea what it was for. Maybe someone was just having fun putting notches on a bone. Maybe someone was trying to count all of their relatives. Maybe someone was counting days between new and full moons, or counting down to an important date.

Without a far richer archaeological assembly than one bone, we have no idea what this particular person might have wanted to count or keep track of. (Also, why would anyone want to keep track of menstrual cycles? You’ll know when they happen.)

The Wolf bone (30,000 years old, Czech Republic,) has received far less interest from folks interested in proclaiming that menstruating African women were the first mathematicians, but is a nice looking artifact with 60 notches–notches 30 and 31 are significantly longer than the others, as though marking a significant place in the counting (or perhaps just the middle of the pattern.)

Everett cites another, more satisfying tally stick: a 10,000 year old piece of antler found in the anoxic waters of Little Salt Spring, Florida. The antler contains two sets of marks: 28 (or possibly 29–the top is broken in a way that suggests another notch might have been a weak point contributing to the break) large, regular, evenly spaced notches running up the antler, and a much smaller set of notches set beside and just slightly beneath the first. It definitely looks like someone was ticking off quantities of something they wanted to keep track of.

Here’s an article with more information on Little Salt Spring and a good photograph of the antler.

I consider the bones “maybes” and the Little Salt Spring antler a definite for counting/keeping track of quantities.

Inca Quipu

Everett also mentions a much more recent and highly inventive tally system: the Incan quipu.

A quipu is made of knotted strings attached to one central string. A series of knots along the length of each string denotes numbers–one knot for 1, two for 2, etc. The knots are grouped in clusters, allowing place value–first cluster for the ones, second for the tens, third for hundreds, etc. (And a blank space for a zero.)

Thus a sequence of 2 knots, 4 knots, a space, and 5 knots = 5,402

The Incas, you see, had an empire to administer, no paper, but plenty of lovely alpaca wool. So being inventive people, they made do.

Everett then discusses the construction of names for numbers/base systems in different languages. Many languages use a combination of different bases, eg, “two twos” for four, (base 2,) “two hands” to signify 10 (base 5,) and from there, words for multiples of 10 or 20, (base 10 or 20,) can all appear in the same language. He argues convincingly that most languages derived their counting words from our original tally sticks: fingers and toes, found in quantities of 5, 10, and 20. So the number for 5 in a language might be “one hand”, the number for 10, “Two hands,” and the number for 20 “one person” (two hands + two feet.) We could express the number 200 in such a language by saying “two hands of one person”= 10 x 20.

(If you’re wondering how anyone could come up with a base 60 system, such as we inherited from the Babylonians for telling time, try using the knuckles of the four fingers on one hand [12] times the fingers of the other hand [5] to get 60.)

Which begs the question of what counts as a “number” word (numeral). Some languages, it is claimed, don’t have words for numbers higher than 3–but put out an array of 6 objects, and their speakers can construct numbers like “three twos.” Is this a number? What about the number in English that comes after twelve: four-teen, really just a longstanding mispronunciation of four and ten?

Perhaps a better question than “Do they have a word for it,” is “Do they have a common, easy to use word for it?” English contains the world nonillion, but you probably don’t use it very often (and according to the dictionary, a nonillion is much bigger in Britain than in the US, which makes it especially useless.) By contrast, you probably use quantities like a hundred or a thousand all the time, especially when thinking about household budgets.

Roman Numerals are really just an advanced tally system with two bases: 5 and 10. IIII are clearly regular tally marks. V (5) is similar to our practice of crossing through four tally marks. X (10) is two Vs set together. L (50) is a rotated V. C (100) is an abbreviation for the Roman word Centum, hundred. (I, V, X, and L are not abbreviations.) I’m not sure why 500 is D; maybe just because D follows C and it looks like a C with an extra line. M is short for Mille, or thousand. Roman numerals are also fairly unique in their use of subtraction in writing numbers, which few people do because it makes addition horrible. Eg, IV and VI are not the same number, nor do they equal 15 and 51. No, they equal 4 (v-1) and 6 (v+1,) respectively. Adding or multiplying large Roman numerals quickly becomes cumbersome; if you don’t believe me, try XLVII times XVIII with only a pencil and paper.

Now imagine you’re trying to run an empire this way.

You’re probably thinking, “At least those quipus had a zero and were reliably base ten,” about now.

Interestingly, the Mayans (and possibly the Olmecs) already had a proper symbol that they used for zero in their combination base-5/base-20 system with pretty functional place value at a time when the Greeks and Romans did not (the ancient Greeks were philosophically unsure about this concept of a “number that isn’t there.”)

(Note: given the level of sophistication of Native American civilizations like the Inca, Aztec, and Maya, and the fact that these developed in near total isolation, they must have been pretty smart. Their current populations appear to be under-performing relative to their ancestors.)

But let’s let Everett have a chance to speak:

Our increasingly refined means of survival and adaptation are the result of a cultural ratchet. This term, popularized by Duke University psychologist and primatologist Michael Tomasello, refers to the fact that humans cooperatively lock in knowledge from one generation to the next, like the clicking of a ratchet. In other word, our species’ success is due in large measure to individual members’ ability to learn from and emulate the advantageous behavior of their predecessors and contemporaries in their community. What makes humans special is not simply that we are so smart, it is that we do not have to continually come up with new solutions to the same old problems. …

Now this is imminently reasonable; I did not invent the calculus, nor could I have done so had it not already existed. Luckily for me, Newton and Leibniz already invented it and I live in a society that goes to great lengths to encode math in textbooks and teach it to students.

I call this “cultural knowledge” or “cultural memory,” and without it we’d still be monkeys with rocks.

The importance of gradually acquired knowledge stored in the community, culturally reified but not housed in the mind of any one individual, crystallizes when we consider cases in which entire cultures have nearly gone extinct because some of their stored knowledge dissipated due to the death of individuals who served as crucial nodes in their community’s knowledge network. In the case of the Polar Inuit of Northwest Greenland, population declined in the mid-nineteenth century after an epidemic killed several elders of the community. These elders were buried along with their tool sand weapons, in accordance with local tradition, and the Inuits’ ability to manufacture the tools and weapons in question was severely compromised. … As a result, their population did not recover until about 40 years later, when contact with another Inuit group allowed for the restoration of the communal knowledge base.

The first big advance, the one that separates us from the rest of the animal kingdom, was language itself. Yes, other animals can communicate–whales and birds sing; bees do their waggle dance–but only humans have full-fledged, generative language which allows us to both encode and decode new ideas with relative ease. Language lets different people in a tribe learn different things and then pool their ideas far more efficiently than mere imitation.

The next big leap was the development of visual symbols we could record–and read–on wood, clay, wax, bones, cloth, cave walls, etc. Everett suggests that the first of these symbols were likely tally marks such us those found on the Lebombo bone, though of course the ability to encode a buffalo on the wall of the Lascaux cave, France, was also significant. From these first symbols we developed both numbers and letters, which eventually evolved into books.

Books are incredible. Books are like external hard drives for your brain, letting you store, access, and transfer information to other people well beyond your own limits of memorization and well beyond a human lifetime. Books reach across the ages, allowing us to read what philosophers, poets, priests and sages were thinking about a thousand years ago.

Recently we invented an even more incredible information storage/transfer device: computers/the internet. To be fair, they aren’t as sturdy as clay tablets, (fired clay is practically immortal,) but they can handle immense quantities of data–and make it searchable, an incredibly important task.

But Everett tries to claim that cultural ratchet is all there is to human mathematical ability. If you live in a society with calculus textbooks, then you can learn calculus, and if you don’t, you can’t. Everett does not want to imply that Amazonian tribesmen with no words for numbers bigger than three are in any way less able to do math than the Mayans with their place value system and fancy zero.

But this seems unlikely for two reasons. First, we know very well that even in societies with calculus textbooks, not everyone can make use of them. Even among my own children, who have been raised with about as similar an environment as a human can make and have very similar genetics, there’s a striking difference in intellectual strengths and weaknesses. Humans are not identical in their abilities.

Moreover, we know that different mental tasks are performed in different, specialized parts of the brain. For example, we decode letters in the “visual word form area” of the brain; people whose VWAs have been damaged can still read, but they have to use different parts of their brains to work out the letters and they end up reading more slowly than they did before.

Memorably, before he died, the late Henry Harpending (of West Hunter) had a stroke while in Germany. He initially didn’t notice the stroke because it was located in the part of the brain that decodes letters into words, but since he was in Germany, he didn’t expect to read the words, anyway. It was only when he looked at something written in English later that day that he realized he couldn’t read it, and soon after I believe he passed out and was taken to the hospital.

Why should our brains have a VWA at all? It’s not like our primate ancestors did a whole lot of reading. It turns out that the VWA is repurposed from the part of our brain that recognizes faces :)

Likewise, there are specific regions of the brain that handle mathematical tasks. People who are better at math not only have more gray matter in these regions, but they also have stronger connections between them, letting the work together in harmony to solve different problems. We don’t do math by just throwing all of our mental power at a problem, but by routing it through specific regions of our brain.

Interestingly, humans and chimps differ in their ability to recognize faces and perceive emotions. (For anatomical reasons, chimps are more inclined to identify each other’s bottoms than each other’s faces.) We evolved the ability to recognize faces–the region of our brain we use to decode letters–when we began walking upright and interacting to each other face to face, though we do have some vestigial interest in butts and butt-like regions (“My eyes are up here.”) Our brains have evolved over the millenia to get better at specific tasks–in this case, face reading, a precursor to decoding symbolic language.

And there is a tremendous quantity of evidence that intelligence is at least partly genetic–estimates for the heritablity of intelligence range between 60 and 80%. The rest of the variation–the environmental part–looks to be essentially random chance, such as accidents, nutrition, or perhaps your third grade teacher.

So, yes, we absolutely can breed people for mathematical or linguistic ability, if that’s what the environment is selecting for. By contrast, if there have been no particular mathematical or linguistic section pressures in an environment (a culture with no written language, mathematical notation, and very few words for numbers clearly is not experiencing much pressure to use them), then you won’t select for such abilities. The question is not whether we can all be Newtons, (or Leibnizes,) but how many Newtons a society produces and how many people in that society have the potential to understand calculus, given the chance.

I do wonder why he made the graph so much bigger than the relevant part
Lifted gratefully from La Griffe Du Lion’s Smart Fraction II article

Just looking at the state of different societies around the world (including many indigenous groups that live within and have access to modern industrial or post-industrial technologies), there is clear variation in the average abilities of different groups to build and maintain complex societies. Japanese cities are technologically advanced, clean, and violence-free. Brazil, (which hasn’t even been nuked,) is full of incredibly violent, unsanitary, poorly-constructed favelas. Some of this variation is cultural, (Venezuela is doing particularly badly because communism doesn’t work,) or random chance, (Saudi Arabia has oil,) but some of it, by necessity, is genetic.

But if you find that a depressing thought, take heart: selective pressures can be changed. Start selecting for mathematical and verbal ability (and let everyone have a shot at developing those abilities) and you’ll get more mathematical and verbal abilities.

But this is getting long, so let’s continue our discussion next week.

Unemployment, Disability, and Death

Source: NPR, Bureau of Labor Statistics, Social Security Administration
Credit: Lam Thuy Vo

I’ve been reading about the rise of disability, eg NPR’s Unfit for Work: The Startling Rise of Disability in America:

In the past three decades, the number of Americans who are on disability has skyrocketed… every month, 14 million people now get a disability check from the government. The federal government spends more money each year on cash payments for disabled former workers than it spends on food stamps and welfare combined. … The vast majority of people on federal disability do not work. Yet because they are not technically part of the labor force, they are not counted among the unemployed.

In other words, people on disability don’t show up in any of the places we usually look to see how the economy is doing. But the story of these programs — who goes on them, and why, and what happens after that — is, to a large extent, the story of the U.S. economy. It’s the story not only of an aging workforce, but also of a hidden, increasingly expensive safety net.

A friend of mine was homeless for a couple of decades. During that time he was put on disability. To this day, he doesn’t know why. He kept trying to fight it. It offended his sensibilities that some bureaucrat thought he was “disabled.” He wanted to prove to them that he was able, that he could still work and do valuable things.

He eventually ended up with full-blown schizophrenia, so the government official was probably correct in the first place–people who are homeless for multiple years tend to have something wrong with them, even if they themselves don’t recognize it. But he didn’t have schizophrenia then. Then he was just poor, and “disability” is backup welfare for the poor.

If that doesn’t seem obvious, ask yourself what disability means. For the government, disability isn’t a matter of how much pain you’re in or how many limbs you have; it’s a matter of whether you’re too impaired to work.

The article points out that “unemployment” numbers are kept artificially low by not counting the disabled among the unemployed, even though many of the “disabled” are really “people who can’t get job”:

There’s a story we hear all the time these days that doesn’t, on its face, seem to have anything to do with disability: Local Mill Shuts Down. Or, maybe: Factory To Close. …

But after I got interested in disability, I followed up with some of the guys to see what happened to them after the mill closed. One of them, Scott Birdsall, went to lots of meetings where he learned about retraining programs and educational opportunities. At one meeting, he says, a staff member pulled him aside.

“Scotty, I’m gonna be honest with you,” the guy told him. “There’s nobody gonna hire you … We’re just hiding you guys.” The staff member’s advice to Scott was blunt: “Just suck all the benefits you can out of the system until everything is gone, and then you’re on your own.”

Scott, who was 56 years old at the time, says it was the most real thing anyone had said to him in a while.

There used to be a lot of jobs that you could do with just a high school degree, and that paid enough to be considered middle class. I knew, of course, that those have been disappearing for decades. What surprised me was what has been happening to many of the people who lost those jobs: They’ve been going on disability.

Note: the text string “imm” does not appear anywhere in the article.

In Hale County, Alabama, nearly 1 in 4 working-age adults is on disability.

Source: NPR Bureau of Labor Statistics, Social Security Administration
Credit: Lam Thuy Vo

As the article discusses, since the definition of “disabled” depends on your ability to get (or not) jobs, it depends, in turn, on the kinds of jobs a person is qualified to work. A programmer who has lost both legs in an accident can, with a few accommodations, still program perfectly well, whereas a farmer who needs to be able to do manual labor all day cannot. It’s easier to work despite a back problem if you have a college degree and can qualify for a white-collar job where you can sit down for most of the day. It’s harder if you have to carry heavy objects.

If you have a back problem and the only work you can get involves standing and carrying heavy things, well, that’s going to hurt.

Humans are fine at standing. Being on your feet a lot isn’t abstractly a problem. The Amish do tons of manual labor and they’re fine. But the Amish get to take bathroom breaks whenever they want. They can stretch or sit down if they need to. They get to dictate their own movements.

If you’re working at McDonald’s, your movements are dictated by the needs of the kitchen and the pace of the customers.

And that’s assuming you can get a job:

[Scott] took the advice of the rogue staffer who told him to suck all the benefits he could out of the system. He had a heart attack after the mill closed and figured, “Since I’ve had a bypass, maybe I can get on disability, and then I won’t have worry to about this stuff anymore.” It worked; Scott is now on disability.

Scott’s dad had a heart attack and went back to work in the mill. If there’d been a mill for Scott to go back to work in, he says, he’d have done that too. But there wasn’t a mill, so he went on disability. It wasn’t just Scott. I talked to a bunch of mill guys who took this path — one who shattered the bones in his ankle and leg, one with diabetes, another with a heart attack. When the mill shut down, they all went on disability.

Source: NPR Bureau of Labor Statistics, Social Security Administration
Credit: Lam Thuy Vo

The human body isn’t designed to stand in one place all day. We’re designed to move. A strong or desperate person can do it,but the vast majority find it unpleasant or painful. Do it for years, combine it with another condition, close the factory… and you’ll find a lot of people willing to take that disability check over moving to a new city to try their luck at the next factory, again and again and again as each factory shuts down, moves, or fires everyone and replaces them with immigrants willing to work for wages that make disability sound attractive:

But disability has also become a de facto welfare program for people without a lot of education or job skills. … Once people go onto disability, they almost never go back to work. Fewer than 1 percent of those who were on the federal program for disabled workers at the beginning of 2011 have returned to the workforce since then, one economist told me.

People who leave the workforce and go on disability qualify for Medicare… They also get disability payments from the government of about $13,000 a year. This isn’t great. But if your alternative is a minimum wage job that will pay you at most $15,000 a year, and probably does not include health insurance, disability may be a better option.

But, in most cases, going on disability means you will not work, you will not get a raise, you will not get whatever meaning people get from work. Going on disability means, assuming you rely only on those disability payments, you will be poor for the rest of your life. That’s the deal. And it’s a deal 14 million Americans have signed up for.

I know people who’ve taken this deal. The really sad part is the despair. When people are filing for disability, it means they’ve given up. It’s like we decided to have Universal Basic Income, only we structured it the wort way possible to make recipients miserable.

I mean, this is AMERICA. Our ancestors were PIONEERS. They BUILT this place from the ground up.
My grandmother still lives in the house my grandfather built. Nearby, you can still visit the house my great-grandfather built. Those houses have all sorts of oddities because they were built by hand with whatever was available.

And say what you will, much of America is still beautiful. Forests mountains lakes rivers grasslands deserts. Beautiful.

An elderly woman I know lives in an an area with stunning natural beauty. “I hate it here,” she complains. Why? Is she blind? People stay inside and watch TV and grow lonelier.

I saw this “wine glass” at the store last night.

It was advertised as “for mom!” because what every kid wants is a drunk, alcoholic caregiver.

The marketing of chic-tee-hee isn’t it cute that we’re alcoholics? alcoholism to women is disgusting. It’s a sign of how far we’ve sunk that people see this as funny instead of a desperate cry for help.

And I don’t think I need to delve into the statistics on the opiate crisis and rising death rates among younger white women. All of the people who’ve lost their lives to drug addictions.

. Most of you live near museums, rivers, forests, parks, or other lovely places.

I can’t solve our problems. But please, don’t stop living. Keep fighting.

Homeschooling Corner: Erdos, Fibonacci, and some Really Big Numbers

One of the nice things about homeschooling is that it is very forgiving of scheduling difficulties and emergencies. Everyone exhausted after a move or sickness? It’s fine to sleep in for a couple of days. Exercises can be moved around, schedules sped up or slowed down as needed.

This week we finished some great books (note: I always try to borrow books from the library before considering buying them. Most of these are fun, but not books you’d want to read over and over):

The Boy who Loved Math: The Improbable Life of Paul Erdos, by Deborah Heligman, was a surprise hit. I’ve read a bunch of children’s biographies and been consistently disappointed; the kids loved this one. Improbable, I know.

I suppose the moral of the story is that kids are likely to enjoy a biography if they identify with the subject. The story starts with Erdos as a rambunctious little boy who likes math but ends up homeschooled because he can’t stand regular school. My kids identified with this pretty strongly.

The illustrations are nice and each page contains some kind of hidden math, like a list of primes.

Professor Astro Cat’s Frontiers of Space, by Dominic Walliman. This is a lovely book appropriate for kids about 6-11, depending on attention span and reading level. We’ve been reading a few pages a week and recently reached the end.

Minecraft Math with Steve, by Steve Math. This book contains 30 Minecraft-themed math problems (with three sub-problems each, for 90 total.) They’re fairly simple multiplication, subtraction, division, and multiplication problems, probably appropriate for kids about second grade or third grade. A couple of sample problems:

Steve wants to collect 20+20 blocks of sand. how much is that total?

Steve ends up with 42 blocks of sand in his inventory. He decides that is too much so drops out 12 blocks. How many blocks remain?

A bed requires 3 wood plank and 3 wools. If Steve has 12 wood planks and 12 wools, how many beds can he build?

This is not a serious math book and I doubt it’s “Common Core Compliant” or whatever, but it’s cute and if your kids like Minecraft, they might enjoy it.

We are partway into Why Pi? by Johnny Ball. It’s an illustrated look at the history of mathematics with a ton of interesting material. Did you know the ancient Greeks used math to calculate the size of the Earth and distance between the Earth and the moon? And why are there 360 degrees in a circle? This one I’m probably going to buy.

Really Big Numbers, by Richard Evan Schwartz. Previous books on “big numbers” contained, unfortunately, not enough big numbers, maxing out around a million. A million might have seemed really good to kids of my generation, but to today’s children, reared on Numberphile videos about Googols and Graham’s number, a million is positively paltry. Really Big Numbers delivers with some really big numbers.

Let’s Estimate: A book about Estimating and Rounding Numbers, by David A. Adler. A cute, brightly illustrated introduction. I grabbed notebooks and pens and made up sample problems to help the kids explore and reinforce the concepts as we went.

How Big is Big? How Far is Far? by Jen Metcalf. This is like a coffee table book for 6 yr olds. The illustrations are very striking and it is full of fascinating information. The book focuses both on relative and absolute measurement. For example,  5’9″ person is tall compared to a cat, but short compared to a giraffe. The cat is large compared to a fly, and the giraffe is small compared to a T-rex. My kids were especially fascinated by the idea that clouds are actually extremely heavy.

Blockhead: The Life of Fibonacci, by Joseph D’Agnes. If your kids like Fibonacci numbers (or they enjoyed the biography of Erdos,) they might enjoy this book. It also takes a look at the culture of Medieval Pisa and the adoption of Arabic numerals (clunkily referred to in the text as “Hindu-Arabic numerals,” a phrase I am certain Fibonacci never used.) Fibonacci numbers are indeed found all over in nature, so if you have any sunflowers or pine cones on hand that you can use to demonstrate Fibonacci spirals, they’d be a great addition to the lesson. Otherwise, you can practice drawing boxes with spirals in them or Pascal’s triangles. (This book has more kid-friendly math in it than Erdos’s)

Pythagoras and the Ratios, by Julie Ellis. Pythagoras and his cousins need to cut their panpipes and weight the strings on their lyres in certain ratios to make them produce pleasant sounds. It’s a fun little lesson about ratios, and if you can combine it with actual pipes the kids can cut or recorders they could measure, glasses with different amounts of water in them or even strings with rock hanging from them, that would probably be even better.

Older than Dirt: A Wild but True History of Earth, by Don Brown. I was disappointed with this book. It is primarily an overview of Earth’s history before the dinosaurs, which was interesting, but the emphasis on mass extinctions and volcanoes (eg, Pompeii) dampened the mood. I ended up leaving out the last few pages (“Book’s over. Bedtime!”) to avoid the part about the sun swallowing up the earth and all life dying at the end of our planet’s existence, which is fine for older readers but not for my kids.

Hope you received some great games and books last month!

Book on a Friday: Squid Empire: The Rise and Fall of the Cephalopods by Danna Staaf

Danna Staaf’s Squid Empire: The Rise and Fall of the Cephalopods is about the evolution of squids and their relatives–nautiluses, cuttlefish, octopuses, ammonoids, etc. If you are really into squids or would like to learn more about squids, this is the book for you. If you aren’t big on reading about squids but want something that looks nice on your coffee table and matches your Cthulhu, Flying Spaghetti Monster, and 20,000 Leagues Under the Sea decor, this is the book for you. If you aren’t really into squids, you probably won’t enjoy this book.

Squids, octopuses, etc. are members of the class of cephalopods, just as you are a member of the class of mammals. Mammals are in the phylum of chordates; cephalopods are mollusks. It’s a surprising lineage for one of Earth’s smartest creatures–80% mollusk species are slugs and snails. If you think you’re surrounded by idiots, imagine how squids must feel.

The short story of cephalopodic evolution is that millions upon millions of years ago, most life was still stuck at the bottom of the ocean. There were some giant microbial mats, some slugs, some snails, some worms, and not a whole lot else. One of those snails figured out how to float by removing some of the salt from the water inside its shell, making itself a bit buoyant. Soon after its foot (all mollusks have a “foot”) split into multiple parts. The now-floating snail drifted over the seafloor, using its new tentacles to catch and eat the less-mobile creatures below it.

From here, cephalopods diversified dramatically, creating the famous ammonoids of fossil-dating lore.

Cross-section of a fossilized ammonite shell, revealing internal chambers and septa

Ammonoids are known primarily from their shells (which fossilize well) rather than their fleshy tentacle parts, (which fossilize badly). But shells we have in such abundance they can be easily used for dating other nearby fossils.

Ammonoids are obviously similar to their cousins, the lovely chambered nautiluses. (Please don’t buy nautilus shells; taking them out of their shells kills them and no one farms nautiluses so the shell trade is having a real impact on their numbers. We don’t need their shells, but they do.)

Ammonoids succeeded for millions of years, until the Creatceous extinction event that also took out the dinosaurs. The nautiluses survived–as the author speculates, perhaps because they lay large eggs with much more yolk that develop very slowly, infant nautiluses were able to wait out the event while ammonoids, with their fast-growing, tiny eggs dependent on feeding immediately after hatching simply starved in the upheaval.

In the aftermath, modern squids and octopuses proliferated.

How did we get from floating, shelled snails to today’s squishy squids?

The first step was internalization–cephalopods began growing their fleshy mantles over their shells instead of inside of them–in essence, these invertebrates became vertebrates. Perhaps this was some horrible genetic accident, but it worked out. These internalized shells gradually became smaller and thinner, until they were reduced to a flexible rod called a “pen” that runs the length of a squid’s mantle. (Cuttlefish still retain a more substantial bone, which is frequently collected on beaches and sold for birds to peck at for its calcium.)

With the loss of the buoyant shell, squids had to find another way to float. This they apparently achieved by filling themselves with ammonia salts, which makes them less dense than water but also makes their decomposition disgusting and renders them unfossilizable because they turn to mush too quickly. Octopuses, by contrast, aren’t full of ammonia and so can fossilize.

Since the book is devoted primarily to cephalopod evolution rather than modern cephalopods, it doesn’t go into much depth on the subject of their intelligence. Out of all the invertebrates, cephalopods are easily the most intelligent (perhaps really the only intelligent invertebrates). Why? If cephalopods didn’t exist, we might easily conclude that invertebrates can’t be intelligent–invertebrateness is somehow inimical to intelligence. After all, most invertebrates are about as intelligent as slugs. But cephalopods do exist, and they’re pretty smart.

The obvious answer is that cephalopods can move and are predatory, which requires bigger brains. But why are they the only invertebrates–apparently–who’ve accomplished the task?

But enough jabber–let’s let Mrs. Staaf speak:

I find myself obliged to address the perennial question: “octopuses” or “octopi”? Or, heaven help us, “octopodes”?

Whichever you like best. Seriously. Despite what you may have heard, “octopus” is neither ancient Greek nor Latin. Aristotle called the animal polypous for its “many feet.” The ancient Romans borrowed this word and latinized the spelling to polypus. It was much later that a Renaissance scientists coined and popularized the word “octopus,” using Greek roots for “eight” and “foot” but Latin spelling.

If the word had actually been Greek, it would be spelled octopous and pluralized octopodes. If translated into Latin, it might have become octopes and pluralized octopedes,  but more likely the ancient Roman would have simply borrowed the Greek word–as they did with poly pus. Those who perhaps wished to appear erudite used the Greek plural polypodes, while others favored a Latin ending and pluralized it polypi.

The latter is a tactic we English speakers emulate when we welcome “octopus” into our own language and pluralize it “octopuses” as I’ve chosen to do.

There. That settles it.

Dinosaurs are the poster children for evolution and extinction writ large…

Of course, not all of them did die. We know now that birds are simply modern dinosaurs, but out of habit we tend to reserve the word “dinosaur for the hug ancient creatures that went extinct at the end of the Cretaceous. After all, even if they had feathers, they seem so different from today’s finches and robins. For one thing, the first flying feathered dinosaurs all seem to have had four wings. There aren’t any modern birds with four wings.

Wesl… actually, domestic pigeons can be bred to grow feathers on their legs. Not fuzzy down, but long flight feathers, and along with these feathers their leg bones grow more winglike. The legs are still legs’ they can’t be used to fly like wings. They do, however, suggest a clear step along the road from four-winged dinosaurs to two-winged birds. The difference between pigeons with ordinary legs and pigeons with wing-legs is created by control switches in their DNA that alter the expression of two particular genes. These genes are found in all birds, indeed in all vertebrates,and so were most likely present in dinosaurs as well.

…and I’ve just discovered that almost all of my other bookmarks fell out of the book. Um.

So squid brains are shaped like donuts because their eating/jet propulsion tube runs through the middle of their bodies and thus through the middle of their brains. It seems like this could be a problem if the squid eats too much or eats something with sharp bits in it, but squids seem to manage.

Squids can also leap out of the water and fly through the air for some ways. Octopuses can carry water around in their mantles, allowing them to move on dry land for a few minutes without suffocating.

Since cephalopods are somewhat unique among mollusks for their ability to move quickly, they have a lot in common, genetically, with vertebrates. In essence, they are the most vertebrate-behaving of the mollusks. Convergent evolution.

The vampire squid, despite its name, is actually more of an octopus.

Let me quote from the chapter on sex and babies:

This is one arena in which cephalopods, both ancient and modern, are actually less alien than many aliens–even other mollusks. Slugs, for instance, are hermaphroditic, and in the course of impregnating each other their penises sometimes get tangled, so they chew them off. Nothing in the rest of this chapter will make you nearly that uncomfortable. …

The lovely argonaut octopus

In one living coleoid species, however, sex is blindingly obvious. Females of the octopus known as an argonaut are five times larger than males. (A killer whale is about five times larger than an average adult human, which in turn is about five times large than an opossum.)

This enormous size differential caught the attention of paleontologists who had noticed that many ammonoid species also came in two distinct size, which htey had dubbed microconch (little shell) and macroconch (big shell). Bot were clearly mature, as they had completed the juvenile part of the shell and constructed the final adult living chamber. After an initial flurry of debate, most researchers agreed to model ammonoid sex on modern argonauts, and began to call macroconchs females and microconcs males.

Some fossil nautiloids also come in macroconch and microchonch flavors, though it’s more difficult to be certain that both are adults…

However, the shells of modern nautiluses show the opposite pattern–males are somewhat large than females… Like the nautiloid shift from ten arms to many tens of arms, the pattern could certainly have evolved from a different ancestral condition. If we’re going to make that argument, though, we have to wonder when nautliloids switched from females to males as the larger sex, and why.

In modern species that have larger females, we usually assume the size difference has to do with making or brooding a lot of eggs.Female argonauts take it up a notch and actually secrete a shell-like brood chamber from their arms, using it to cradle numerous batch of eggs over their lifetime. meanwhile, each tiny male argonaut get ot mate only once. His hectocotylus is disposable–after being loaded with sperm and inserted into the female, it breaks off. …

By contrast, when males are the bigger sex, we often guess that the purpose is competition. Certainly many species of squid and cuttlefish have large males that battle for female attention on the mating grounds. They display outrageous skin patterns as they push, shove, and bite each other. Females do appear impressed; at least, they mate with the winning males and consent to be guarded by them. Even in these species, though, there are some mall males who exhibit a totally different mating strategy. While the big males strut their stuff, these small males quietly sidle up to the females, sometimes disguising themselves with female color patterns. This doesn’t put off the real females, who readily mate with these aptly named “sneaker males.” By their very nature, such obfuscating tactics are virtually impossible to glean from the fossil record…

More on octopus mating habits.

This, of course, reminded me of this graph:

In the majority of countries, women are more likely to be overweight than men (suggesting that our measure of “overweight” is probably flawed.) In some countries women are much more likely to be overweight, while in some countries men and women are almost equally likely to be overweight, and in just a few–the Czech Republic, Germany, Hungary, Japan, and barely France, men are more likely to be overweight.

Is there any rhyme or reason to this pattern? Surely affluence is related, but Japan, for all of its affluence, has very few overweight people at all, while Egypt, which is pretty poor, has far more overweight people. (A greater % of Egyptian women are overweight than American women, but American men are more likely to be overweight than Egyptian men.)

Of course, male humans are still–in every country–larger than females. Even an overweight female doesn’t necessarily weigh more than a regular male. But could the variation in male and female obesity rates have anything to do with historic mating strategies? Or is it completely irrelevant?

Back to the book:

Coleoid eyes are as complex as our own, with a lens for focusing light, a retina to detect it, and an iris to sharpen the image. … Despite their common complexity, though, there are some striking differences [between our and squid eyes]. For Example, our retina has a blind spot whee a bundle of nerves enters the eyeball before spreading out to connect to the font of every light receptor. By contrast, light receptors in the coleoid retina are innervated from behind, so there’s no “hole” or blind spot. Structural differences like this how that the two groups converged on similar solution through distinct evolutionary pathways.

Another significant difference is that fish went on to evolve color vision by increasing the variety of light-sensitive proteins in their eyes; coleoids never did and are probably color blind. I say “probably ” because the idea of color blindness in such colorful animals has flummoxed generations of scientists…

“I’m really more of a cuddlefish”

Color-blind or not, coleoids can definitely see something we humans are blind to: the polarization of light.

Sunlight normally consists of waves vibrating in all directions. but when these waves are reflected off certain surface, like water, they get organized and arrive at the retina vibrating in only one direction. We call this “glare” and we don’t like it, so we invented polarized sunglasses. … That’s pretty much all polarized sunglasses can do–block polaraized light. Sadly, they can’t help you decode the secret messages of cuttlefish, which have the ability to perform a sort of double0-talk with their skin, making color camouflage for the befit of polarization-blind predators while flashing polarized displays to their fellow cuttlefish.

That’s amazing. Here’s an article with more on cuttlefish vision and polarization.

Overall, I enjoyed this book. The writing isn’t the most thrilling, but the author has a sense of humor and a deep love for her subject. I recommend it to anyone with a serious hankering to know more about the evolution of squids, or who’d like to learn more about an ancient animal besides dinosaurs.