# Homeschooling Corner: A Mathematician’s Lament, by Paul Lockhart

Paul Lockhart’s A Mathematician’s Lament: How School Cheats us of our Most Fascinating and Imaginative Artform is a short but valuable book, easily finished in an afternoon.

Lockhart’s basic take is that most of us have math backwards. We approach (and thus teach) it as useful but not fun–something to be slogged through, memorized, and then avoided as much as possible. By contrast, Lockhart sees math as more fun than useful.

I do not mean that Lockhart denies the utility of balancing your checkbook or calculating how much power your electrical grid can handle, but most of the math actual mathematicians do isn’t practical. They do it because they enjoy it; they love making patterns with numbers and shapes. Just because paint has a very practical use in covering houses doesn’t mean we shouldn’t encourage kids to enjoy painting pictures; similarly, Lockhart wants kids to see mathematics as fun.

But wait, you say, what if this loosey-goosey, free-form, new math approach results in kids who spend a lot of time trying to re-derive pi from first principles but never really learning algebra? Lockhart would probably counter that most kids never truly master algebra anyway, so why make them hate it in the process? Should we only let kids who can paint like the Masters take art class?

If you and your kids already enjoy math, Lockhart may just reinforce what you already know, but if you’re struggling or math is a bore and a chore, Lockhart’s perspective may be just what you need to turn things around and make math fun.

For example: There are multiple ways to group the numbers during double-digit multiplication, all equally “correct”; the method you chose is generally influenced by things like your familiarity with double-digit multiplication and the difficulty of the problem. When I observed one of my kids making errors in multiplication because of incorrect regrouping, I showed them how to use a more expanded way of writing out the numbers to make the math clearer–promptly eliciting protests that I was “doing it wrong.” Inspired by Lockhart, I explained that “There is no one way to do math. Math is the art of figuring out answers, and there are many ways to get from here to there.” Learning how to use a particular approach—“Put the numbers here, here, and here and then add them”–is useful, but should not be elevated above using whatever approach best helps the child understand the numbers and calculate the correct answers.

The only difficulty with Lockhart’s approach is figuring out what to actually do when you sit down at the kitchen table with your kids, pencil and paper in hand. The book has a couple of sample lessons but isn’t a full k-12 curriculum. It’s easy to say, “I’m going to do a free-form curriculum that requires going to the library every day and uses every experience as a learning opportunity,” and rather harder to actually do it. With a set curriculum, you at least know, “Here’s what we’re going to do today.”

My own personal philosophy is that school time should be about 50% formal instruction and 50% open-ended exploration. Kids need someone to explain how the alphabet works and what these funny symbols on the math worksheet mean; they also need time to read fun books and play with numbers. They should memorize their times tables, but a good game can make times tables fun. In short, I think kids should have both a formal, straightforward curriculum or set of workbooks (I have not read enough math textbooks to recommend any particular ones,) and a set of math enrichment activities, like tangrams, pattern blocks, reading about Penrose the Mathematical Cat, or watching Numberphile on YouTube.

(Speaking of Penrose, I thought the chapter on binary went right over my kids’ heads, but yesterday they returned all of their answers in math class in binary, so I guess they picked up more than I gave them credit for.)

YouCubed.org is an interesting website I recently discovered. So far we’ve only done two of the activities, but they were cute and I suspect the website will make a useful addition to our lessons. If you’ve used it, I’d love to hear your thoughts on it.

That’s all for now. Happy learning!

# Anthropology Friday: Japan pt 4/4

Welcome back to Anthropology Friday. Today we are finishing up with Sidney L. Gulick’s Evolution of the Japanese, Social and Psychic, published in 1903. Gulick was a Puritan missionary who moved to Japan shortly after the “opening of Japan” and Meiji Restoration. He wrote at a time when very Japanese society was changing at break-neck speed and very few accounts of Japan existed at all in the West.

I find anthropology interesting on two levels. First, there is the pure information about another culture, and second, the meta-information about the author–what leads the author to highlight particular things or portray a culture a particular way?

As Gulick makes clear, his purposes in writing the book were two-fold: to introduce his audience to a little-known culture and to provide evidence against the theory that different races have particular temperaments by highlighting differences between the Japanese and Chinese. Gulick attributes attributes maters of national character to environmental or economic conditions.

(As usual, quotes will be in “” instead of blocks)

The Development of a sense of moral obligation to those outside one’s own group:

“Are Japanese cruel or humane? The general impression of the casual tourist doubtless is that they are humane. They are kind to children on the streets, to a marked degree; the jinrikisha runners turn out not only for men, women, and children, but even for dogs. The patience, too, of the ordinary Japanese under trying circumstances is marked; they show amazing tolerance for one another’s failings and defects, and their mutual helpfulness in seasons of distress is often striking. To one traveling through New Japan there is usually little that will strike the eye as cruel.

“But the longer one lives in the country, the more is he impressed with certain aspects of life which seem to evince an essentially unsympathetic and inhumane disposition. I well remember the shock I received when I discovered, not far from my home in Kumamoto, an insane man kept in a cage. He was given only a slight amount of clothing, even though heavy frost fell each night. Food was given him once or twice a day. He was treated like a wild animal, not even being provided with bedding. …

“The treatment accorded to lepers is another significant indication of the lack of sympathetic and humane sentiments among the people at large. For ages they have been turned from home and house and compelled to wander outcasts, living in the outskirt of the villages in rude booths of their own construction, and dependent on their daily begging, until a wretched death gives them relief from a more wretched life. So far as I have been able to learn, the opening of hospitals for lepers did not take place until begun by Christians in recent times.

“A history of Japan was prepared by Japanese scholars under appointment from the government and sent to the Columbian Exposition in 1893; it makes the following statement, already referred to on a previous page: “Despite the issue of several proclamations … people were governed by such strong aversion to the sight of sickness that travelers were often left to die by the roadside from thirst, hunger, or disease, and householders even went to the length of thrusting out of doors and abandoning to utter destitution servants who suffered from chronic maladies…. Whenever an epidemic occurred, the number of deaths that resulted was enormous.”[N]

“But we must not be too quick to jump to the conclusion that in this regard we have discovered an essential characteristic of the Japanese nature. …

“How long is it since the Inquisition was enforced in Europe? Who can read of the tortures there inflicted without shuddering with horror? … How long is it since witches were burned, not only in Europe by the thousand, but in enlightened and Christian New England? … How long is it since slaves were feeling the lash throughout the Southern States of our “land of freedom”?… The fact is that the highly developed humane sense which is now felt so strongly by the great majority of people in the West is a late development, and is not yet universal. It is not for us to boast, or even to feel superior to the Japanese, whose opportunities for developing this sentiment have been limited. …

“In the treatment of the sick, the first prerequisite for the development of tenderness is the introduction of correct ideas as to the nature of disease and its proper treatment. As soon as this has been effectually done, a great proportion of the apparent indifference to human suffering passes away. The cruelty which is to-day so universal in Africa needs but a changed social and industrial order to disappear. The needed change has come to Japan. Physicians trained in modern methods of medical practice are found all over the land. In 1894 there were 597 hospitals, 42,551 physicians, 33,921 nurses and midwives, 2869 pharmacists, and 16,106 druggists, besides excellent schools of pharmacy and medicine.[O]

EvX: This might feel a bit unfair to Japan, but Gulick was writing not long before Japan went on a rampage through east Asia and killed 10-14 million people.

Gulick is also correct that uncharitable attitudes toward folks not in one’s family or ingroup were fairly common in the West until fairly recently. The past 200 years or so have seen a remarkable change in ideas about one’s moral obligations toward strangers.

Aesthetics

“In certain directions, the Japanese reveal a development of æsthetic taste which no other nation has reached. The general appreciation of landscape-views well illustrates this point. The home and garden of the average workman are far superior artistically to those of the same class in the West. There is hardly a home without at least a diminutive garden laid out in artistic style with miniature lake and hills and winding walks. …

“The general taste displayed in many little ways is a constant delight to the Western “barbarian” when he first comes to Japan. Nor does this delight vanish with time and familiarity, though it is tempered by a later perception of certain other features. Indeed, the more one knows of the details of their artistic taste, the more does he appreciate it. The “toko-no-ma,” for example, is a variety of alcove usually occupying half of one side of a room. It indicates the place of honor, and guests are always urged to sit in front of it. The floor of the “toko-no-ma” is raised four or five inches above the level of the room and should never be stepped upon. In this “toko-no-ma” is usually placed some work of art, or a vase with flowers, and on the wall is hung a picture or a few Chinese characters, written by some famous calligraphist, which are changed with the seasons. The woodwork and the coloring of this part of the room is of the choicest. The “toko-no-ma” of the main room of the house is always restful to the eye; this “honorable spot” is found in at least one room in every house…

“The Japanese show a refined taste in the coloring and decoration of rooms; natural woods, painted and polished, are common; every post and board standing erect must stand in the position in which it grew. A Japanese knows at once whether a board or post is upside down, though it would often puzzle a Westerner to decide the matter. The natural wood ceilings and the soft yellows and blues of the walls are all that the best trained Occidental eye could ask. Dainty decorations called the “ramma,” over the neat “fusuma,” consist of delicate shapes and quaint designs cut in thin boards, and serve at once as picture and ventilator. The drawings, too, on the “fusuma” (solid thick paper sliding doors separating adjacent rooms or shutting off the closet) are simple and neat, as is all Japanese pictorial art.

“Japanese love for flowers reveals a high æsthetic development. Not only are there various flower festivals at which times the people flock to suburban gardens and parks, but sprays, budding branches, and even large boughs are invariably arranged in the homes and public halls. Every church has an immense vase for the purpose. The proper arrangement of flowers and of flowering sprays and boughs is a highly developed art. … An acquaintance of mine glories in 230 varieties of the plum tree, all in pots, some of them between two and three hundred years old. Shinto and Buddhist temples also reveal artistic qualities most pleasing to the eye.”

EvX: And on that pleasant note, let us end our Japanese journey. See you next Friday.

# Cathedral Round-Up #28: They’re not coming for George Washington, that’s just a silly right-wing conspiracy–

Is that… George Washington? With rusty nails pounded into his face?

Holding up “cascading fragments of his slave records.”

Oh. I see.

Carry on, then.

I was going to write about Harvard forbidding its female students from forming female-only safe spaces (College will Debut Plans to Enforce Sanctions Next Semester) in an attempt to shut down all single-gender frats and Finals Clubs, but then Princeton upped the ante with Can Art Amend Princeton’s History of Slavery?

No. Of course not.

Princeton University [has] a new public-art project that confronts the school’s participation in the nation’s early sins. On Monday, the university unveiled Impressions of Liberty, by the African American artist Titus Kaphar. The sculpture is the conceptual core of a campus-wide initiative that begins this fall and aims to reconcile the university’s ties to slavery. The Princeton and Slavery Project’s website has released hundreds of articles and primary documents about slavery and racism at Princeton…

Attaching strips of canvas or other material to the faces of people he disapproves of is apparently one of Kaphar’s shticks.

I’m old enough to remember when George Washington was admired for freeing all of his slaves in an era when most people took slavery for granted. Today he is castigated for not having sprung from the womb with a fully modern set of moral opinions.

Impressions of Liberty is Kaphar’s portrait of Samuel Finley–fifth president and one of the original trustees of Princeton (1761-1766)–interwoven with photographs of black actors in historical dress etched in glass.

For generations, slave-owning Christians—including Princeton’s founders—used religious ideas to justify a horrific national practice, [Kaphar] noted; Finley is holding a bible in Impressions of Liberty.

Note the framing: yes, Christians used religion to justify owning slaves. So did Muslims, Jews, Hindus, Buddhists, pagans, and atheists. There’s nothing unique about Christians and slavery aside from the fact that Finley was Christian. No mention is made of pagan Africans who captured and sold each other into slavery, nor of Muslims who raided Africa and Europe in search of slaves. There were Jewish slave merchants and Confederates, as well, for slavery was a near-universal practice justified by people all over the world prior to its abolition by whites in the 1800s. The article mentions none of that; only Christians are singled out for criticism.

The article doesn’t say how much Princeton paid for the sculpture it commissioned to castigate the memory of one of its founders. The work currently stands outside MacLean House, but will soon be moved indoors, to Princeton’s permanent art collection. MacLean House–completed in 1756–is a national landmark that was home to Princeton’s first presidents, including Samuel Finley. It also housed George Washington during the Battle of Princeton.

According to the article:

On the one hand, according to records, Princeton was a bastion of liberty, educating numerous Revolutionary War leaders and in 1783 hosting the Continental Congress… At the same time, Sandweiss found that the institution’s first nine presidents all owned slaves at some point, as did the school’s early trustees. She also discovered that the school enrolled a significant number of anti-abolitionist, Southern students during its early years; an alumni delivered a pro-slavery address at the school’s 1850 commencement ceremony. …

Princeton’s racist history enabled it to provide social and political benefits for alumni—an advantage that students will continue to enjoy well into the future.

While I happen to think that universities have it much too good these days and deserve to be taken down a notch, I find this claim extremely dubious. Harvard and Yale are located in staunchly abolitionist New England and had very few ties to slavery, (Mr. Yale apparently knew a guy who had slaves, and Harvard Law School received some money from a guy who had slaves,) yet these schools are arguably even wealthier and more powerful than closer-to-the-South and more-tied-to-slavery Princeton. Stanford was founded after slavery was outlawed, and yet its students enjoy social and political benefits on par with Princeton’s.

We could argue that the entire area of the Confederacy reaped the economic benefits of slavery, yet today this region is much poorer than the Free States of the North. There isn’t just no correlation between slavery, wealth, and power–there’s actually a negative correlation. Slavery, if it has any effect at all, makes a region poorer and weaker.

… Princeton University is spreading the mission across various pieces of art through a show this fall entitled “Making History Visible: Of American Myths And National Heroes.” At the exhibit’s entrance, viewers begin with Kaphar’s piece Monumental Inversion: George Washington—a sculpture of the leader astride his horse, made out of wood, blown glass, and steel. The sculpture depicts the former president’s dueling nature: He’s glorified within a great American equestrian monument but he’s also sitting astride a charred cavity, surrounded by glass on the ground. In juxtaposing Kaphar’s artwork and a George Washington plaster bust, “Making History Visible” forces visitors, hopefully, to see and feel the contradiction in colonial leaders who sought freedom from tyranny but did not extend that ideal to slaves.

I repeat: George Washington freed all of his slaves.

We might question the point of all this. Kaphar is free to make his art, of course. His paintings display quite excellent technical skill, I admit. But why do we, as a society, feel the need to commission and display attacks on our founders? Princeton’s students could just as happily go to class each day without looking at images of Finley’s slaves; unlike Washington, Finley isn’t famous and most students were probably blissfully unaware of his slaveholding until someone decided to stick a sculpture dedicated to it on the lawn.

How do Princeton’s black students feel after walking past a sculpture depicting slaves? Uplifted? Happy? Ready to go to class and concentrate on their lectures? I doubt it. Art may be “powerful” or “open dialogues,” but no one seems to feel better after viewing such pieces.

No, I don’t see how this selective dwelling on the past improves anything.

A world in which images of your founders and heroes are defaced, their corpses judged and rusty nails are driven into their portraits: it’s like a cruel dystopia, Lewis’s That Hideous Strength or 1984. According to Wikipedia:

During and after the October Revolution, widespread destruction of religious and secular imagery took place, as well as the destruction of imagery related to the Imperial family. The Revolution was accompanied by destruction of monuments of past tsars, as well as the destruction of imperial eagles at various locations throughout Russia. According to Christopher Wharton, “In front of a Moscow cathedral, crowds cheered as the enormous statue of Tsar Alexander III was bound with ropes and gradually beaten to the ground. After a considerable amount of time, the statue was decapitated and its remaining parts were broken into rubble”.[40]

The Soviet Union actively destroyed religious sites, including Russian Orthodox churches and Jewish cemeteries, in order to discourage religious practice and curb the activities of religious groups.

You know, they tell us, “No one is attacking George Washington; that’s just a crazy right-wing conspiracy theory,” and then they go and do it.

Incidentally, Georgetown, according to the article, “announced last year that it would grant admissions preference to descendants of slaves whose sale it profited from in the early 1800s.” How do you qualify for that? Do you have to prove that you’re descended from the specific slaves involved, or can you be descended from any American slaves? Because I had ancestors who were enslaved, too, and I’d like to get in on this racket.

In the end, the article answers its titular question:

When Impressions of Liberty is removed from Maclean House in December and enters Princeton’s permanent museum collection, its greatest achievement may lie in the realization that no apology or recompense can ever suffice. …

“No civil-rights project can ever fully redeem anything.”

# Clinton vs. Bush, or Why you should have Multiple Children

As the only heir of the immensely wealthy and powerful Clinton family, Chelsea has been thrust into the public spotlight following her mother’s electoral defeat.

Unfortunately for the Blue Tribe she is supposed to lead, Mrs. Chelsea isn’t too bright. Her Twitter comment was intended as a critique of the claim that Confederate statues and monuments should not be torn down because they symbolize part of America’s history.

This statement depends entirely on churches Chelsea has personally visited. “I have not personally seen this” is a bad argument. All it takes is a few churches she hasn’t attended that happen to have Lucifer statues to disprove her whole point.

And if you know anything about churches, you know that some of them have an awful lot of statues. The Milan Cathedral has 3,400 of them! They cover these things with gargoyles–do you really want to make a political argument that hinges on whether or not there’s a Lucifer in there somewhere?

But you don’t have to travel to famous Italian cathedrals to hunt for the Devil; I have a statuette of Satan defeated by Michel the Archangel about ten feet away on my mantle. Do you know how many statues there are of this guy? Both Popes got together in 2013 to consecrate a new statue of him–complete with Lucifer–in the middle of the holy Vatican City.

Satan also shows up in Christian art and iconography in a variety of disguises, such as a Dragon (defeated by St. George) and a serpent (trod upon by the Virgin Mary.)

If we expand our search to include paintings and stained glass, we find almost endless examples, such as the famous Sistine Chapel frescoes (Michelangelo put the Mouth of Hell right over the Pope’s chair, I hear.)

But even if we limit ourselves to freestanding statues solely of Lucifer himself–not of him being defeated or crushed, not in symbolic form nor painted on the walls, we still have this rather cute little Devil seated outside Marienkirche church in Lübeck, Germany; this large and creepy statue of Lucifer tangled in power lines in the Holy Trinity Church in Marylebone, Westminster; a frightening devil from the church of Sainte-Marie-Madeleine de Rennes-le-Château; Satan pushing the damned into the Leviathan’s mouth, a 12th century Romanesque Carving from the Church Sainte Foy, France; Satan again; carving of Satan being cast out of Heaven from Pisa, Italy; the Devil weighing souls and leading away the damned, Notre Dame, France; another from Notre Dame; devils carved into a church in Lincolnshire, England; a little devil in St. Severin, France; Satan on a pillar, Chatellerault, France; statue of the Devil at the Grotto of St. Anthony, Belgium; and for that matter, there are a lot of frankly obscene carvings in older churches.

We could do this all day, but I think you get the point: there are a lot of depictions of the Devil in Christian churches. Having been raised Methodist is no excuse; somewhere between attending Sidwell Friends, Stanford, Oxford, Columbia, etc., Chelsea has surely learned something about European art.

Considering Chelsea’s level of worldliness–one of the privileged glitterati who get to spend their lives drifting from board to board of different companies and exclusive soirees for the rich and famous–you’d expect her to have at least noticed the carvings on a European cathedral or two.

Even Chelsea’s writing career shows few signs of brilliance: she’s written two books for kids (one of those a picture book) and co-authored one for adults, which has–wow–absolutely rock-bottom reviews. Considering her kids’ books got good reviews, I don’t think this is a troll campaign–it looks like her book is actually terrible.

Unfortunately for the increasingly old and decrepit senior Clintons, lack-luster Chelsea is the only egg in their basket: they have no other kids to prop her up or take the limelight for her.

By contrast, President and first lady George H. W. and Barbara Bush had 6 children–George Walker Bush, Pauline Robinson “Robin” Bush (1949–1953, died of leukemia), John Ellis “Jeb” Bush, Neil Mallon Pierce Bush, Marvin Pierce Bush, and Dorothy Bush Koch.[9] George “W” Bush, although not noted for intellectual excellence, managed to follow in his father’s footsteps and also become President; his brother Jeb was governor of Florida; and Neil and Marvin are doing well for themselves in business.

According to Wikipedia, George and Barbara’s five surviving children have produced 14 grand children (including two adoptees) and 7 great-grandchildren, for a total of 24 living descendants. Chelsea Clinton, while obviously younger, has only 2 children.

Having one child is an effective way to concentrate wealth, but the Bush family, by putting its eggs into more baskets, has given itself more opportunities for exceptional children to rise to prominence and make alliances (marriages, friendships) with other wealthy and powerful families.

The Clintons, by contrast, now have only Chelsea to lead them.

# Gay marriage didn’t win; traditional marriage lost

From the evolutionist point of view, the point of marriage is the production of children.

Let’s quickly analogize to food. Humans have a tremendous variety of customs, habits, traditions, and taboos surrounding foods. Foods enjoyed in one culture, like pork, crickets, and dog, are regarded as disgusting, immoral, or forbidden in another. Cheese is, at heart, rotten vomit–the enzyme used to make cheese coagulate is actually extracted from a calf’s stomach lining–and yet the average American eats it eagerly.

Food can remind you of your childhood, the best day of your life, the worst day of your life. It can comfort the sick and the mourning, and it accompanies our biggest celebrations of life.

We eat comfort food, holiday food, even sacrificial food. We have decadent luxuries and everyday staples. Some people, like vegans and ascetics, avoid large classes of food generally eaten by their own society for moral reasons.

People enjoy soda because it has water and calories, but some of us purposefully trick our taste buds by drinking Diet Coke, which delivers the sensation of drinking calories without the calories themselves. We enjoy the taste of calories even when we don’t need any more.

But the evolutionary purpose of eating is to get enough calories and nutrients to survive. If tomorrow we all stopped needing to eat–say, we were all hooked into a Matrix-style click-farm in which all nutrients were delivered automatically via IV–all of the symbolic and emotional content attached to food would wither away.

The extended helplessness of human infants is unique in the animal kingdom. Even elephants, who gestate for an incredible two years and become mature at 18, can stand and begin walking around shortly after birth. Baby elephants are not raised solely by their mothers, as baby rats are, but by an entire herd of related female elephants.

Elephants are remarkable animals, clever, communicative, and caring, who mourn their dead and create art:

But from the evolutionist point of view, the point of elephants’ family systems is still the production of elephant children.

Love is a wonderful, sweet, many-splendored thing, but the purpose of marriage, in all its myriad forms–polygamy, monogamy, polyandry, serial monogamy–is still the production of children.

There are a few societies where marriage as we know it is not really practiced because people depend on alternative kin networks or women can largely provide for themselves. For example, 70% of African American children are born out of wedlock; and among the avuncular Apache:

In the Southwest United States, the Apache tribe practices a form of this, where the uncle is responsible for teaching the children social values and proper behavior while inheritance and ancestry is reckoned through the mother’s family alone. (Modern day influences have somewhat but not completely erased this tradition.)

Despite the long public argument over the validity of gay marriage, very few gay people actually want to get married. Gallop reports that after the Obergefell v. Hodges ruling, the percent of married gay people jumped quickly from 7.9% to 9.5%, but then leveled off, rising to only 9.6% by June 2016.

In contrast, 46% of US adults are married.

Even this number, though, is in sharp decline: in 1960, 72% of adults were married; by 2010, only 51% were.

The situation is similar throughout the Western world. Only 51% of Brits are married. In Italy, the crude marriage rate (the number of new marriages per 1,000 people), has fallen from 7.35 in 1970 to only 4.21 in 2007. Only 58.9% of Japanese are married.

Declining marriage rates across the developed world have been accompanied by declining fertility rates and rising illegitimacy rates:

As Wikipedia notes:

Only 2% of [Japanese] births occur outside of marriage[35] (compared to 30-60% in Europe and North America) due to social taboos, legal pressure, and financial hurdles.[32] Half of Japan’s single mothers live below the poverty line, among the highest for OECD countries.[36][37][38][39]

In other words, the Japanese welfare state, while generous, does not encourage single motherhood. Wikipedia also provides a discussion of the causes of declining Japanese marriage rates:

The annual number of marriages has dropped since the early 1970s, while divorces have shown a general upward trend.[29] …

The decline of marriage in Japan, as fewer people marry and do so later in life, is a widely cited explanation for the plummeting birth rate.[29][30][31][32] Although the total fertility rate has dropped since the 1970s (to 1.43 in 2013[33]), birth statistics for married women have remained fairly constant (at around 2.1) and most married couples have two or more children. Economic factors, such as the cost of raising a child, work-family conflicts, and insufficient housing, are the most common reasons for young mothers (under 34) to have fewer children than desired. …

Between 1990 and 2010, the percentage of 50-year-old people who had never married roughly quadrupled for men to 20.1% and doubled for women to 10.6%.[41][42] The Welfare Ministry predicts these numbers to rise to 29% of men and 19.2% of women by 2035.[43] The government’s population institute estimated in 2014 that women in their early 20s had a one-in-four chance of never marrying, and a two-in-five chance of remaining childless.[44]

Recent media coverage has sensationalized surveys from the Japan Family Planning Association and the Cabinet Office that show a declining interest in dating and sexual relationships among young people, especially among men.[44][45][46] However, changes in sexuality and fertility are more likely an outcome of the decline in family formation than its cause.[47][48] Since the usual purpose of dating in Japan is marriage, the reluctance to marry often translates to a reluctance to engage in more casual relationships.[30]

In other words, marriage is functionally about providing a supportive way of raising children. In a society where birth control does not exist, children born out of wedlock tend not to survive, and people can easily get jobs to support their families, people tended to get married and have children. In a society where people do not want children, cannot afford them, are purposefully delaying childbearing as long as possible, or have found ways to provide for them without getting married, people simply see no need for marriage.

“Marriage” ceases to mean what it once did, reserved for old-fashioned romantics and the few lucky enough to afford it.

Mass acceptance of gay marriage did change how people think of marriage, but it’s downstream from what the massive, societal-wide decrease in child-bearing and increase in illegitimacy have done to our ideas about marriage.

# The big 6 part 6: The Vigesimal Olmecs

It appears that the Olmecs–our final civilization in this series (1500-400 BC)–had a vigesimal, or base 20, counting system.

Counting is one of those things that you learn to do so young and so thoroughly that you hardly give it a second thought; after a few hiccups around the age of five, when it seems logical that 11=2, the place value system also becomes second nature. So it is a bit disconcerting to realize that numbers do not actually divide naturally into groups of ten, that’s just a random culturally determined thing that we happen to do. (Well, it isn’t totally random–ten was probably chosen because our ancestors were counting on their fingers.)

But plenty of societies throughout history have used other bases. The Yuki of California used base 8 (they counted the spaces between fingers;) the Chumash use(d) base 4; Gumatj uses base 5. There are also reports of bases 12, 15, 25, 32, and 6. (And many hunter-gatherer societies never really developed words for numbers over three or so, though they easily employed phrases like “three threes” to mean “nine.”)

The Yoruba, Olmec, Maya, Aztec, Tlingit, Inuit, Bhutanese, Atong, Santali, Didei, Ainu all use (or used) base 20. Wikipedia suggests that the Mayans may have used their fingers and toes to count; I suggest they used the knuckles+fingertips on one hand, or in a sort of impromptu place-value system, used the fingers of one hand to represent 1-5, and the fingers of the other hand to represent completed groups of five. (eg, 3 fingers on your left hand = 3; 3 fingers on your right hand = 15.)

Everything I have seen of reliable genetics and anthropology suggests that the Olmecs and Mayans were related–for example, one of the first known Mayan calendars/Mayan dates was carved into the Mojarra Stela by the “Epi-Olmec” people who succeeded the Olmecs and lived in the Olmec city of Tres Zapotes. Of course this does not mean that the Olmecs themselves developed the calendar or written numbers, (though they could have,) but it strongly implies that they had the same base-20 counting system.

You can compare for yourself the numbers found on the Tres Zapotes stela (above) and the Mayan numerals (left.)

In base-10, we have special words for multiples of 10, like ten, twenty, ninety, hundred, thousand, etc. In a base-20 system, you have special words for multiples of 20, like twenty, (k‘áal, in Mayan;) forty, (ka’ k’áal, or “two twenties;”) four hundred, (bak;) 8,000, (pic;) 160,000 (calab;) etc.

Wikipedia helpfully provides a base-20 multiplication table, just in case you ever need to multiply in base-20.

The Olmecs, like the Egyptians and Sumerians, produced art (particularly sculptures,) monumental architecture, (pyramids,) and probably had writing and math. They raised corn, chocolate, (unsweetened,) squash, beans, avocados, sweet potatoes, cotton, turkeys, and dogs. (It appears the dogs were also eaten, “Despite the wide range of hunting and fishing available, midden surveys in San Lorenzo have found that the domesticated dog was the single most plentiful source of animal protein,[93]” possibly due to the relative lack of other domesticated animals, like cows.)

They also appear to have practiced ritual bloodletting (a kind of self-sacrifice in which the individual makes themselves bleed, in this case often by drawing sharp objects through their tongues, ears, or foreskins, or otherwise cutting or piercing these,) and played the Mesoamerican ballgame popular later with the Mayans and Aztecs. Whether these practices spread via cultural diffusion to other Meoamerican cultures or simply indicate some shared cultural ancestry, I don’t know.

Their sculptures are particularly interesting and display a sophisticated level of artistic skill, especially compared to, say, Norte Chico (though in its defense, Norte Chico did come earlier):

Frank Johnson, in his post Mystery Solved: Olmecs and Transoceanic Contact

A lot of people think the Olmec stone heads look a lot like Africans (and I can see why,) but–as lots of people have pointed out–they also look a lot like the local Indians who live in the area today, and so far I haven’t run across any genetic studies that indicate African DNA (which is quite distinctive) in any Native American population (aside from the DNA we all share from our common, pre-out-of-Africa ancestors, 70,000-100,000 years ago.) (There is one tiny isolated tribe over in Baja CA, [Mexico,] quite far from where the Olmecs lived, who do have some interesting DNA stuff going on that could indicate contact with Africa or somewhere else, but it could also just indicate random genetic mutation in an extremely isolated, small population. At any rate, they are irrelevant to the Olmecs.)

Frank Johnson, in his post Mystery Solved: Olmecs and Transoceanic Contact, goes through the laundry list of questionable claims about the Olmecs and does a great job of laying out various proofs against them. While I would not totally rule out the possibility of trans-Atlantic (or trans-Pacific) contact between various groups, just because human history is long and full of mysteries, the most sensible explanation of the origins and cultural development of Olmec society is the simplest: the Olmecs were a local indigenous people, probably closely related to most if not all of their neighbors, who happened to start building cities and pyramids.

# The Big 6 Civilizations (Pt. 3: Indus Valley)

3. Indus Valley

The Indus Valley civilization (IVC) has got to be the most obscure of the big six. If you challenged the average person to list the world’s first six relatively independent civilizations, they’d probably guess “Egypt, Mesopotamia, Greece, Rome, China, and, um, Africa? Israel?” Eventually they might hit on “Incas and Aztecs/Mayans,” which are geographically about right. But few would guess that the Indus Valley, located in modern-day Pakistan and India, was one of the world’s first three big civilizations, predating the Chinese by almost a millennium and a half.

This is partially explained by random luck: Egypt and Mesopotamia both feature in the Bible and are relatively easy to get to from Europe, (Egypt moreso than Mesopotamia,) and early archaeology appears to have been driven largely by a desire to uncover the truth behind the Homeric epics and the Bible. (And I have a much easier time accessing archaeological materials written in English.)

China is an enormous, famous country that has the resources to promote its own heritage, and the cultures of the Americas are famous because they’re nearby and because they’re included in the history of the conquering of the Americas, which we learned in school.

Pakistan, by contrast, is hard to get to, not part of the American colonial narrative, doesn’t feature in the Bible, and doesn’t have China’s fame and resources. On top of that, if the Wikipedia talk page on the Indus Valley Culture is correct, Pakistan may not be all that interested in the IVC due to it not being Muslim.

India, by contrast, proudly claims the IVC as part of its history–the IVC page is “part of a series on the history of India,” but not “part of a series on the history of Pakistan.”

Additionally, the IVC, while it left behind plenty of cities, buildings, etc., did not build the kind of monumental structures that draw tourists, like the Great Pyramids of Egypt or Chichen Itza, Mexico. More than a thousand IVC cities or settlements have been discovered, many with granaries, public baths, hydraulic systems, and obvious urban planning (their cities are laid out in grids with excellent-for-the-time sewer systems,) but almost no enormous temples, castles, pyramids, or other obviously ceremonial sites.

Also, we have no knowledge of their language and have yet to decipher any of their written language–if they had a written language at all. (Everything you want to know about the IVC script and why we haven’t deciphered it yet.)

The Egyptians helpfully covered their temples in hieroglyphics and left behind so many written records that we have things like Egyptian math textbooks containing fictional, satirical stories about how to not be a scribe. From Mesopotamia we have the Epic of Gilgamesh.

But from the IVC we have only short inscriptions–if they are inscriptions at all–most on small seals. Most of these inscriptions are only a few characters long, greatly hindering our ability to decipher them. We don’t know what they mean, or even if they are a written language at all.

What we do know:

The IVC (aka the Harappan, after one of their chief cities,) emerged around 3,300 BC in what is now  Pakistan and India. It lasted for about 2,000 years; then essentially disappeared, its people either merging into other populations or migrating away. Over a thousand Harappan cities or settlements have been identified, most of them in Pakistan but a few in Afghanistan and a contested number in India. (Since India is eager to claim the IVC as its own, there are allegations that Indian archaeologists are inflating the number of significant sites on their side of the border.)

(Afghanistan, of course, does not have the resources for archaeology, but it is also really dry, so there probably weren’t that many sites there to start with.)

The IVC likely descended from the Mehrgarh culture (see map). Mehrgarh was a small farming settlement founded around 6,500 BC:

The earliest farming in the area was developed by semi-nomadic people using plants such as wheat and barley and animals such as sheep, goats and cattle. The settlement was established with simple mud buildings and most of them had four internal subdivisions. Numerous burials have been found, many with elaborate goods such as baskets, stone and bone tools, beads, bangles, pendants and occasionally animal sacrifices, with more goods left with burials of males. Ornaments of sea shell, limestone, turquoise, lapis lazuli and sandstone have been found, along with simple figurines of women and animals. Sea shells from far sea shore and lapis lazuli found as far away as present-day Badakshan, Afghanistan shows good contact with those areas. …

In April 2006, it was announced in the scientific journal Nature that the oldest (and first early Neolithic) evidence for the drilling of human teeth in vivo (i.e. in a living person) was found in Mehrgarh. According to the authors, their discoveries point to a tradition of proto-dentistry in the early farming cultures of that region. “Here we describe eleven drilled molar crowns from nine adults discovered in a Neolithic graveyard in Pakistan that dates from 7,500 to 9,000 years ago.”

Ouch.

Major IVC cities include Harappa, Mohenjo-daro, Dholavira, Ganeriwala, and Rakhigarhi.

[Harappa] is believed to have had as many as 23,500 residents and occupied about 150 hectares (370 acres) with clay sculptured houses

… Harappan society was not entirely peaceful, with the human skeletal remains demonstrating some of the highest rates of injury (15.5%) found in South Asian prehistory.[11] Paleopathological analysis demonstrated that leprosy and tuberculosis were present at Harappa, with the highest prevalence of both disease and trauma present in the skeletons from Area G (an ossuary located south-east of the city walls).[12] Furthermore, rates of cranio-facial trauma and infection increased through time, demonstrating that the civilization collapsed amid illness and injury.

Genetically, Harappan skeletons belong to haplogroup L-M20, which today is found primarily in Pakistan and the west coast of India:

In Pakistan, it has highest frequency in Baluchistan.[2] In India, it has higher frequency among Dravidian castes, but is somewhat rarer in Indo-Aryan castes.[3] They make a case for an indigenous origin of L-M76 in India, by arguing that the spatial distributions of both L-M76 HG frequency and associated microsatellite variance show a pattern of spread emanating from southern India. By linking haplogroup L-M76 to the Dravidian speakers, they simultaneously argue for an Indian origin of Dravidian languages (Sengupta 2006).

There is apparently some controversy over whether the invading Indo-Europeans (who brought the Sanskrit language to India) drove the Harappans out of Pakistan and into India. India’s a big place that can absorb a lot of people, but it looks to me like many of the Harappans stayed put.

Meanwhile, in Mohenjo-Daro:

The Citadel – a mud-brick mound around 12 metres (39 ft) high – is known to have supported public baths, a large residential structure designed to house about 5,000 citizens, and two large assembly halls. The city had a central marketplace, with a large central well. Individual households or groups of households obtained their water from smaller wells. … Some houses … include rooms that appear to have been set aside for bathing, and one building had an underground furnace (known as a hypocaust), possibly for heated bathing. Most houses had inner courtyards, with doors that opened onto side-lanes. Some buildings had two stories.[citation needed]

In 1950, Sir Mortimer Wheeler identified one large building in Mohenjo-daro as a “Great Granary”. Certain wall-divisions in its massive wooden superstructure appeared to be grain storage-bays, complete with air-ducts to dry the grain. … However, Jonathan Mark Kenoyer noted the complete lack of evidence for grain at the “granary”, which, he argued, might therefore be better termed a “Great Hall” of uncertain function.[13] Close to the “Great Granary” is a large and elaborate public bath, sometimes called the Great Bath. From a colonnaded courtyard, steps lead down to the brick-built pool, which was waterproofed by a lining of bitumen. The pool measures 12 metres (39 ft) long, 7 metres (23 ft) wide and 2.4 metres (7.9 ft) deep. … Other large buildings include a “Pillared Hall”, thought to be an assembly hall of some kind, and the so-called “College Hall”, a complex of buildings comprising 78 rooms, thought to have been a priestly residence.[citation needed]

Mohenjo-daro had no series of city walls, but was fortified with guard towers to the west of the main settlement, and defensive fortifications to the south. … Mohenjo-daro was successively destroyed and rebuilt at least seven times. Each time, the new cities were built directly on top of the old ones. Flooding by the Indus is thought to have been the cause of destruction.[citation needed]

Why is it all “citation needed”?

A bronze statuette dubbed the “Dancing Girl”, 10.5 centimetres (4.1 in) high[20] and about 4,500 years old, was found in ‘HR area’ of Mohenjo-daro in 1926.[20] … The archaeologist Gregory Possehl said of the statuette, “We may not be certain that she was a dancer, but she was good at what she did and she knew it”. The statue led to two important discoveries about the civilization: first, that they knew metal blending, casting and other sophisticated methods of working with ore, and secondly that entertainment, especially dance, was part of the culture.[20]

I think “dancer” is an overly-poetic interpretation of the statue, but it is a striking work.

In 1927, this soapstone figurine, dubbed “The Priest-King,” (though we don’t know if the Mohenjo-daroians had priests or kings,) was found in a wall-niche in a “building with unusually ornamental brickwork.”

The sculpture is 17.5 centimetres (6.9 in) tall and depicts a bearded man with a fillet around his head, an armband, and a cloak decorated with trefoil patterns that were originally filled with red pigment. … Two holes beneath the highly stylized ears suggest that a necklace or other head ornament was attached to the sculpture. … Drill holes in the center of each circle indicate they were made with a specialized drill and then touched up with a chisel. The eyes are deeply incised and may have held inlay. …[22]

One of the unique features[14] of Dholavira is the sophisticated water conservation system[15] of channels and reservoirs, the earliest found anywhere in the world,[16] built completely of stone. The city had massive reservoirs, three of which are exposed.[17] They were used for storing fresh water brought by rains[15] or to store water diverted from two nearby rivulets.[18] This clearly came in response to the desert climate and conditions of Kutch, where several years may pass without rainfall. A seasonal stream which runs in a north-south direction near the site was dammed at several points to collect water. …

A huge circular structure on the site is believed to be a grave or memorial,[15] although it contained no skeletons or other human remains. The structure consists of ten radial mud-brick walls built in the shape of a spoked wheel.[15] …

These hemispherical structures bear similarity to early Buddhist stupas.[5] The Archaeological Survey of India, which conducted the excavation, opines that “the kind of design that is of spoked wheel and unspoked wheel also remind one of the Sararata-chakra-citi and sapradhi-rata-chakra-citi mentioned in the Satapatha Brahmana and Sulba-sutras“.[5] …

One of the most significant discoveries at Dholavira was made in one of the side rooms of the northern gateway of the city, and is generally known as the Dholavira Signboard. The Harappans had arranged and set pieces of the mineral gypsum to form ten large symbols or letters on a big wooden board[27] … Each sign is about 37 cm (15 in) high and the board on which letters were inscribed was about 3 m (9.8 ft) long.[28] The inscription is one of the longest in the Indus script, with one symbol appearing four times, and this and its large size and public nature make it a key piece of evidence cited by scholars arguing that the Indus script represents full literacy. A four sign inscription with big size letters on a sand stone is also found at this site, considered first of such inscription on sand stone at any of Harappan sites.[1]

More generally:

Indus Valley civilization was mainly an urban culture sustained by surplus agricultural production and commerce, the latter including trade with Sumer in southern Mesopotamia. Both Mohenjo-Daro and Harappa are generally characterized as having “differentiated living quarters, flat-roofed brick houses, and fortified administrative or religious centers.”[8] …
Distinctive seals were used, among other applications, perhaps for identification of property and shipment of goods. Although copper and bronze were in use, iron was not yet employed. “Cotton was woven and dyed for clothing; wheat, rice, and a variety of vegetables and fruits were cultivated; and a number of animals, including the humped bull, were domesticated,”[8] as well as “fowl for fighting“.[9] Wheel-made pottery—some of it adorned with animal and geometric motifs—has been found in profusion at all the major Indus sites. A centralized administration for each city, though not the whole civilization, has been inferred from the revealed cultural uniformity; however, it remains uncertain whether authority lay with a commercial oligarchy. Harappans had many trade routes along the Indus River that went as far as the Persian Gulf, Mesopotamia, and Egypt. Some of the most valuable things traded were carnelian and lapis lazuli.[10]

Obviously we don’t know much at all about IVC mathematics, but:

Excavations … have uncovered evidence of the use of “practical mathematics”. The people of the IVC manufactured bricks whose dimensions were in the proportion 4:2:1, considered favourable for the stability of a brick structure. They used a standardised system of weights based on the ratios: 1/20, 1/10, 1/5, 1/2, 1, 2, 5, 10, 20, 50, 100, 200, and 500, with the unit weight equaling approximately 28 grams … They mass-produced weights in regular geometrical shapes, which included hexahedra, barrels, cones, and cylinders, thereby demonstrating knowledge of basic geometry.[18]

The inhabitants of Indus civilisation also tried to standardise measurement of length to a high degree of accuracy. They designed a ruler—the Mohenjo-daro ruler—whose unit of length (approximately 1.32 inches or 3.4 centimetres) was divided into ten equal parts. Bricks manufactured in ancient Mohenjo-daro often had dimensions that were integral multiples of this unit of length.[19][20]

Among other things, they contain the world’s earliest known system of flush toilets. These existed in many homes, and were connected to a common sewerage pipe. Most houses also had private wells. City walls functioned as a barrier against floods.

The urban areas of the Indus Valley civilization provided public and private baths, sewage was disposed through underground drains built with precisely laid bricks, and a sophisticated water management system with numerous reservoirs was established. In the drainage systems, drains from houses were connected to wider public drains.[1]

Lothal, a port city located in India, contains the world’s earliest known docks, and may have been a Harappan colony, far from the heartland of the IVC:

Before the arrival of Harappan people (c. 3000 BCE), Lothal was a small village next to the river providing access to the mainland from the Gulf of Khambhat. The indigenous people maintained a prosperous economy, attested by the discovery of copper objects, beads and semi-precious stones. … Harappans were attracted to Lothal for its sheltered harbour, rich cotton and rice-growing environment and bead-making industry. The beads and gems of Lothal were in great demand in the west. The settlers lived peacefully with the Red Ware people, who adopted their lifestyle, evidenced from the flourishing trade and changing working techniques. Harappans began producing the indigenous ceramic goods, adopting the manner from the natives.[8]

And, typical of the IVC:

The uniform organisation of the town and its institutions give evidence that the Harappans were a very disciplined people.[12] … Municipal administration was strict – the width of most streets remained the same over a long time, and no encroached structures were built. Householders possessed a sump, or collection chamber to deposit solid waste in order to prevent the clogging of city drains. Drains, manholes and cesspools kept the city clean and deposited the waste in the river, which was washed out during high tide. A new provincial style of Harappan art and painting was pioneered. The new approaches included realistic portrayals of animals in their natural surroundings. Metalware, gold and jewellery and tastefully decorated ornaments attest to the culture and prosperity of the people of Lothal.

Most of their equipment: metal tools, weights, measures, seals, earthenware and ornaments were of the uniform standard and quality found across the Indus civilization. Lothal was a major trade centre, importing en masse raw materials like copper, chert and semi-precious stones from Mohenjo-daro and Harappa, and mass distributing to inner villages and towns. It also produced large quantities of bronze celts, fish-hooks, chisels, spears and ornaments. Lothal exported its beads, gemstones, ivory and shells. The stone blade industry catered to domestic needs—fine chert was imported from the Larkana valley or from Bijapur in modern Karnataka. Bhagatrav supplied semi-precious stones while chank shell came from Dholavira and Bet Dwarka. An intensive trade network gave the inhabitants great prosperity. The network stretched across the frontiers to Egypt, Bahrain and Sumer.[11] One of the evidence of trade in Lothal is the discovery of typical Persian gulf seals, a circular button seal[13]

I love these descriptions, but given the politics involved, I remain wary that the case may be overstated.

So what happened to the IVC? There are many theories, ranging from the far-fetched (“aliens nuked it”) to the perfectly reasonable (“shifting weather patterns made the area too dry.”) Invasion by the Indo-Aryan people could also have destroyed many cities. A massive flood hit Lothal in 1900 BC, which destroyed much of the city. Wikipedia’s description of the aftermath reminds me of the post-apocalyptic nature of the collapse of Rome:

Archaeological evidence shows that the site continued to be inhabited, albeit by a much smaller population devoid of urban influences. The few people who returned to Lothal could not reconstruct and repair their city, but surprisingly continued to stay and preserved religious traditions, living in poorly built houses and reed huts. That they were the Harappan peoples is evidenced by the analyses of their remains in the cemetery. While the trade and resources of the city were almost entirely gone, the people retained several Harappan ways in writing, pottery and utensils. About this time ASI archaeologists record a mass movement of refugees from Punjab and Sindh into Saurashtra and to the valley of Sarasvati (1900–1700 BCE).[17] Hundreds of ill-equipped settlements have been attributed to this people as Late Harappans a completely de-urbanised culture characterised by rising illiteracy, less complex economy, unsophisticated administration and poverty.

# Women in Science–the Bad Old Days

Once we were driving down the highway when my husband said, “Hey, a Federal Reserve Note just flew across the road.”

Me: I think you have been reading too many finance blogs.

Oh look, Silver Certificates:

These bills, from the so-called “Education Series,” were printed in 1896 and feature, rather prominently, women. The \$1 bill has Martha (and George) Washington. The other bills feature women as allegories of science, history, electricity, commerce, manufacturing, and you know, I can’t really tell if the steam and electricity children are supposed to be male or female.

If someone wants to put women on money, I totally support bringing back these bills, because they’re gorgeous.

There’s a certain sadness in looking at these and thinking, “Gosh, maybe people in the 1800s really were smarter than us.” Today, the five dollar bill would offend too many people (it has a breast on it!) and couldn’t get printed. We’ve become Philistines.

There’s also a sense of, “Wait, are you sure this the bad old days of women’s oppression, when people thought women were dumb and couldn’t handle higher education and shit?” Why would people who think women are dumb use women to illustrate the very concept of “science”?

Here’s a painting of MIT’s Alma Mater (Latin for “Nourishing Mother,”) finished in 1923:

(Sorry it’s a crappy photo. I couldn’t find any good photos.)

“Alma Mater,” of course, is used synonymously with “university.” That is, the university itself (all universities,) is female. From the description:

“The central panel is rigidly symmetrical, with the centrally enthroned Alma Mater approached by two groups of acolytes extending laurel wreaths. The composition deliberately recalls the tradition in Christian art of the ascending Madonna attended by saints and apostles. Alma Mater is surrounded by personifications of learning through the printed page, learning through experiment, and learning through the various branches of knowledge. They hover above the Charles River Basin, with a spectral hint of the MIT buildings in the background.”

Here’s a detail:

Unfortunately, I haven’t found good photos of the side paintings, but they sound dramatic:

“The two side panels … bring the elevated scene down to earth with trees that appear to grow straight up from the floor. Unexplained spectral figures glide through this grove. … The right panel, which has been identified as Humanity Led by Knowledge and Invention depicts a mother and children of varying ages progressing from Chaos to Light, accompanied by cherubs bearing the scales of Justice. On the left, the most dark and dramatic mural squarely faces the ethical challenge that has confronted science from the outset. The Latin inscription (from Genesis) in the roundel spells out: “Ye Shall Be Us Gods Knowing Good and Evil.” The lab-coated scientist is crowned by a figure said to be Hygenia (goddess of Health). He stands between two giant jars containing beneficent and malevolent gasses, symbolizing the constructive and destructive possibilities unleashed with every new discovery. With the horrors of the First World War still fresh, soldiers and diplomats gather at the Council table of the World. Dogs of war lurk near evil gasses, while Famine threatens the background. The strangely out-of-scale, dark colossal head within the shadow of the Tree of Knowledge is said to represent Nature; her relation to the rest of the drama is (perhaps deliberately) unclear.”

If you squint, you might be able to make them out:

Before art went to shit, the world was full of lovely paintings of things like “Liberty leading the People” or “The Arts and Sciences,” using allegorical human forms that relied upon people’s understanding and knowledge of ancient Greek mythology–not so ancient when people were actually reading it. I suspect there are so few good photos of this painting because people forget, when surrounded by splendor, that splendor is no longer normal.

This habit of using women as allegorical figures to represent science and learning goes back hundreds, if not thousands of years:

The “Liberal Arts” did not originally refer to silly university classes, but to the knowledge thought essential to the education of all free (liber) people, in order to participate properly in civic life. These essential studies were Grammar, Logic, Rhetoric, Arithmetic, Geometry, Music Theory, and Astronomy (one may assume that the functional ability to read is considered a basic prerequisite for learning, not an endpoint in itself as it is in our modern system.) These studies all culminate in their purist expression in Philosophy, the very love of wisdom.

Notice that all of these allegorical figures are women. Did the depiction of women as the purist ideal of mathematical knowledge make male students doubt their own self-worth and drive them away from serious study?

Then why do people think the inverse?

The trend can be traced back further:

Boticelli depicts the Spring accompanied by the Greek Graces.

The Greek Muses were goddesses of inspiration for literature, science, and the arts. Different people list them differently, (I doubt there was ever any widespread agreement on exactly what the muses represented,) but the lists generally look like, “epic poetry, history, music, poetry, tragedy, hymns, dance, comedy, and astronomy,” or “music, science, geography, mathematics, philosophy, art, drama, and inspiration.”

And who can forget Athena herself, goddess of wisdom and warfare?

# Christianity and the Rise of the Art Instinct

I think there’s a book by the title of “The Art Instinct.” I haven’t read it.If anyone knows of any good sources re human genetics, art, and history, I’d be grateful.

As far as I know, some kind of art exists in all human populations–even Neanderthals and other non-AM primates like homo Erectus, I think, appear to have had occasional instances of some form of art. (I am skeptical of claims that dolphins, elephants, and chimps have any real ability to do art, as they do not to my knowledge produce art on their own in their natural habitats; you can also teach a gorilla to speak in sign language, but it would be disingenuous to suggest that this is something that gorillas naturally do.)

However, artistic production is clearly not evenly distributed throughout the planet. Even when we only consider societies that had good access to other societies’ inventions and climates that didn’t destroy the majority of art within a few years of creation, there’s still a big difference in output. Europe and China are an obvious comparison; both regions have created a ton of beautiful art over the years, and we are lucky enough that much of it has been preserved. But near as I can tell, Europeans have produced more. (People in the Americas, Australia, etc., did not have historical access to Eurasian trade routes and so had no access to the pigments and paints Europeans were using, but people in the Middle East and China did.)

Europeans did not start out with a lot of talent; Medieval art is pretty shitty. European art was dominated by pictures of Jesus and Mary to an extent that whole centuries of it are boring as fuck. Even so, they produced a lot of it–far more than the arguably more advanced cultures of the Middle East, where drawing people was frowned upon, and so painting and sculpture had a difficult time getting a foothold.

I speculate that during this thousand years or so of shitty art, the Catholic Church and other buyers of religious paintings effectively created a market that otherwise wouldn’t have existed otherwise (especially via their extensive taxation scheme that meant all of Europe was paying for the Pope to have more paintings. The (apparently insatiable) demand for religious paintings meant employment for a lot of artists, which in turn meant the propagation of whatever genes make people good at art (as well as whatever cultural traits.) After 700 or a thousand years or so, we finally see the development of art that is actually good–art that suggests some extraordinary talent on the part of the artist.

I further speculate that Chinese art has been through a similar but slightly less extensive process, due to less historical demand, due to the historical absence of an enormous organization with lots of money interested in buying lots of art. Modern life may provide very different incentives, of course.

Thus the long period of tons of boring art may have been a necessary precursor to the development of actually good art.