# The World is Written in Beautiful Maths

This is a timelapse multiple exposure photo of an arctic day, apparently titled “Six Suns” (even though there are 8 in the picture?) With credit to Circosatabolarc for posting the photo on Twitter, where I saw it. Photo by taken by Donald MacMillan of the Crocker Land Expedition, 1913-1917.

Attempting to resolve the name-suns discrepancy, I searched for “Six Suns” and found this photo, also taken by Donald MacMillan, from The Peary-MacMillian Arctic Museum, which actually shows six suns.

I hearby dub this photo “Eight Suns.”

A reverse image search turned up one more similar photo, a postcard titled “Midnight Sun and Moon,” taken at Fort McMurray on the Arctic Coast, sometime before 1943.

As you can see, above the arctic circle, the sun’s arc lies so low relative to the horizon that it appears to move horizontally across the sky. If you extended the photograph into a time-lapse movie, taken at the North Pole, you’d see the sun spiral upward from the Spring Equinox until it reaches 23.5 degrees above the horizon–about a quarter of the way to the top–on the Summer Solstice, and then spiral back down until the Fall Equinox, when it slips below the horizon for the rest of the year.

In other news, here’s a graph of size vs speed for three different classes of animals–flying, running, and swimming creatures–all of which show the same shape. “A general scaling law reveals why the largest animals are not the fastest” H/T NatureEcoEvo

I love this graph; it is a beautiful demonstration of the mathematics underlying bodily shape and design, not just for one class of animals, but for all of us. It is a rule that applies to all moving creatures, despite the fact that running, flying, and swimming are such different activities.

I assume similar scaling laws apply to mechanical and aggregate systems, as well.

# Anthropology Friday Preview: Reindeer Herders

The Lord is my shepherd; I shall not want.
He maketh me to lie down in green pastures:
he leadeth me beside the still waters. …
Yea, though I walk through the valley of the shadow of death, I will fear no evil:
for thou art with me; thy rod and thy staff they comfort me.

About a month ago, one of you requested information on pastoralist/herding societies: What’s their deal? How do they fit into the broader picture of human economic strategies?

To be honest, I’ve never read much about pastoralist societies (outside the Bible.) The one thing I know off-hand is that the vegetarian claim that we would all have more food to eat if we stopped raising animals (roughly speaking, it takes about 10 pounds of plants to produce one pound of meat, give or take a few pounds depending on species,) is flawed due to the fact that livestock often eats plant matter that humans can’t digest (eg, cornstalks) or is pastured on marginal land that can’t be efficiently farmed. (Too dry, rocky, or cold.)

According to Wikipedia:

Pastoralists produce food in the world’s harshest environments, and pastoral production supports the livelihoods of rural populations on almost half of the world’s land. Several hundred million people are pastoralists, mostly in Africa and Asia. Pastoralists manage rangelands covering about a third of the Earth’s terrestrial surface and are able to produce food where crop production is not possible.

Most farms that I am familiar with have at least some animals. If raising animals were a net-calorie loss for humans, I’d expect farmers who don’t raise animals to be more successful than those who do, making the existence of cows and chickens difficult to explain.

Pastoralists raise a variety of animals, commonly llamas, goats, sheep, cattle, yaks, reindeer, and camels. Humanity’s oldest domesticated animal is probably the dog, whose ancestors joined us on the hunt about 15,000 years ago (more on this in a bit.) Our second oldest is the goat, which we realized about 12,000 years ago was easier to keep nearby than to hunt one down every time we wanted a meal.

2,000 years after we mastered the art of taming goats, we decided to tackle a much larger beast: the wild auroch, ancestor of the modern cow. And around 7,000 to 5,500 years ago, someone said to themselves, “Hey, what if we sat on these things?” and we got the donkey, camel, and horse. The reindeer joined us around 5,000 years ago, and the llama joined us abound 4,500 years ago. (All of this according to Wikipedia.)

(Humans have domesticated other animals, like pigs and chickens, but these species’ behavior doesn’t lend them to pastoralism.)

Just as agriculture has developed independently in different human societies, pastoralism probably has, too–the reindeer herders of Siberia probably didn’t pick up the idea from Middle Eastern goatherds, after all. From what I’ve read so far, it looks like we can divide pastoralists into four main groups:

Desert fringe nomads like the Tuareg and Masai, who raise drought-tolerant animals in dry scrublands;

Open steppe nomads like the Mongols or American cowboys, who follow their herds across vast inland oceans of grass;

Arctic circle nomads like the Sami or the Nenets, who depend almost entirely on reindeer for their livelihoods; and

Mountain pastoralists like the Swiss and Quechua of Peru, who raise fluffy, shearable sheep and llamas.

Going back to Wikipedia:

Pastoralists are among the most flexible populations. … The products of the herd animals are the most important resources, although the use of other resources, including domesticated and wild plants, hunted animals, and goods accessible in a market economy are not excluded. …

In East Africa, different animals are taken to specific regions throughout the year that correspond to the seasonal patterns of precipitation.[12] Transhumance is the seasonal migration of livestock and pastoralists between higher and lower pastures.

Some pastoralists are constantly moving, which may put them at odds with sedentary people of towns and cities. The resulting conflicts can result in war for disputed lands. These disputes are recorded in ancient times in the Middle East. Other pastoralists are able to remain in the same location which results in longer-standing housing. …

Somali pastoralists keep their animals in one of the harshest environments but they have evolved of the centuries. Somalis have well developed pastoral culture where complete system of life and governance has been refined. …

On the assumption that pastoralist societies could work differently depending on the environment and/or animals involved, I have been trying to track down good works on a variety of different groups. (This is tricky, since I don’t already know much about nomadic societies nor what the best anthropology works on the subject are.) So for our first book, I’ll be reviewing Tim Ingold’s Hunters Pastoralists and Ranchers [PDF]: Reindeer Economies and their transformations, published in 1980.

From the blurb:

Throughout the northern circumpolar tundras and forests, and over many millennia, human populations have based their livelihood wholly or in part upon the exploitation of a single animal species–the reindeer. Yet some are hunters, others pastoralists, while today traditional pastoral economies are being replaced by a commercially oriented ranch industry. In this book, drawing on ethnographic material from North America and Eurasia, Tim Ingold explains the causes and mechanisms of transformations between hunting, pastoralism and ranching, each based on the same animal in the same environment, and each viewed in terms of a particular conjunction of social and ecological relations of production. In developing a workable synthesis between ecological and economic approaches in anthropology, Ingold introduces theoretically rigorous concepts for the analysis of specialized animal-based economies, which cast the problem of ‘domestication’ in an entirely new light.

On the subject of domesticated reindeer, Wikipedia notes:

DNA analysis indicates that reindeer were independently domesticated in Fennoscandia and Western Russia (and possibly Eastern Russia).[109] … They are raised for their meat, hides, and antlers and, to a lesser extent, for milk and transportation. Reindeer are not considered fully domesticated, as they generally roam free on pasture grounds. In traditional nomadic herding, reindeer herders migrate with their herds between coast and inland areas according to an annual migration route and herds are keenly tended.

The use of reindeer for transportation is common among the nomadic peoples of northern Russia (but not in Scandinavia). Although a sled drawn by 20 reindeer will cover no more than 20–25 km a day (compared to 7–10 km on foot, 70–80 km by a dog sled loaded with cargo, and 150–180 km by a dog sled without cargo), it has the advantage that the reindeer will discover their own food, while a pack of 5–7 sled dogs requires 10–14 kg of fresh fish a day.[110]

“They’re certainly a dying culture,” says Harvard-trained anthropologist Hamid Sardar-Afkhami.
Sardar, who spent years living with the Dukha and documenting their way of life, believes there were once around 200 families living in this remote part of Mongolia.
Nowadays, he thinks there are probably only 40 families left with about 1,000 reindeer.
“The number of families has fallen because a lot of them have been synthesized with the mainstream community,” he says. “Many of them have moved to the towns and even to the capital cities.”
The biggest threat in Sardar-Afkhami’s view is the defection from the younger Dukha generation, who don’t want to live in the harsh conditions in the taiga (or “snow forest”).
“They want to go down and stay in warm cabins in the winter, maybe buy a car and drive,” he says.

# Why are Mammals Brown? (pt. 1)

Compared to colorful fish, lizards, birds, and even ladybugs, we mammals are downright drab. I see no particular environmental reason for this–plenty of mammals live in areas with trees or grass where green fur or spots might help them blend in, or have such striking patterns–like a zebra–that I hardly think a blue stripe would result in more lion attacks.

I think there are two main reasons mammals are mostly brown, instead of showing the vibrant colors of other species:

1. Some colors are difficult to produce.

Blue, for example. Walk into the forest or a meadow on an average day, and you’ll see a lot of green. Anything not green is likely brown. Outside a garden, there are very few naturally blue or purple plants.

It’s no coincidence that early human art uses colors that could be easily produced from the natural environment, like brown, black, (charcoal,) and yellow. By the Roman era, we could produce purple dye, but it was so hard to obtain from such rare sources (shells) that it was prohibitively expensive for mere mortals, hence why it was called “royal purple.” The European tradition of painting the Virgin Mary’s cloak blue also hails from the days when blue pigments were expensive, and thus a sign of exalted status.

A purple dye cheap enough for average people to buy and wear wasn’t invented until 1856, by William Henry Perkin.

I’m not sure exactly why blue and purple are so hard to produce, but I think it’s because light toward the violent end of the spectrum is higher energy than light toward the red end. As Bulina et al state:

Pigments in nature play important roles ranging from camouflage coloration and sunscreen to visual reception and participation in biochemical pathways. Considering the spectral diversity of pigment-based coloration in animals one can conclude that blue pigments occur relatively rare (as a rule blue coloration results from light diffraction or scattering rather than the presence of a blue pigment). At least partially this fact is explained by an inevitably more complex structure of blue pigments compared to yellow-reds. To appear blue a compound must contain an extended and usually highly polarized system of the conjugated π-electrons.

Okay… So, because blue and purple are more energetic, they require molecules that have more double bonds and are less common in nature. (Why double bonds are less common is a matter I’ll leave for a chemistry discussion.)

You’re probably used to thinking of color as an inherent property of the objects around you–that a green leaf is green, or a red bucket is red, in the same way that the leaf and bucket have a particular mass and are made of their particular atoms.

But turn off the lights, and suddenly color goes away. (Mass doesn’t.)

The colors we see are created by light “bouncing” (really, being absorbed and then re-emitted) off objects. Within the visible spectrum, red light requires the least energy to produce (because it has the widest wavelength,) and violent takes the most energy.

But nature, being creative, has come up with alternative way to produce blues and purples that doesn’t depend on electron energy levels: structure.

Unless you are a color scientist you are probably accustomed to dealing with chemical colors. For example, if you take a handful of blue pigment powder, mix it with water, paint it onto a chair, let it dry, then scrape it off the chair, and grind it back into powder, you expect it to remain blue at all stages in the process (except if you get a bit of chair mixed in with it.)

By contrast, if you scraped the scales off a blue morpho butterfly’s wings, you’d just end up with a pile of grey dust and a sad butterfly. By themselves, blue morpho scales are not “blue,” even under regular light. Rather, their scales are arranged so that light bounces between them, like light bouncing from molecule to molecule in the air. Or as Ask Nature puts it:

Many types of butterflies use light-interacting structures on their wing scales to produce color. The cuticle on the scales of these butterflies’ wings is composed of nano- and microscale, transparent, chitin-and-air layered structures. Rather than absorb and reflect certain light wavelengths as pigments and dyes do, these multi scale structures cause light that hits the surface of the wing to diffract and interfere.

The same process is at work in the peacock’s plumage and bluebird’s blue:

Soft condensed matter physics has been particularly useful in understanding the production of the amorphous nanostructures that imbue the feathers of certain bird species with intensely vibrant hues. The blue color of the male Eastern bluebird (Sialia sialis), for example, is produced by the selective scattering of blue light from a complex nanostructure of b-keratin channels and air pockets in the hairlike branches called feather barbs that give the quill its lift. The size of the air pockets determines the wavelengths that are selectively amplified.

When the bluebird’s feathers are developing, feather barb cells known as medullary keratinocytes expand to their boxy final shape and deposit solid keratin around the periphery of the cell—essentially turning the walled-in cells into soups of ß-keratin suspended in cytoplasm. Next, b-keratin filaments free in the cytoplasm start to bind to each other to form larger bundles. As these filaments become less water-soluble, they begin to come out of solution—a process known as phase separation—ultimately forming solid bars that surround twisted channels of cytoplasm. These nanoscale channels of keratin remain in place after the cytoplasm dries out and the cell dies, resulting in the nanostructures observed in the feathers of mature adults.

“The bluebird doesn’t lay down a squiggly architecture and then put the array of the protein molecules on top of it,” Prum explains. “It lets phase separation, the same process that would occur in oil and vinegar unmixing, create this spatial structure itself.”

The point at which the phase separation halts determines the color each feather produces.

This kind of structural color works great if your medium is scales, feathers, carapaces, berries, or even CDs, but just doesn’t work with hair, which we mammals have. Unlike the carefully hooked together structure of a feather or the details of a butterfly’s scales, hair moves. It shakes. It would have to be essentially solid to create structural color, and it’s not.

So for the most part, bright colors like green, blue, and purple are expensive, energy-wise, to produce chemically, and mammals don’t have the option birds, fish, lizards, and insects have of producing them structurally.

To be continued…

# Anthropology Friday: In the Shadow of Man, by Jane Goodall (1/5)

Today we begin our discussion of In the Shadow of Man, (published in 1971,) an account of Dame Jane Goodall’s observations of chimpanzees in the Gombe National Park, Tanzania. If you haven’t finished the book yet, don’t panic; feel free to join the discussion anyway, or keep the questions in mind and answer them later. Also, remember that these questions are only meant to help inspire you; if you want to discuss some other aspect of the book or propose your own questions, go ahead.

1. What did you think of the book? Favorite part, least favorite part?
2. Do you agree with Jane’s claim that this was the first observation of tool making in animals, or does something like a beaver building a dam count? What constitutes “tool making”?*
3. To what extent do you think the study of chimps aids in our understanding of ourselves? Do chimps make useful human analogues?
4. What do you think is the nature of chimpanzee “consciousness”? Do they experience the world in some way similar to ourselves?
5. What do you think of the role of dominance (and violence) in chimp social life?

6. What about the role of play, friendship, and love?
7. Do we do ourselves a disservice by comparing humans to common chimps (pan troglodytes) instead of pygmy chimps/aka bonobos (pan paniscus)?
8. Do you think Jane’s use of feeding stations, which potentially raised the level of chimp-on-chimp violence in the Gombe, compromised her research?
9. I found it very interesting that chimps would fight over relatively low-value bananas, but not over high-value meat. Why do you think they did?
10. Is it a good idea to use chimpanzee child-rearing methods with human children?
11. Should humans do more to protect chimpanzees, both in the wild and captivity?
12. Is it possible for chimps to act “morally” or have what we would call a “moral conscious?” Can we condemn the chimps for their treatment of Old Mr. McGregor?
13. If chimps (or other animals) have emotions, are we morally obligated to be kind to them?

14. After the publication of this book, war broke out among the Gombe chimps, shocking Jane (more on this later.) Was her surprise warranted, or would you have expected it, based on the violence described in the book?
15. Why do you think social grooming is so important to chimpanzees?
16. Do humans have any behaviors similar to social grooming? If not, why?
17. It must take an extraordinary sort of person to sequester themselves in the forest (in the age before cellphones or internet,) for months or years on end. Could you ever do such a thing?
18. Should we read another book? If so, which?

*Jane actually notes in the bibliography that reports of chimpanzee toolmaking were published back in 1925, but perhaps these were not well-known outside of the primatology field:

Tool-using is discussed by Harry Beatty in “A Note on the Behavior of the Chimpanzee,” under General Notes of the Journal of Mammalology, Vol. 32 (1951), p. 118, and by Fred G. Merfield and H. Miller in Gorillas Were My Neighbors (London: Longmans, 1956); Wolfgang Kohler reported studies of tool-using and toolmaking by groups of captive chimpanzees in The Mentality of Apes (New York: Harcourt, Brace, 1925).

Reports of tool use in apes date back to 1843, or perhaps earlier.

It is most likely true that, prior to the publication of Jane’s research, most people–even those interested in apes–weren’t aware of their tool-making abilities. After all, this was not the age of Wikipedia and easy research, when a few clicks of a mouse could bring you to an 1843 paper on primatology. Jane may have actually changed the body of well-known chimpanzee facts, just as Columbus changed the body of well-known continents facts, even though plenty of people had arrived in the Americas before him.

But I still think this all rather neglects the humble beaver, who cuts down trees, strips them of leaves and branches, and then arranges them into large dams, radically altering riverine environments to suit his needs. The world’s largest beaver dam is 850 meters long and still potentially growing.

But enough quibbling — on with the discussion. (Remember, you are welcome to join in even if you haven’t read the book.)

(I’ll be posting my normal excerpts + commentary next week.)

# Anthropology Friday: Animal Souls

I hear the Pope has declared that dogs can get into Heaven, now. (I guess technically he can do that? Like, the opposite of excommunication? But don’t only humans have souls under Catholic doctrine? Can some Catholic expert clarify?)

Continuing with Edward B. Tylor’s Primitive Culture:

“In now passing from the consideration of the souls of men to that of the souls of the lower animals, we have first to inform ourselves as to the savage man’s idea, which is very different from the civilized man’s, of the nature of these lower animals. …

“Savages talk quite seriously to beasts alive or dead as they would to men alive or dead, offer them homage, ask pardon when it is their painful duty to hunt and kill them. A North American Indian will reason with a horse as if rational. Some will spare the rattlesnake, fearing the vengeance of its spirit if slain; others will salute the creature reverently, bid it welcome as a friend from the land of spirits, sprinkle a pinch of tobacco on its head for an offering, catch it by the tail and dispatch it with extreme dexterity, and carry off its skin as a trophy.

“If an Indian is attacked and torn by a bear, it is that the beast fell upon him intentionally in anger, perhaps to revenge the hurt done to another bear. When a bear is killed, they will beg pardon of him, or even make him condone the offence by smoking the peace-pipe with his murderers, who put the pipe in his mouth and blow down it, begging his spirit not to take revenge.

S”o in Africa, the Kafirs will hunt the elephant, begging him not to tread on them and kill them, and when he is dead they will assure him that they did not kill him on purpose, and they will bury his trunk, for the elephant is a mighty chief, and his trunk is his hand that he may hurt withal. The Congo people will even avenge such a murder by a pretended attack on the hunters who did the deed.

“Such customs are common among the lower Asiatic tribes. The Stiens of Kambodia ask pardon of the beast they have killed; the Ainos [Ainu] of Yesso kill the bear, offer obeisance and salutation to him, and cut up his carcase. The Koriaks, if they have slain a bear or wolf, will flay him, dress one of their people in the skin, and dance round him, chanting excuses that they did not do it, and especially laying the blame on a Russian. But if it is a fox, they take his skin, wrap his dead body in hay, and sneering tell him to go to his own people and say what famous hospitality he has had, and how they gave him a new coat instead of his old one. The Samoyeds excuse themselves to the slain bear, telling him it was the Russians who did it, and that a Russian knife will cut him up. The Goldi will set up the slain bear, call him ‘my lord’ and do ironical homage to him, or taking him alive will fatten him in a cage, call him ‘son’ and ‘brother’ and kill and eat him as a sacrifice at a solemn festival. …”

“Even now the Norse hunter will say with horror of a bear that will attack man, that he can be “no Christian bear.” …

“Men to whom the cries of beasts and birds seem like human language, and their actions guided as it were by human thought, logically enough allow the existence of souls to beasts, birds, and reptiles, as to men. The lower psychology cannot but recognize in beasts the characteristics which it attributes to the human soul, namely, the phenomena of life and death, will and judgment, and the phantom seen in vision or in dream. As for believers, savage or civilized, in the great doctrine of metempsychosis, these not only consider that an animal may have a soul, but that this soul may have inhabited a human being, and thus the creature may be in fact their own ancestor or once familiar friend. …

“North American Indians held every animal to have its spirit, and these spirits their future life; the soul of the Canadian dog went to serve his master in the other world; among the Sioux, the prerogative of having four souls was not confined to man, but belonged also to the bear, the most human of animals. The Greenlanders considered that a sick human soul might be replaced by the sorcerer with a fresh healthy soul of a hare, a reindeer, or a young child. Maori tale-tellers have heard of the road by which the spirits of dogs descend to Reinga, the Hades of the departed; the Hovas of Madagascar know that the ghosts of beasts and men, dwelling in a great mountain in the south called Ambondrombe, come out occasionally to walk among the tombs or execution-places of criminals. The Kamchadals held that every creature, even the smallest fly, would live again in the under- world. The Kukis of Assam think that the ghost of every animal a Kuki kills in the chase or for the feast will belong to him in the next life, even as the enemy he slays in the field will then become his slave. The Karens apply the doctrine of the spirit or personal life-phantom, which is apt to wander from the body and thus suffer injury, equally to men and to animals. The Zulus say the cattle they kill come to life again, and become the property of the dwellers in the world beneath. …”

“Animals being thus considered in the primitive psychology to have souls like human beings, it follows as the simplest matter of course that tribes who kill wives and slaves, to dispatch their souls on errands of duty with their departed lords, may also kill animals in order that their spirits may do such service as is proper to them. The Pawnee warrior’s horse is slain on his grave to be ready for him to mount again, and the Comanche’s best horses are buried with his favourite weapons and his pipe, all alike to be used in the distant happy hunting-grounds. 1 In South America not only do such rites occur, but they reach a practically disastrous extreme. Patagonian tribes, says D’Orbigny, believe in another life, where they are to enjoy perfect happiness, therefore they bury with the deceased his arms and ornaments, and even kill on his tomb all the animals which belonged to him, that he may find them in the abode of bliss; and this opposes an insurmountable barrier to all civilization, by preventing them from accumulating property and fixing their habitations.

Certain Esquimaux, as Cranz relates, would lay a dog’s head in a child’s grave, that the soul of the dog, who is everywhere at home, might guide the helpless infant to the land of souls. In accordance with this, Captain Scoresby in Jameson’s Land found a dog’s skull in a small grave, probably a child’s. Again, in the distant region of the Aztecs, one of the principal funeral ceremonies was to slaughter a techichi, or native dog ; it was burnt or buried with the corpse, with a cotton thread fastened to its neck, and its office was to convey the deceased across the deep waters of Chiuhnahuapan, on the way to the Land of the Dead. The dead Buraet’s favourite horse, led saddled to the grave, killed, and flung in, may serve for a Tatar example. In Tonquin, even wild animals have been customarily drowned at funeral ceremonies of princes, to be at the service of the departed in the next world. …

“Among the nations of the Aryan race in Europe, the prevalence of such rites is deep, wide, and full of purpose. Thus, warriors were provided in death with horses and housings, with hounds and falcons. Customs thus described in chronicle and legend, are vouched for in our own time by the opening of old barbaric burial-places. How clear a relic of savage meaning lies here may be judged from a Livonian account as late as the fourteenth century, which relates how men and women slaves, sheep and oxen, with other things, were burnt with the dead, who, it was believed, would reach some region of the living, and find there, with the multitude of cattle and slaves, a country of life and happiness. … It is mentioned as a belief in Northern Europe that he who has given a cow to the poor will find a cow to take him over the bridge of the dead, and a custom of leading a cow in the funeral procession is said to have been kept up to modern times.”

EvX, here: Turning to the European intellectual tradition on the subject of animal souls, Tylor observes:

“Although, however, the primitive belief in the souls of animals still survives to some extent in serious philosophy, it is obvious that the tendency of educated opinion on the question whether brutes have soul, as distinguished from life and mind, has for ages been in a negative and sceptical direction. The doctrine has fallen from its once high estate. It belonged originally to real, though rude science. It has now sunk to become a favourite topic in that mild speculative talk which still does duty so largely as intellectual conversation, and even then its propounders defend it with a lurking consciousness of its being after all a piece of sentimental nonsense.”

Sentimental nonsense, and may it remain that way.