The other day I stumbled across an intriguing paper on the arXiv e-print server. Written by Guillermo Sequera of Paraguay’s National Secretariat of Culture and Alejandro Gangui of the University of Buenos Aires, the paper bears the title “The Tomárâho conception of the sky.”

The Tomárâho are an ethnic aboriginal group whose members live in part of the Gran Chaco, an arid, flat, Alaska-sized region that encompasses parts of Bolivia, Argentina, Paraguay, and Brazil. The photo below, taken by Mark Hoschek, shows a sunset in the Paraguayan Gran Chaco.

Perhaps because their homeland is far from the Paraguay River, the Tomárâho were not subdued by the first wave of Spanish colonists who reached the Gran Chaco in the 16h century. But, as Sequera and Gangui recount in their paper, by the end of the 19th century, an Anglo-Argentinian conglomerate had appropriated the Tomárâho land and impressed the Tomárâho people to chop down the local hardwood trees for timber.

Sequera lived among the Tomárâho in the late 1980s and early 1990s. He saw for himself the poor conditions that the people still endure. He also discovered that the Tomárâho have—and continue to have—a rich, mythical conception of the heavens, Earth, and the underworld.

To fully appreciate the Tomárâho conception of the sky, you should read Sequera and Gangui’s paper. Here’s a short summary of the six above-ground strata. They came into existence following the catastrophic collapse of the giant tree that supported the Tomárâho universe in the distant past.

1. Porr iut(lower sky), the solid, dry abode of men that extends to the height of the tallest palm tree.
2. Porr pehet(half sky), the humid zone where clouds form and rain originates. The abode of rushbirds and storm spirits.
3. Porr pixt(true sky), the zone of thick fog where Lapyxe the rainmaker and other spirits live alongside the Sun and Moon.
4. Porr yhyr(high sky), the location of Venus and the other planets, the stars, and the Milky Way. “With the exception of a few particularly visionary shamans,” write Sequera and Gangui, “nobody has the power to enter this distant and profound sky.”
5. Porr uhur(horizon sky), the threshold between the known and unknown.
6. Porr nahnyk (cold sky), “an indefinite space which goes beyond the inner skies, the region where the universe extends and the unknown predominates. It is a profound, airless sky,” write Sequera and Gangui.

When I read Sequera and Gangui’s paper, I tried in vain to remember my first impression of the night sky. I grew up in Conwy, a small old town on the coast of North Wales. There, the air is always moist and the skies are often cloudy. I didn’t knowingly see the Milky Way until, at the age of 27, I visited a beach at night in a remote part of Kyushu, Japan.

By then I was an astrophysicist. My scientific conception of the cosmos corresponded more or less to the last and most forbidding of the Tomárâho’s six strata. Now, as a writer, I value the creativity that went into conceiving the Tomárâho universe. And I’m grateful to Sequera and Gangui for recording and interpreting it for us.

Charles Day

If you consult Wikipedia for the definition of the Péclet number, you’ll find at the bottom of the page a list of all the dimensionless numbers used in fluid dynamics. There are 52 of them, from Archimedes to Womersley. All but two are named after an engineer, scientist, or mathematician. The exceptions are capillary and Deborah.

The Deborah of the dimensionless number is the fourth judge or ruler mentioned in the Book of Judges. After foretelling the Israelites’ victory over the Canaanites in chapter 4, she sings a hymn of victory in chapter 5. As translated in the 1769 King James version, verses 3–5 read as follows:

Hear, O ye kings; give ear, O ye princes; I, even I, will sing unto the LORD; I will sing praise to the LORD God of Israel.

LORD, when thou wentest out of Seir, when thou marchedst out of the field of Edom, the earth trembled, and the heavens dropped, the clouds also dropped water.

The mountains melted from before the LORD, even that Sinai from before the LORD God of Israel.

Deborah’s vivid image of mountains turning to liquid evidently inspired Marcus Reiner. In August 1963 he gave an after-dinner speech at the Fourth International Congress on Rheology, which was held in Providence, Rhode Island. After noting that “flowed” is closer than “melted” to the original Hebrew, he pointed out that mountains do indeed flow—even when not smitten by God—provided one observes them on a time scale of divine length. Reiner went on to define the Deborah number, D:

D = relaxation time / observation time

The Deborah number isn’t the only term that Reiner originated. In the same speech, which was reproduced in Physics Today‘s January 1964 issue, Reiner recounted how he and Eugene Bingham challenged themselves in 1928 to come up with a name for a new and growing field that encompassed plastic flow and colloid chemistry. The name they chose, rheology, comes from the Greek word rheo (ρεω), which means “to flow.”

The name must have caught on quickly. The Society of Rheology formed the following year.

Charles Day