Trig Warning: 3700-Year-Old Babylonian Tablet

     A Babylonian clay tablet known as Plimpton 322 was discovered early in the 20th century in present-day Iraq. An Australian mathematician, Dr. David Mansfield, who has been analyzing its meaning, announced his conclusions in late August, 2017, saying that "cracking the meaning of the tablet, as big as the palm of a human hand, could simplify our study of triangles."


      Up to now, trigonometry has been based on study of angles and irrational numbers. The analysis of Plimpton 322 reveals that the Babylonians used ratios during 2800 to 1700 BC.  “This gives us a different way of looking at trigonometry,” Dr. Mansfield said. “The beautiful thing about it is that it’s much simpler.” 


      "Trigonometry is not a fusty, {I find the use of the word"fusty" is awesome here!} esoteric branch of mathematics. It is essential to architecture, engineering, astronomy, surveying, and even oceanography. Up to now, it’s been taught using Greek principles. But this tablet proves that the Babylonians beat the Greeks in the discovery of trigonometry by about 1,000 years."

       The tablet was unearthed in southern Iraq, believed to be near the onetime Sumerian city of Larsa, by Edgar Banks, a collector of antiquities in the 1890s. Banks was not collecting cuneiform tablets as an archaeologist, but while using his position as the American consul to Baghdad. He sold the tablets to universities, libraries, and museums.

      "The Greek astronomer Hipparchus has been considered the father of trigonometry. But this tablet was created long before Hipparchus lived."

      Dr. Mansfield said, “Babylonian mathematics may have been out of fashion for more than 3,000 years but it has possible practical applications in surveying, computer graphics and education.”


      "The tablet got its name because an American publisher and collector named George Arthur Plimpton bought it. (He is the grandfather of writer and editor George Plimpton, founder of the Paris Review and author of Paper Lion.) In 1936, not long before he died, Plimpton donated the Babylonian tablet along with many other manuscripts to Columbia University."

     "In the 1940s, researchers who were studying the tablet concluded that the cuneiform numbers on it corresponded to the Pythagorean Theorem. But that was far as they got until Dr. Mansfield and his team took up the challenge.

      The tablet “is a fascinating mathematical work that demonstrates undoubted genius,” says Dr. Mansfield. “The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry.”

Not at all a fusty fuss, eh?
Steph

Elk in downtown Evergreen, CO >>>



DNA of Ancient Canaanites: Levant, Lebanon, and Lines

      Researchers have deciphered the complete DNA of five Canaanite skeletons. By comparing these five Canaanite genomes with those of other ancient and modern populations, the scientists identified the Canaanites’ ancestors and discovered their descendants were modern Lebanese people.

     The results, reported July 27 in the American Journal of Human Genetics, give new insight into the origins and fate of a people whose story has largely been told through the secondhand accounts of its contemporaries.

     "The Canaanites emerged in the Levant, a region east of the Mediterranean Sea, 3,000 to 4,000 years ago. This cultural group, which established extensive trade networks and colonies across the Mediterranean region, left behind few written records, perhaps because they wrote on papyrus rather than clay. So most knowledge of the Canaanites comes from ancient Egyptian, Hebrew and Greek documents."

     "But, doubt surrounds some of those accounts. For one thing, Greek historians thought the Canaanites originated near the Persian Gulf, whereas archaeological records suggest they arose from farming communities that settled the Levant up to 10,000 years ago. For another, the Old Testament makes reference to the destruction of Canaanite communities, but some of their cities, such as Sidon in Lebanon, appear to have been continually inhabited through the present day."

      
     "Researchers reconstructed the genomes of the 3,700-year-old remains of five Canaanites unearthed in Sidon. Comparisons of these genomes with those of other ancient Eurasian peoples indicate that Canaanite ancestry was split roughly 50-50 between the early farmers who settled the Levant and immigrants of Iranian descent who arrived later, between 6,600 and 3,550 years ago."

     “You’d need a lot of migration for roughly half of the population to be replaced by the incoming Iranian-related populations,” says Iosif Lazaridis, a geneticist at Harvard Medical School who was not involved in the study. “This must have been some important event in the history of the Near East.” One possibility is the spread of the Akkadian Empire, which controlled a region spanning from the Levant to Iran between 4,400 and 4,200 years ago. That connection may have presented the opportunity for interbreeding between these far-flung populations."

     "The researchers also determined that modern Lebanese people can attribute about 93 percent of their ancestry to the Canaanites. The other 7 percent comes from Eurasians who probably arrived in the Levant 3,700 to 2,200 years ago. Study coauthor Chris Tyler-Smith, was surprised by how much Canaanite heritage dominated modern Lebanese DNA. He says he expected to see a more mixed gene pool because so many populations have crossed through the Levant in the last few thousand years."

     "This study alone may not paint the complete picture of the Canaanite lineage, says Aaron Burke, an archaeologist at UCLA, because the researchers examined the genomes of only five Canaanites."

      "However, the study’s Canaanite genetic data do provide “a snapshot of history in the area,” Lazaridis said. Identifying which populations crop up in the Canaanite lineage — and when — can help trace the historical movements of people throughout the Near East. With DNA analyses of enough ancient people, Lazaridis says, “I think it will be possible to reconstruct the whole timeline of what happened in Lebanon and other parts of the world.” 

No lamentations; looking forward to more data!
Steph

"Fire Stranger" Pyroxene and Young Martian Clay

       Pyroxenes are isosilicates which are one of the most common constituents of the lithosphere of earth. They are also prominent minerals in the uplifted rocks on Mars.

       The name pyroxene comes from the Greek words for fire (πυρ) and stranger (ξένος). Pyroxenes were so named because of their presence in lavas, where they are sometimes present as crystals in volcanic glass. It was originally assumed they were impurities in the glass, hence the name "fire strangers". However, they are merely early-forming minerals that crystallized before the lava erupted.

      The most recent data from Mars show that clay found at impact sites near uplifted pyroxene uplifts is believed to be clay-rich impact melt material (i. e. authigenic), rather than clay pulled to the surface by impacts. This authigenic clay is now dated at 2 billion years or less rather than 3.7 billion years, as previously thought.

Brown University geologists, not affiliated with Coffee ;-), describe their research in a press release yesterday.

And, interestingly a hexagonal pattern shows up in craters on Mars as well:

     Mars and earth seem more and more similar every day. . .

       I am taking a Wild Clay painting class next month with a friend's brother here in Colorado. It may come in especially handy, if I ever go to Mars to check out the melted, wild, young clay.

Ka-O, don't be a fire stranger,
Steph

Bonus: Cliff Palace, Mesa Verde National Park, CO, with 70 lanterns, December 2015

"Styling" Stylolites. . .

"Styling" Stylolites

      It has been a long day in a big, downtown building with many stylolites:

     The official definition of a stylolite (The Free Dictionary) is: "A secondary structure found along contacting surfaces of adjacent calcareous rock layers, the contact zone appearing in cross section as a series of jagged interlocking up-and-down projections that resemble a suture or the tracing of a stylus."

     What they really are are reminders that limestone, under pressure, changes to marble and the dark bits of various insoluble minerals  like pyrite, clays, and iron oxides remain in the stylolites making them visible.  Stylolite is from two Greek words, stylos or pillar and lithos or stone. The stylolites are serrated or tooth-like surfaces at which darker minerals have been removed by pressure dissolution, in a process that decreases the total volume of rock. In other words, they are dark reminders of intense compression and stress:

     I believe it is no accident that they are found in Courtroom buildings around the world. They may look styling and cool, but they are reminders that dissolution under pressure leaves behind a dark, dark image. And, similar to the vegetable ash layer in the Humboldt Fog Cheese, (See November, 19, 2013 post)  it is that layer to which our eyes are drawn. 

     Yes, stylolites can be quite beautiful:

      I hope to remember that in decompressing this evening (pun very assuredly intended) from today's proceedings.

      Next week: I am considering writing about hydraulic fracturing or fracking. We shall see. Thoughts?

      Here's hoping your day did not include stylolites (unless you are researching or admiring them).

Stylolitically,

Word Woman (aka Scientific Steph)

Cheese Imitates Geology: Thin Vegetable Ash Layer and Thin Iridium-rich Clay Layer

Cheese Imitates Geology: Thin Vegetable Ash Layer and Thin Iridium-Rich Clay Layer

 

      There is a small, wicker cheese basket at my local grocery store filled with little snippets of cheeses--the ends of various imported wheels and logs. This one caught my eye:

 

          I unwrapped it last night and found this written on the wrapper (just so you know I'm not making this up):

     A hairline layer of vegetable ash?! Oh my. 

     Of course, the iridium-rich clay layer found at the boundary of the Cretaceous period (about 65 million years ago) with the overlying Paleogene sediments first documented by Luis and Walter Alvarez (shown below) in Italy, sprang to mind. The limestone layers beneath the red clay are full of numerous species of foraminifera (forams) and the thick limestone beds above contain only one foram species. In between is this iridium-rich later of clay. In Italy. In Germany. In the Netherlands. In the U.S. All over the world.

      Iridium is a rare, silvery, white transition metal of the platinum family found in meteorites. It was named for the Greek goddess Iris after the rainbow colors in its salts and less than 3 tons a year are mined world-wide:

     Iridium is associated with the massive K-Pg extinction including the non-flying dinosaurs and a huge, diverse, plant population. (The boundary was called the K-T boundary for Cretaceous-Tertiary when the Alvarezes discovered it. The International Stratigraphic Nomenclature Committee has recently deprecated the Tertiary Period though; it now must be called Paleogene.) [First Pluto is no longer a planet; now we can't call it the K-T boundary any more. Sigh...]  And the likely location of the meteorite hitting the earth in the Gulf of Mexico is also well documented.

       What strikes me (no pun intended, okay, maybe...) about naming conventions in geology and in all areas, actually, is the creativity and force in coming up with these descriptive terms. As Clementine says to Joel when talking about her newest hair color in the film Eternal Sunshine Sunshine of the Spotless Mind, "Naming hair colors. Somebody has that job. I want that job!"

        Calling the thin layer of vegetables in the Humboldt Fog Cheese "Vegetable Ash" is truly inspired to this geologist and cheese eater.

         Last week: puddingstones that look like pudding. This week: Cheese that looks like limestone layers with a hairline layer of ash. It doesn't get much better than that full circle.

        Thanks for reading. I look forward to your comments, thoughts, and cheesy ideas.


Until then, "say cheese!" (And mean it).

Humboldtly yours,
Word Woman (aka Scientific "Vegetable Ash Layer" Steph)