Monday, August 28, 2017

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 >>>


73 comments:

  1. Replies
    1. The Land Before Time, mentioned in this article, has a bad reputation in my family. It was the first movie we took our son to, when he was just three. When the lights came up at the end of the film, he was in tears, and it took us a very long time to paste him back together. As usual in kids' films, they kill off the parent dinosaurs early on to get your attention, and the baby dinosaurs in the movie have a big independent adventure and come out OK in the end. He was sure that "OK in the end" would involve the parents not being dead, and was devastated when that turned out not to be the case, and the baby dinosaur ended up with his grandparents. He had a thing about death long after that (we had to hustle him out of an exhibit on the Etruscans at age five), and we've never forgiven that film.

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    2. I never saw that movie. What a terrible experience for your son! Tough for a little guy. My sympathies.

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    3. Funny how the brain works - when I was 6 or 7 I saw "The Astounding She-Monster" on the creature feature TV show. A really stupid movie, but the image of the killing creature would enter my dreams well into adulthood. I finally figured out the movie title, and tracked down a DVD - ironically from an online store 3000 miles away but only 2 blocks from where I worked in high school.

      One viewing (only partial, actually, it was a REALLY bad movie) and I never had that dream again.

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  2. So, what does the tablet actually say?

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  3. When I saw the name George Plimpton, my hoax-detecting antennae tingled. I remember Sidd Finch.

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  4. Replies
    1. Not the Margaret Hamilton I was expecting (I'm melting)!

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    2. Yes, jan, I read a similar article about Margaret Hamilton (with the same photos) earlier this year.

      Paul, that was my first thought, also!

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  5. The illustration above, of a 3-4-5 right triangle, is OK, but it doesn't prove the Pythagorean Theorem, which is true for all right triangles. This little animation does the trick better.

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  6. WW (and others): I uploaded some eclipse snap shots to https://www.dropbox.com/sh/4n590tyenhkn15d/AABVI-9uj13w_oTbO7NroD2na?dl=0. Let me know if it doesn't work, I've never read the instructions for using Dropbox.

    Just curious, why did you decide to stay in Colorado and not go to the totalitarian state for the eclipse?

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    1. Wonderful images, eco. They show up just fine.

      As to your question, just too much to do to take the number of days off (as you did) to fully experience the eclipse and not ridiculous traffic.

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    2. Too bad, but I understand the conflicts. I used the event as an excuse to force a vacation, one which my clients couldn't push back on. I'm glad I did.

      I had no traffic issues, though I didn't leave until a couple of hours after the event - lunch, chatting with fellow campers, then breaking down the tent, etc. Folks in Oregon had horrible delays, one of my clients said 9 hours to drive 180 miles.

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    3. Yeah, it took friends 18 hours to go about that distance here. Being stuck in traffic is one of my least favorite things. That's what made Arkansas in April such a joy--no traffic anywhere in the state!

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    4. Yikes, 18 hours is insane, that's about 50% longer than it took me to drive the 750 miles to Idaho. Though I've been stuck for 2 hours trying to go 12 blocks to get out of San Francisco.

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    5. Yes, getting out and d r i v i n g is great. Crawling is not.

      Speaking of crawling, my friends had a baby and a toddler on that 18-hour drive back to Colorado. 'Nuff said.

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  7. The Bay Area could use a long eclipse today and this weekend; Walnut Creek is expected to reach 117° F today!

    My little spot on the globe, only 12 miles away, is only going to be 95°. But no air conditioning here. That's your toast of the town, hoping no fires start.

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    1. Wow, so fiery! Stay as cool as possible. . .

      We will be in the low '90's here. A swamp (evaporative) cooler works great in our house. Maizie is a fan ;-).

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    2. And I do hope any fires are kept away. . .

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    3. Swamp coolers (and whole house fans) are great for hot-dry places like Colorado, New Mexico, Arizona. Of course they're not so good in hot-humid places like New Orleans or the East Coast.

      Berkeley usually stays in the 70°'s, even in the summer. Actually our warmest days are usually late September-October, and we typically only get about 5 days above 90° per year. Walnut Creek frequently gets >100°, but I've never seen it hit 117.

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    4. "Fiery Furnace" in Arches National Park, UT, comes to mind. . .

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    5. Arches has long been on my list; Fiery Furnace looks, well, pretty cool.

      Ever hear of magnetotactic bacteria? I'm meeting with a potential client today who specializes in their study. Better than studying why dogs face north to poop, I suppose. I wonder what results when the long overdue magnetic field reversal happens.

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    6. Fiery Furnace is incredible. We went in early January and saw nary a soul on our hike.

      Magnetotactic bacteria are new to me. Quite wild! Yes, the pole flip will likely flip out many living things. . .

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  8. You can learn interesting things while lost in cyberspace.

    We're planning to get together with my wife's brother and sister and all our descendants in the Hudson Valley in October. Someone suggested seeing the Great Jack O'Lantern Blaze at Van Cortlandt Manor, which plays off the Sleepy Hollow legend. It's best seen at night, and someone asked when does it get dark there in late October? So, I find a site that gives the times of sunset, civil twilight, nautical twilight, and astronomical twilight, and I passed that along, with a link to the Wikipedia page on twilight.

    Which led me to the page on the Earth's Shadow. Which led me to the page on Brocken spectre (a new one for me). Which led to the page on Glory (not the movie). Which led to the page on Kármán vortex street. (In case anyone asks if you can tell them how to get to Kármán vortex street, now you know.) Which, besides explaning what these vortices are and how they form, also explained why tall smokestacks have spiral projections to prevent them, which is the same reason the antenna on my Prius has a spiral wire wrapped around it, which I've always wondered about.

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    Replies
    1. That was a long trip with interesting side trips! "Civil twilight" is new to me. . .

      The jack-o-lantern blaze sounds fun.

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  9. <<< An Evergreen, CO, friend, send this image of her "downtown."

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    Replies
    1. I guess they just made their way back from Reno...

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    2. (You can't spell EVERGREEN, CO without R-E-N-O...)

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    3. Indeed. Looks like a "NEER" VERGE.

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    4. Oh deer. Is there an easy way to see a large version of the picture that I haven't herd about? When I click on your profile and "view image full size" it's very small.

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    5. Hi eco, I added a full-size version of the image above. Enjoy!

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    6. Thanks, I guess it behooves drivers to be careful.

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    7. That picture is from 2013, it appears.

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    8. Yes, I thought it was a little early in the year. . .

      Yes, it is an older image.

      But, still fun!

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  10. This guy says the weight of Harvey's rains has caused Houston to sink. Was this measured, or is it just theoretical? Have we seen this effect of weather before? Has the weight off all the skyscrapers in modern cities caused them to sink, too? The "jumping on a mattress" analogy has me thinking about that kids' rhyme, only with some geologist shaking her finger, saying "No more monkeys jumping on the bed!"

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    1. Interesting article, jan. The geophysicist cited says the numbers are real. Hmmmm. No more monkeys jumping on the bed, indeed!

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    2. My high school physics teacher used to smugly say that he could move the earth. Then he would jump and say that his mass would cause the earth's mass to move, albeit very slightly.

      To modern cities, it somewhat depends. New York is built on bedrock, so any depression would be very, very slight, though possibly measurable.

      In general the building codes mandate that buildings not exceed the soil's bearing capacity, which varies based on the soil type, groundwater level, etc. Around here they use a default bearing capacity of 1500 psf, which is plenty for standard spread footings for low rise buildings, 3 stories or so.

      With taller buildings or gooey soils (infill or Bay muck), you have to bring in a soils engineer. With smaller buildings I've used a "raft slab", basically a thicker slab on grade that can float on the worst soil. For larger structures piers are often used - either dug deep enough to hit solid rock, or friction piles which rely on surface tension. Even then that doesn't always work, as in these condos that Joe Montana and other famous people call home. I've only been in the ground floor branch of my bank, I don't know the overall effects.

      A bigger problem in many cities, including Shanghai, is land subsidence caused by pumping out groundwater. They claim that's the cause of the tilting condos, we'll see if it's true.

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    3. Thanks for your insight about soils and slabs, eco. I have a sinking feeling. . .

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    4. Eco, I believe the article was talking about the actual crust (which includes bedrock, of course) sinking, not just soil compaction.

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    5. If so he should not have used the jumping on a mattress analogy, which is mostly compaction of the top layer, depending on what kind of springs you have.

      Shouldn't there be a regular flexing of the crust under places that experience severe tidal fluctuations? Like the Bay of Fundy or the Severn Estuary?

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    6. eco, I could not find research about flexing of the crust beneath tides in places like the Bay of Fundy, but it makes sense.

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  11. Replies
    1. With web cams cheap and available, fire lookouts seem silly.

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    2. Already happened in a lot of places, I remember this NPR story. Infrared mode seems like a big advantage for spotting night fires. A digital record of where the fire starts might be useful too, especially for human made fires.

      We have relatively poor eyesight, especially at long distance. There was an interesting experiment in sea rescues 40 or so years ago. Finally, a good use for pigeons.

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    3. Yes, web cams and other surveillance make more sense, of course. The peace and quietude of being a fire lookout sounds lovely, though.

      eco, pigeon told, eh? ;-)

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    4. One (actually up to 4) can stay at many fire lookouts. Seems like most don't have water. But many had road access nearby.

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    5. Thanks, eco. Squaw Mountain and Jersey Jim both look like good spots in Colorado.

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    6. Though one of the visitor photos from Squaw Mountain show the bright lights of Denver. Beautiful, perhaps, but less of a feeling like you're away.

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    7. True. Jersey Jim looks more remote.

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  12. Replies
    1. Very cool images, frightening when you think about what's actually going on. Anybody ever been through a hurricane? I've only experienced them in dying tropical storm stage.

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    2. Scary stuff.

      Same here as to experiencing the tropical storm stage.

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    3. I remember walking down the street against the winds of Hurricane Belle on Long Island in 1976, just to see what it was like. That was just barely a hurricane by the time it made landfall. It was windy and rainy, just as the TV weathermen always demonstrate.

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  13. Something's going on with Blogspot. I just posted a comment, and instead of appearing right away, I got a message to the effect that my comment will appear after approval, and it hasn't appeared yet.

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    1. Hmmm. jan, I had to approve your (and eco's) messages to have them post. I've not changed settings so I wonder what's going on.

      Perhaps try another test post?

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  14. Looks like a remarkable place, reminds me of the dunes at the north end of Death Valley, though they weren't nearly so tall.

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  15. Test post. Does this need approval?

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    Replies
    1. Yes, it did. . .but I changed one more thing. Hoping that will do the trick.

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    2. I had the same thing with approval earlier. We'll try this one.

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    3. Whatever you changed was the right thing, it now has on demand posting again.

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  16. Death Valley is cool, too. It's been awhile for me (late '70's).

    I can watch the CO sand for hours from different points on the dunes.

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  17. Replies
    1. Laughing at yourself is a very helpful trait.

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    2. Reminds me of the closing scene of Koyaanisqatsi. But don't click if you haven't seen the whole film.

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    3. Good to see this again, eco. Thanks for the clip.

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  18. The 200th(!) blog post of Partial Ellipsis of the Sun on "Two Hundredth Post: More Continental Crust on South America's Andean Plateau" is now up.

    {The "slab" talk on NPR's Sunday Puzzle brought this week's topic to mind.}

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