People like Pythagoras and Euclid reimagined the pyramid builders’ rope as perfectly straight (not sagging a little), so thin that it had no thickness at all, and extending forever beyond the posts. Crazy. They called it a “line” and found that they could reason about such things, proving new statements by deductions from what they already knew.
Those ancient geometers discovered much that was true and good and beautiful in the imagined world of points and lines, and a few of them took the first tentative steps toward using their discoveries to help answer questions about the experienced world of posts and ropes and much else. Eratosthenes kept the promise made by “geo”+”metry” when he measured the circumference of planet Earth, even tho it was impractical to try to wrap a tape measure around it.
Modern STEM is rooted in ancient geometry (among other things), and a long hard slog has progressed from measuring the Earth to understanding it. Our understanding is not perfect and never will be, but maybe it is good enough to help us save the Earth. From us. I hope we can rise to that challenge, and that I have risen to this one:
- The colorful frame around the image is upsized from my much smaller diagram for Bhaskara’s elegant proof of Pythagoras’ Theorem. The resulting fuzziness of the points and line segments is a reminder that we cannot experience the ideal perfection of geometric shapes. But we can refer to the shapes when we tell each other stories about what we experience! (Tho often hard to read w/o wrangling equations, scientific theories are among the best stories we can tell.) The colors of the line segments tie the image to the theorem’s bottom line w/o using letters that would clutter the diagram:
a² + b² = c²
- The Blue Marble image overlaid on the diagram was downloaded from NASA Visible Earth: The Blue Marble. Making NASA’s image cost a lot more than making mine. That’s OK. It was money well spent.
– above post (on phone) or beside it (on desktop). –
Tho I am not quite old enough to have been following the news on 1942-11-10, I remember what Winston Churchill said then to mark the victory at El Alamein:
“Now this is not the end.
It is not even the beginning of the end.
But it is, perhaps, the end of the beginning.”
That first victory in 1942 ended the beginning of the long hard slog to rid the world of fascism. The riddance was temporary. Perhaps 2020 can begin the long hard slog to repair the damage done to the USA by about four decades of coddling plutocrats and four years of coddling bigots. Perhaps 2020 can begin to free the USA and other nations from creeping fascism disguised as conservatism.
For the moment anyway, here is the answer to the question about 2020 that I posed soon after the disastrous 2016 election:
Our flag is still there.
As soon as I could see clearly again, I started this post. Tho I am a compulsive polisher and normally let things marinate for many hours before I revisit and revise, I pressed the [Publish] button after less than an hour. I had to get back to the battle, to doing what little I can to help organizations like VoteVets fight for constitutional democracy against the corrupt fascist in the White House and his enablers.
While I have only been to Machu Pichu vicariously, I have long admired the skills and can-do spirit of Inca stonemasons who made sturdy walls from precisely aligned stones of various shapes. Precise alignment is a lot harder with stone than with fruit.
The exquisitely crafted walls of Machu Pichu’s now-roofless buildings have endured centuries of frost heaves and neglect. What high purposes might the buildings have served? Were any of them schools or hospitals or research institutes?
Nope. The buildings were summer homes for the emperor and courtiers top 0.1% and temples think tanks for the priests pundits who told them that their wealth and privileges were rewards for pleasing the gods creating jobs. Machu Pichu endures in more ways than one.
Remember in November.
Image Sources for Machu Pichu
In wartime, ignorant and impulsive pols can somehow make horrendous situations even worse. So it is with the pandemic. Medical workers (including EMT-s and hospital support staff as well as doctors and nurses) have been sent into battle with inadequate personal protective equipment for themselves and inadequate intensive care facilities for their patients. Stockpiling such stuff would cost money. Might even need to raise taxes on those who can work from home, if they need to work at all. And so on.
It’s so much easier to claim that all is well until all Hell breaks loose, then claim that all will be well when the weather warms up, if we just go back to work and drink a little bleach.
The governors of some states have stepped up. Learning from each other and from countries (like New Zealand and South Korea) that took the threat seriously, they made tough decisions. They include a few Republicans (like Hogan in Maryland and DeWine in Ohio) and more Democrats. It is too early to be sure, but they just might have saved the USA from criminal incompetence in the White House. Federalism works.
The doctor in Wuhan who first sounded the alarm about COVID-19 was punished for “spreading rumors” and later died of the disease. Remember him also today, along with our essential civilian workers and those who serve in our military. Remember that dark money and gerrymandering and vote suppression have sickened American democracy but not yet killed it.
Remember in November.
As Abraham Lincoln said when somebody objected to his fondness for corny jokes during the Civil War:
«I laugh because I must not cry.»
So far, the COVID-19 crisis is still not as bad as the Civil War. The USA survived that, partly because the POTUS was caring and competent.
Visit the post reblogged here to see a fine collection of cartoons and jokes.
After performing tragedies, the ancient Greeks always staged comedies, often making fun of the tragedies they’d just presented. Why? Comedy relief. Likewise, humor flourishes during wars and epidemics. Morbidity? No, survival. When we’re under attack, we ridicule our attackers and tease ourselves. Why? Because it helps us cope, reminds us we’re in this together and, well, simply provides comedy relief. Those Greeks had it right.
Click on any image to enlarge it, or to start slide show.
Some Pandemic Humor found Online
- I’ll tell you a coronavirus joke now, and check back in two weeks to see if you got it.
- Finland has closed its borders. That’s right, no one is allowed to cross the finish line.
- I ran out of toilet paper and had to start using the New York Times. Man, the Times are rough.
- Kids who came of age during the millennium are called Millennials. With…
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Is the sea at Capri’s shoreline still as clear now as it was when I was there in 1977? I hope so.
While we’re on the subject of clarity, let’s note that it is not clear whether the eponymous goats really did live on ancient Capri. But it is clear that the island sited precursors of Mar-a-Lago for Imperial Rome’s fat tyrants.
From the outside, the Blue Grotto (Tiberius’ private pool) looks much like the (other?) grotto in my photo. The view from inside is entirely different.
A cave entrance right at the shoreline can sometimes work magic.
Blue Grotto (Capri) [edited image]
Capri Shoreline, Long Ago
Goats traverse cliffs while
pink whale swims in blue grotto.
“Buy me!” says the wonderfully colored gourd. I refuse:
“No, I’ve already bought what I need for this year’s fall decorations. There’s no room for another gourd.”
“But I’m new and special. Look at the feathering between my greens.”
I put the gourd in the cart, check out, and drive home. As I unpack the groceries, I happen to set the new gourd down in a way that is vaguely reminiscent of a reclining nude. Then I recall a milestone in photographic history.
§2: 1927 — 1930
Edward Weston’s meticulous closeup photos of scores of common objects (notably bell peppers) are marvels of imagination and ingenuity. They also prompt one critic to remark that Weston’s peppers look like nudes while his nudes look like peppers.
Weston works in grayscale (aka “black and white”). The color of a pepper would only be a distraction anyway. While people have various skin colors, nobody’s skin is red or green.
“Buy us!” say 3 colorful gourds. I refuse:
“No, I’ve already bought an extra gourd that I will use to salute Edward Weston.”
“Last year, U bought a total of 10. We’ll just bring it up to 8.”
“Last year’s gourds were smaller and came in bags of 5.”
“Weston bought more than 30 peppers.”
“But he could eat them when he was done shooting.”
I’m a pushover. ¯\_(ツ)_/¯
§4: Now and Forever
Remember when cameras used analog film, color darkroom work was sorcery, and color prints faded under museum lighting? Artistic photographers had to work in grayscale. Viewers did not pine for color in the masters’ photos.
Sadly, some photographers mistook a temporary necessity for a permanent virtue. Wanna create a colorful image? Buy some tubes of paint. Stick with grayscale for artistic photography.
The sweeping general assertion of grayscale’s intrinsic superiority was a gross insult to Eliot Porter (and to all who hiked the trails he blazed in color photography).
Some photos do look better in grayscale than in color. Maybe something with interesting contours and textures happens to have distracting colors. Grayscale is great for Weston’s peppers.
Sometimes progress replaces an old thing with a new one that is all-around better, as in the transition from analog film to digital pixels. The transition from obligatory grayscale to color (in varying degress of saturation) is a subtler kind of progress that adds choices. Lots of choices.
Photo editing software supports having some color classes or parts of an image be more saturated than others. Done casually and obtrusively, it can be gimmicky. Done carefully and subtly, it can work with other edits to greatly improve a photo. One of the contemporary photographers I admire steps thru instructive examples:
If U choose to desaturate a photo (either partially or all the way to grayscale), I may disagree with that choice. I will still respect it, but only as a specific choice. What I won’t respect is a blanket assertion that photos “should” be in grayscale. Or in color. Or have shallow depth of focus. Or have everything in focus. Or whatever.
Here is one blanket pronouncement that I do respect, in photography and beyond:
Don’t hide behind sweeping generalities.
Own your choices.
Happy July 4th!
– above post (on phone) or beside it (on desktop). –
Let’s start by summarizing the older surprises that I posted in response to a CDHK episode. Credits for the images below are at the end of this post for readability.
The first surprise was that that so much motion could fit in a haiku:
A shell exploded!
Water slowly filled the hole
and held the whole sky.
Of course, my haiku that is like a movie was inspired by this classic World War I haiku that is like a still photo:
© Maurice Betz
A shell hole
In its water
Held the whole sky.
The second surprise was that I did not have a stable preference between these haiku. Like someone viewing the classic ambiguous image that can be seen as a duck facing one way or as a rabbit facing the other, I flip-flopped between the still photo by Betz and the movie by me. So did at least 2 readers of my old post.
Here is the new third surprise. After writing yet another shell hole haiku, I finally have a stable preference. My preferred haiku is like a movie that starts after the explosion:
Water slowly filled
the shell blast’s muddy crater.
It held the whole sky.
Unable to find appropriate and affordable period images, I used contemporary images: a generic explosion and a puddle that looks much like the water-filled shell hole. The puddle photo has been cropped to be more nearly square.
Big limestone columns
sang silent hymns to honor
sleazy pagan gods.
Old Greek thoughts and deeds
built bigger things than temples.
When I say Merry Xmas (pronounced like “MEH-ree KRIS-muhs”), it might be heard as an unwelcome hint that the hearer is (or should be) a Christian. I suppose I should say something like Happy Holidays or Season’s Greetings instead, but the generic salutations for this time of year sound bland and vague to ears as old as mine. Can anybody suggest something with more pizzazz but w/o religious implications?
I decorate for the winter solstice (with multicultural Xmas lights and wreaths) and hope it is OK to wish U a
– above post (on phone) or beside it (on desktop). –