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On Today’s Menu:
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** Share a fresh slice of cake for a very old mathematician’s birthday.
** Linger to ponder the winding path knowledge takes through time.
** Savor a last ½ cup on a trip through Sicily, circa 1999.
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I have found it!
– Archimedes of Siracusa
Slice of Cake:
became laws of physics.
– Shannon Quinn & Simon Whistler 1
Other than the year of his birth (287 BCE),
we don’t really know when Archimedes’ real birthday is—
But let’s called it March 14.
The man who first determined the value of Pi (π)
should be celebrated on Pi Day.2
Archimedes worked out the value of π through an exhaustive method called the Method of Exhaustion. First he drew a circle and two polygons. The circle was circumscribed inside one of the polygons, the other (slightly smaller) polygon was inscribed inside the circle.
Archimedes used the Pythagorean Theorem to calculate the areas of two polygons.
The area of the circle would have to lie somewhere in between.4
But how about if the polygons and circle were smaller? Or even smaller?
He then calculated Pi using infinitesimals—ever smaller numbers—similar to what would later used in integral calculus.
Archimedes knew, however, that this method of calculating Pi would always be an approximation.
To this day, pi is still an approximation.
Archimedes invented and discovered a lot more than Pi.
He is also credited with a few things he didn’t invent.
For instance, Archimedes did not invent the lever,
but he worked out the calculations that govern the laws of levers.
And his applications for balances, pulleys, and fulcrums revolutionized
shipping, warfare, and the transportation of his day.
Archimedes wrote about his discoveries; but sadly,
few of Archimedes writings have survived.
His autobiography, co-written with his friend Heracleides, has never been found.
Was Archimedes married? Did he have children? We don’t know.
However, we do have this insight into Archimedes’ personality
written by the the 1st century CE historian Plutarch,
who describes Archimedes as so hyper-focused on his work that he tended to forget everything else.
Archimedes would forget his food and
neglect his person, to the degree that
when he was occasionally carried by absolute violence
to bathe or have his body anointed,
he used to trace geometrical figures in the ashes of the fire
and diagrams in the oil on his body…
[He would be] in a state of entire preoccupation and,
in the truest sense, divine possession
with his love and delight in science.
Archimedes also worked on problems of fluid mechanics, dealing with the buoyancy of objects in water.
Here is another story about Archimedes
told by Vitruvius, a Roman architect, writing in the first century BCE:
A local goldsmith in Siracusa was commissioned by the king to create
a wreath crown of solid gold. The king wanted to place it as tribute
on a statue of his favorite Greek god.
The goldsmith finished the crown and presented it to the king.
But the king became suspicious: Was this crown really pure gold?
Or was the goldsmith swindling the king? Perhaps he used a cheaper metal like silver to make the crown, then coated it with gold so it would look pure, and pocketed the extra profit.
The king asked Archimedes to determine the composition of the crown—
but he ordered that the crown not be damaged in the process.
Archimedes obsessed over this problem, working out mathematical formulas day and night with no success. Eventually his students could no longer stand Archimedes’ lack of self-care and they dragged him off to the baths. When Archimedes lay down in the tub, some water splashed out onto the floor—he suddenly understood that his body displaced the water in the tub in a way that was measurable and could be used to calculate weight.
Archimedes was then so excited by this discovery that he leapt out of the bath and, without stopping to dress, ran through the streets shouting, ‘Eureka! I have found it!’
The solution which occurred,
when he stepped into his bath and caused it to overflow,
was to put a weight of gold equal to the crown and known to be pure
into a bowl which was filled with water to the brim.
Then the gold would be removed and the king’s crown put in, in its place.
An alloy of lighter silver would increase the bulk of the crown
and cause the bowl to overflow.
Archimedes and the king ran the experiment.
The crown failed. The goldsmith was convicted of forgery.
Here is Archimedes formula:
(mass of an object) – (apparent mass when submerged) = (density of water) x (volume of the object)
This formula is now called the Archimedes Principle and it’s still used by engineers today.
** Happy 2,308th Birthday **
Archimedes of Siracusa
– born March 14, 287 BCE (or so)
in Siracusa, Sicily
Written on the body is a secret code
only visible in certain lights:
the accumulation of a lifetime gather there.
In places the palimpsest is so heavily worked
that the letters feel like braille…
I didn’t know that Louise would have reading hands.
She has translated me into her own book.
– from Written on the Body (1993)
by Jeanette Winterson
I’ve been thinking this week about how knowledge comes to us.
And how haphazard and arbitrary a path it can take.
When I was in Sicily, I visited The Valley of the Temples outside Agrigento. It was a fascinating place, but many of the temples, especially the Temple of Heracles, were mostly toppled and very damaged—and not just by time. The temples here were burnt by the Carthaginians in the 5th century BCE and further destroyed by the Romans in the 4th century CE.
One stunning exception is the Temple of Concordia, which stands dramatically with its 38 Doric columns preserved for almost 2500 years.
But the reason it’s still standing is because it was turned into a Christian church in the 6th century CE. Walls were cut, rooms destroyed, other walls were added— it became nothing like the Greek temple it had been. And yet this is what saved it. When the alterations were removed in 1785, as much of the original building as possible was restored. Now the beauty of the Greek architecture can again be admired and studied.
In other words, those who reviled the Greek religion took over and recklessly ruined the temple, making it over into their own vision—yet if they hadn’t, we would not today have access to the vision and work of the original Greek temple.
How does knowledge come to us? What haphazard and arbitrary path does it take?
There is a luscious, $10 word that I just recently learned: Palimpsest.
A palimpsest is a parchment manuscript which,
after the writing has been partially erased, is used again,
the former writing being more or less visible.
That’s the literal definition. But palimpsest also seems rich in metaphoric possibilities.
Another definition of palimpsest says:
Something having diverse layers or aspects apparent beneath the surface.
In the year 1229 CE,
parchments containing three of Archimedes’ writings were recycled and reused
to create a new book. The ink was scraped off, the parchment was washed,
folded in half, then rebound with other ancient parchments
and written over with Christian liturgical prayers.
Yet, even with all this, Archimedes writing was still somewhat visible.
This book-within-a-book was discovered and photographed in Istanbul around the beginning the 20th century—then lost again for another 70 years, to show up at auction in New York in 1998.
The tale of how this fragile text—now called the Archimedes Palimpsest—
was found, carefully cleaned, analyzed used infrared and x-rays, and now made freely available to read and study makes for a fascinating story.3
William Noel of Walters Art Museum in Baltimore
gives a terrific TED talk about recovering the Archimedes Palimpsest.3
(I’ll put a link to it in footnote number 3.)
Maybe all knowledge is a palimpsest. Learning on top of learning. New facts obscuring some older facts, while revealing others. I do find it fascinating that as technology moves us forward into the future, it also has the potential to open up more and more of the past.
Remembering does not entail a simple
plotting of …moments along a chronology; instead…
memory is a palimpsest that is continually being written over,
but never perfectly so.
This is because the newer writings or memories
never completely conceal the older ones,
and several layers of memory can coexist simultaneously.
– from Cuban Palimpsests (2005)
by José Quiroga
“Half Cup More”
If you think of the island of Sicily as a clock face…
my 2019 trip there began at the 3 o’clock position, landing in Catania.
Prof B and I then spent three weeks, traveling clockwise:
Siracusa at 5 o’clock, Ragusa & Modica at 6 and 6:30,
The Temples at Agrigento at 9 o’clock, and beautiful Erice at 11 o’clock.
Here is some of my travel journal from that trip.
Friday 4 October
This trip is started really well. Once we finally got to the hotel—after a marathon 18-hour travel day—it was really hard to want to leave again. But we did. For a sunset walk and a good dinner with nice red wine. (I didn’t like the prosecco, though… It weirdly tasted like beer!)
We danced in the Piazza Bellini under the bella luna. (Two women passing by applauded us.) Ran to see and hear the bells ringing in the campanili—they rang at 6:30 and again at 7pm. Very good guitar player busking in the square. (Her name was Eva.)
Espresso shots to get us started. Nice outdoor café. Strong espresso—we both needed to add sugar. Found out the word for sparkling water is frizzante.
Turns out we’re staying in the art district. “Art & Fun” the signs says. There was so much pretty street art—even if we didn’t get to see any actual galleries.
I bought a couple of small things in a shop that made beautifully detailed leather bags and purses.
Lovely lunch: breads, spreads, cheeses. Pasta with grilled vegie side plate.
And we stumbled on a Roman Amphitheater… Catania wasn’t supposed to be this interesting! It was just supposed to be somewhere to rest for a day or so and recover from jet lag.
on train from
Catania to Siracusa
As we were waiting to check out of our hotel in Catania this morning, the man at the desk noticed we were talking about an unusual painting on the wall high above the front desk. It’s a family crest, he told us, a bird flanked by symbols of their livelihood: shipping and apothecaries. His eyes lit up to show us this. Would we like to see more? So we got a spontaneous tour from Jacquamo—based on his and our mutual excitement over old architecture and hidden histories.
Jacquamo showed us that what is now the hotel reception area was once the courtyard of a wealthy merchant family’s home. The flowers in the ceiling were from the 1800s—though not the whole ceiling itself. The niche for a saint, above what had been a fountain or water feature, was from the 1600s.
Then he showed us an upstairs room where the ceiling was original—and covered with interesting murals, now beautifully restored. Near the window was the likeness of an eye in a pyramid (a bit like what’s on a US dollar bill). In the hallway, we could see the original vaulted ceiling with flower ornaments and the modern hotel room built like a box beneath it.
Jacquamo said that his boss bought the building 12 years ago, they took out a sub-roof and were shocked at all the historic details they discovered.
Big storm today. Very windy. Rain comes and goes. The sea outside our window is LOUD. And very restless. Not at all peaceful or calming. The waves keep getting bigger.
Here in sunny Italy, it’s not sunny.
Clearly, King Poseidon is pissed.
A room with sea view
seems a good idea—unless the sea
decides to move in.
Today we walked along the sea wall, watching waves crashing into the protective rock arm that guards the little port at Ortigia, then we crossed the bridge onto the small island that is the ancient ‘Old City’ of Siracusa.
After morning tea in an English tea shop, we made our way through the narrow streets in search of the Archimedes museum. It was well worth the walk.
My favorite part of the exhibit was a wooden bobbin-winder with a heart shape. The man who invented machines of war also made this pretty tool to help women with their spinning.
Another favorite was learning how, through his calculations, Archimedes discovered that:
A cone circumscribed within a cylinder equals 1/3 the volume of the cylinder.
And a sphere circumscribed within a cylinder equals 2/3 the volume of the cylinder.
In other words:
Sphere + Cone = Cylinder.
It turns out this was a favorite of Archimedes himself.
His geometric proofs and equations were what he was most proud of.
He even asked that a circle and cylinder be inscribed on his tomb.
We took a day-trip train ride into the picturesque mountain town of Noto. Lovely meal at L’Opera Café. Being out in the high noon sun was not ideal. I found a cool gallery and spent a long time trying to decide what to buy. Everything was beautiful with such rich colors.
Bike ride this morning. Sunny day—our first truly sunny day. Very hot ride with very little shade. Still, we had almost unending, gorgeous views of the sea—plus the luxury of a 7-km path dedicated to walkers & bicycles. (No cars to worry about!)
As we neared the turn-around spot, a man coming toward us said something to us in Italian and pointed back down the path. Next a runner also tried to tell us something. I heard a dog barking. Were they saying there was a mean dog ahead? I could see one dog up on the hill to the left and I thought maybe I saw one on the road ahead of us.
The third person we met was adamant. Through gestures he made clear that “Beyond here is not safe and not okay.” We turned around.
The next person we came to shook his head no when we asked “Do you speak English?” but then said, in English, “Dog. One, two, three, four, five…”
Oh! A pack of feral dogs? Out of control? Good thing we’d turned around.
Modica is my favorite place in Sicily so far! I’m so glad we’re here for my birthday. And not just because of the wonderful chocolate that Modica is famous for.
Our B&B is on the main street of the old part of town. Once upon a time, this street was a river—and the town was built up the east bank. Up, up, up. That’s where we walked today. Up through streets as steep as stairs, and some streets that are stairs.
We stopped into the big grand Cathedral of San Giorgio. Very gold-flourish-and-pale-blue-paint elegant. A mural of George on a horse killing the dragon. We continued our climb up, up, up and reached a nice overlook. Continued up even higher and found another church, except this one was all closed up.
Right as I was beginning to wilt, we came upon a restaurant just opening its doors for lunch. We followed 3 or 4 men on the way in—each one got kisses on both cheeks from the proprietor holding the door. (None for us, though. I should have told him it was my birthday.)
Coming back down the many, many steps, my right knee hurt a bit. But after that nice lunch, how refreshed and re-energized I felt! Even the breeze felt cooler. It was a nice birthday.
Today, after a failed attempt to organize a bike ride for ourselves, we hiked up the other bank. This side of Modica felt more rural. Homes here are just as old-seeming, but they’re further apart, with bigger plots of land. Turtles, a turkey, lots of olive trees, and at least one pomegranate. Lots of cats.
Our destination was a restaurant at the top of the hill.
A former restaurant, it turns out. Now a private house. No lunch option. We hiked all the way back down with no refreshers other than patchy shade and my one bottle of water. B took heaps of photos.
We were very grateful (again) that there’s a restaurant right downstairs from our B&B. (No commute.)
When traveling, the picturesque, the perfect finds, delicious meals, and delightful surprises have to be balanced with disappointing stretches of tedium, discomfort, confusion, exhaustion, errors, tempers, and seriously mediocre food. This is the truth.
On the hot walk back today, I thought: When we were younger, B and I would have been blaming each other, snipping, inflicting silent treatments. Not that we don’t sometimes still. But not much. Mostly we’re civil, forgiving, and very grateful to have each other.
Yesterday we took another day trip—a bus ride into Ragusa. Also a mountain town. Ragusa is pretty—and very green for Sicily. There’s a river running through in a tree-filled gorge that is crossed by traffic bridges, one pedestrian bridge, and—far below—a train bridge.
Ragusa had been destroyed by an earthquake in the 1800s then was ‘stubbornly’ rebuilt along the medieval street layout within the older, lower section of town.
Once we got to the piazza of the main Duomo (Duomo of San Giorgio), it became very touristy. And not just ‘touristici’ but it seemed oddly plagued by pairs of tourists, all ages, but all couples, everywhere we went. Never more than two couples in any one street or stairway we happened into—but always another pair. Sometimes the same pair. The young couple, in shorts and t-shirts; the arguing middle-age couple; and the elderly man with a disapproving stare and a wife who was very busy about the shops.
I liked the inside of the Duomo—I stood right under the dome itself, which was clear windows and full of light. More dramatic perhaps on a day like today with this mix of sun and cloud. A stained glass window of Jesus praying in the Garden of Gethsemane (slumbering friends in the background) lit up while I sat looking at it… Really beautiful.
We arrived and got checked in. Relaxing small beach town. It’s not quite sunset, but I’m falling asleep.
Holy Audubon, batman! That’s a lotta birds. Very loud birds. They’re somewhere just outside my window and I can’t see even one. Are they in that tree? It’s just outside the gate and looks thick enough to hide a flock.
The birds are just waking up now, noisily. I looked them up. They’re cisalpine sparrows. I bet there’s 3000 of them. Now they’re flying off to important morning bird-business. Beyond their tree I can see a guy fishing in the Mediterranean. Another room with a nice view.
I’m sitting here eating pieces of only-slightly-stale baguette with pistachio-cheese cubes (which B had wisely packed for our train ride yesterday) and waiting for 8:30 when breakfast starts downstairs. I’m beginning to feel that 3 weeks is a long trip…
This is our ‘day off.’ The proprietor, Gabriel, did laundry for us yesterday morning. Most of it is still hanging right out front, for all to walk by and see my undies. Can’t manage to mind. No one in Italy has dryers, it seems. Laundry was our Job #1 for this, our penultimate location.
Job #2 was to see the Valley of the Temples outside Agrigento—which we did for about 3 hours yesterday, from around 3:45 pm til sunset. It was very touristy, but all outdoors with plenty of open space, and it was very, very worth it.
My favorite, I think, was Hercules Temple. What was still standing and what was lying as rubble felt so dramatic.
I just found out that Erice is pronounced air-eh-CHAY. (After calling it ‘Eris’ for the past 2 weeks.)
That’s where we’re going next. Last stop. Erice is also where B is giving a talk for an academic conference.
Stunning mountain location. The streets are true cobblestone with very restricted car access. The town is beset with tourists—but mostly only at midday. By late afternoon, they’ve all disappeared. The room seems to be made of stone, like a castle or a cloister.
There’s a pretty brass bed and two tall, thin window casements looking out over the rooftops to the sea. In the middle distance, some huge rock-mountain looms over a thin beach.
The wifi is shaky. The water pressure is dismal. But, oh, what a view!
Cuddled in. Such a quiet room, a monastery room, looking out on the expanse of the Mediterranean Sea, one sailboat far from shore.
That wool hoody I brought, which seemed absurd for the beach weather of San Leone, has come in very handy in stormy Erice.
Getting to dinner last night was an adventure. It wasn’t so far to walk, but the streets had turned into steams, and the slick, wet cobblestones made us tread carefully. Fog-shrouded street lights, rain clattering, and terrific thunder: Romantic, atmospheric, gothic. More than slightly hazardous. My shoes turned squelchy.
One of those thunder claps took out the wifi. Who knows when it’ll be back on. (I wonder how these hoards of acedemics will deal with a night and morning with no internet?)
Last night dinner’s was at a long table full of Prof B’s colleagues. Near the end of the meal, while everyone was ordering drinks and desserts, I got up and moved about four chairs down to an empty seat to be near some women who were talking about something other than the academic-business-y topics that B and the other men around me had been deep into for the last hour. B saw what I was doing and gave me a wry smile. He knows my tolerance level for ‘shop talk.’ I really enjoyed the rest of the evening!
It’s a cloudy, slightly windy day. I’ve picked up a slight cold, so I’m laying low today. B should be back soon. Perhaps he’ll have news. There may or may not be a transportation strike—we’ve heard rumors. But tomorrow’s flight, which was supposed to have begun our journey home, is certainly cancelled. Which means the next two flights, like little dominoes, toppled into the hopeless column. The whole complicated journey now has to be re-scheduled. And I, who have begun to long for home, will have to wait another day.
Here’s what we were supposed to do:
Friday: from Erice to Palermo by hired van – fly to Rome – fly to Amsterdam – fly home to SLC.
Getting re-booked was a long anxious phone call following a frantic scramble for information online. Yuk. But! we are now booked on a flight for Saturday morning.
The journey now looks like this:
Saturday: from Erice – to Palermo by hired van – fly to Rome – fly to Atlanta – fly home to SLC.
I’m reading a book I picked up in Siracusa by Italo Calvino called If On a Winter’s Night a Traveller.
If on an autumn’s night a traveler finds herself on a mountaintop in Northern Sicily, in a rain storm, with a head cold… the vacation is over.
The rain, though, rather cheered me up. Now I’ve a story to tell and no expectations to do too much. Relax today. Pack tomorrow. Go home Saturday.
Give me a place on which to stand,
and I will move the earth.
on his work with levers
Thank you for reading!
— Kelly J Hardesty
Scroll down to the end—and you can leave me note!
Always so lovely to hear from you.
You Can Read More…
notes & footnotes
Archimedes: The Greatest Mind in Ancient History
a BioGraphics video
written by Shannon Quinn
hosted by Simon Whistler
Pi Day is March 14 because the date 3/14
(using the American style of writing month/day)
is like the mathematical constant pi
which begins 3.14…
The earliest official celebration of Pi Day
was at San Francisco’s Exploratorium, where they measured,
sliced, and ate many fruit pies on March 14, 1988.
The first Pi Day was the brainchild of Larry Shaw,
the Exploratorium’s “Prince of Pi”
Read more about this at:
You can hear the astounding story of recovering
the Archimedes Palimpsest
in this terrific TED talk by William Noel,
Curator of Manuscripts and Rare Books at the
Walters Art Museum in Baltimore
A Brief History of Pi (π)
a science museum in San Francisco, California.
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© Kelly J Hardesty 2022