A Pendulum Day

“I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth.”
― Umberto Eco, Foucault’s Pendulum

But if fell later as they tried to move another piece. Note the rare “suspended section” of blocks. I’m not sure of the physics of leaving a few behind for a handful of microseconds.

Along with my Difficult Reading Book Club I’m plowing ahead through Umberto Eco’s Foucault’s Pendulum – ten pages or so a day. It’s enjoyable, though truly difficult. I feel I should be looking up every odd word – searching out details on every unique concept – but there are pages to get through so I soldier on. Have to come back later. I’d take notes – but they would be longer than the tome itself.

One concept that haunts my dreams is the eponymous swinging orb. I knew about the Foucault Pendulum, of course. I have even seen one – a big, famous one – at the Smithsonian in Washington (though it looks like it isn’t there any more). I knew the theory, that the pendulum is actually always going in the same plane, but the earth moves under it. The more I thought about it the more I realized it isn’t that simple.

What follows is some boring, technical crap. If that doesn’t interest you, here’s some cute cat photos.

Ok, I can imagine a Foucault Pendulum at the North Pole. I can see it moving around in 24 hours.

But, I thought, what about one at the equator? Wouldn’t it be stationary?

So I looked it up online and I was right. It would not move.

But what threw me off were the latitudes in between. Because there is an angle between the string of the pendulum and the rotation of the earth – it rotates, but slower. The closer to the equator, the longer it takes to go around. The precession period for an ideal pendulum and support system is 23.93 hours (a sidereal day) divided by the sine of the latitude. In the middle of the US, this is about 32 hours. This period of time is called a pendulum day.

sidereal day(23.93 hours)<solar day(24 hours)<pendulum day(varies by latitude) (though I guess there is a latitude near the north pole where the pendulum day is the same as the solar day….)

The problem that I have is this: imagine the pendulum at our latitude… it goes through a 24-hr. cycle… now the pendulum is in exactly (more or less) the same spot that it was at the beginning… yet the pendulum, because the pendulum day is longer than 24 hours, is not at the same spot.

If the pendulum is truly staying the same… and the earth moving beneath it… why doesn’t it return to the same relative spot in 24 hours?

I spent way too much time thinking about it. I kept thinking about cones.

I’m not sure I’ve completely worked it out – but this site helps. Here is the meat of the text:

The ‘plane’ of the pendulum’s swing is not fixed in space

It is worthwhile correcting a common misunderstanding about Foucault’s Pendulum. It is sometimes said (perhaps poetically) that the pendulum swings in a plane fixed with respect to the distant stars while the Earth rotates beneath it. This is true at the poles. (It is also true for a pendulum swinging East-West at the equator.) At all other latitudes, however, it is not true. At all other latitudes, the plane of the pendulum’s motion rotates with respect to an inertial frame.

It is easy to deal with this misunderstanding. Consider a pendulum at the equator, swinging in a North South plane. It’s obvious from symmetry that the plane of this pendulum doesn’t rotate with respect to the earth and that, relative to an inertial frame, it rotates once every 24 hours.

Alternatively, consider the motion of a point on the earth at a place that is neither at the poles or the equator. During a day, a vertical line at that place traces out a cone, as shown in the sketch at right. (If the earth were not turning, the half angle of the cone would be 90° minus the latitude.) During each cycle of the pendulum, when it reaches its lowest point its supporting wire passes very close to the vertical. So, at each lowest point of the pendulum, its wire is a different line in this cone. This cone is not a plane, so those lines do not all lie in the same plane!

For yet another argument, consider the motion of the pendulum after one rotation of the earth. With respect to the earth, the period of precession of the pendulum is 23.9 hours divided by the sine of the latitude. For most latitudes, this is considerably longer than a day. So, after the earth has turned once, the pendulum has not returned to its original plane with respect to the earth. For example, our pendulum in Sydney precesses at a rate of one degree every seven minutes, or one complete circle in 43 hours.

(I apologize for emphasizing this rather obvious point. I only do so because a correspondent has pointed out to me that many web pages about the Foucault pendulum – and even, allegedly, a few old text books! – make the mistake of stating that the pendulum swings in a fixed plane while the earth rotates beneath it.)

So, what is the path of motion of the pendulum? Remember that the point of suspension of the pendulum is accelerating around Earth’s axis. So the forces acting on the pendulum are a little complicated, and to describe its motion requires some mathematics. (Indeed, even talking of a ‘plane’ of motion on a short time scale is an approximation because even in half a cycle the supporting wire actually sweeps out a very slightly curved surface.)

Now my head hurts. Unfortunately I can’t relax. I have my reading to do.

Sweet dreams.

Short Story Of the Day, Whump Whump Whump by Bill Chance

The station was a squat peninsula in a vast sea of corn on the south side of the highway. The tall, green, thick stalks blocked any breeze that might have been able to stir.  Russ was bent over, trying to carefully meter out exactly five dollars’ worth of fuel, “click, whoosh, click, whoosh” but he still gazed across the highway where hay fields stretched to the horizon.

—-Bill Chance, Whump Whump Whump

Decatur, Texas

I have been feeling in a deep hopeless rut lately, and I’m sure a lot of you have too. After writing another Sunday Snippet I decided to set an ambitious goal for myself. I’ll write a short piece of fiction every day and put it up here. Obviously, quality will vary – you get what you get. Length too – I’ll have to write something short on busy days. They will be raw first drafts and full of errors.

I’m not sure how long I can keep it up… I do write quickly, but coming up with an idea every day will be a difficult challenge. So far so good. Maybe a hundred in a row might be a good, achievable, and tough goal.

Here’s another one for today (#20). What do you think? Any comments, criticism, insults, ideas, prompts, abuse … anything is welcome. Feel free to comment or contact me.

Thanks for reading.



Whump Whump Whump

It was hot, even for July in the plains, and Russ Hathoway felt like he took a physical blow every time he left or entered the little cinder block building to tend to the pumps. It was as much of a shock to enter the cold of the inside, with the humming window units spaced around the back wall, as it was to battle with the searing sun. He was pumping gas all summer to make enough money to pay for his tuition. He was working toward a math degree at the state university. He didn’t know how he would ever make it – not only money-wise, but the other kids, mostly from countries he had never heard of, were so, so much smarter than he was.

And now he was stuck working at this gas station in the middle of nowhere. The customers liked him though, and the owner noticed the place made more money when Russ was manning the pumps. So the owner and his whole family piled in the station wagon and took off for the whole month, leaving the place for Russ alone. That was fine, more hours, more money. And in the slow times Russ could pull his textbook out and jot calculations on the chalkboard behind the counter – get a head start on the fall semester. In that summer of ’77 gas had jumped to sixty-two and nine/tenths cents per gallon and the customers always complained about it – like Russ had any influence on oil prices.

The station was a squat peninsula in a vast sea of corn on the south side of the highway. The tall, green, thick stalks blocked any breeze that might have been able to stir.  Russ was bent over, trying to carefully meter out exactly five dollars’ worth of fuel, “click, whoosh, click, whoosh” but he still gazed across the highway where hay fields stretched to the horizon. Today a “Green Monster” – a giant spindly machine armed with a crew of young men Russ’ age moved around the field scooping up rectangular bales with a probing conveyor belt until the crew grabbed and stacked the compressed fodder into a growing cube – like giant green fuzzy sugar cubes.

He knew some of the boys working on the Monster – they were bronzed and shirtless, which looked pretty fun to Russ, struggling in his oil-stained uniform and Standard Oil cap. His distraction caused him to give one click to many and the total jumped to $5.10.

“Shit,” Russ muttered. He didn’t mind giving the customer and extra dime of fuel, but he knew the station owner carefully checked the amounts stored inside the pumps against what the cash register said he sold and if there was a significant difference, he would chew Russ out and dock his salary.

One morning, business was slow – almost no cars disturbed the heat wave ripples rising from the asphalt highway. Russ was sitting on the little plastic chair with his textbook spread open. He would scratch his head, scribble in a spiral notebook, or squiggle on the chalkboard. To his left was the giant cash register with its brass keys, deep polished wood, and stark cash signs sticking up above. He remembered how difficult the register was to operate when he first started, pushing the keys and pulling the heavy lever to register the sale and open the cash box.

Now he could work the thing without even looking at it. He enjoyed the rhythm, effort, and most of all, the sound of the mechanism as it did its work. He would make up little poems to go along with the cadence of the operation, “Thank You HapPy People,” he would mutter to himself.

To his right was the calculator. It was used to add up charges and discounts to the gas station’s commercial accounts – diesel semis or fleets of delivery trucks. The owner had worked out special rates and prices with these companies and the calculator was needed to figure out the charges. The owner and his kids struggled with this, but for Russ it was second nature.

This big box of numbers fascinated him. It was an Olivetti Divisumma 24, made in Italy with exquisite craftsmanship. Every two months a technician stopped by and removed the case, exposing an impossibly complex three dimensional jungle of wheels, gears, and levers. He would adjust and lubricate the delicate mechanism while Russ stared over his shoulder.

Russ had a strong innate curiosity and he couldn’t help but try to figure out how it worked. It had an electric motor inside that set all the gears turning, but all the logic, all the intelligence of the thing was mechanical – set inside that metal brain of tiny interlocking parts.

It would add by moving gears and printing out the result on a little strip of paper (the technician always replaced the ribbon). Multiplication was simply addition done over and over. Russ would multiply two numbers and listen to the repeated whump whump whump of the mechanism as it moved around, adding over and over again. Subtraction, again, was simple. It was only addition in reverse.

What Russ found really fascinating was that the machine could divide. It took him a while to figure that one out. It divided by adding. The smaller number, the divisor, would simply be added up over and over until it was just less than the dividend, the large number. The calculator would then print this whole number out, along with a remainder.

Russ couldn’t help but try this out. He was amazed by this simple bit of arithmetic. He would try it with evenly divided numbers and then with operations that left a remainder. He guessed this crude arithmetic was fine for financial calculations – “how many gallons can someone buy?”, for example, and “how much change was left?”.

That morning, though, a question occurred to him. What would happen if he entered a formula where the machine had to divide by zero? It would try and add that zero over and over again, but it would never increase. Russ shook his head and casually reached over, entering 7 divided by zero, and pushed the equal sign.

Whump, Whump, Whump, Whump,” the machine started in. That made sense, it was trying to add that zero up. An hour later, though, it was still going “Whump, Whump, Whump,” and Russ was starting to get worried. He pulled on all the levers and pushed all the buttons but nothing changed. “Whump, Whump, Whump.”

After staring at it and thinking a bit, Russ unplugged the machine. The noise stopped. Relieved, he plugged it back in, but it started in, “Whump, Whump, Whump.” Russ let it run all day.

“Oh, Shit! man, I’m in big trouble now,” Russ said out loud.

The old man told him that it cost seven hundred and fifty dollars. And now he had broken it. The owner will be docking Russ’ pay ‘til the cows come home.

Seven hundred fifty. At three bucks and hour, less taxes…. That was almost two semesters of tuition.

Whump, Whump, Whump.”

It would be two weeks before the owner came back. Russ left a notebook by the machine and did all the calculations by hand, but that would only get him by until the owner saw what he had done. All day the sound haunted him. Sometimes he would unplug it for relief from the noise, but he always let it run all night.

He would come in the morning to open up, hoping it had stopped in the night, but was always greeted by that infernal sound.

Whump, Whump, Whump,” the calculator droned on in the background.

Days moved into weeks and Russ began to worry more and more. He had no idea what he would do when the owner returned.

He thought of lying to the owner, saying it, “Just started up by itself.” That didn’t sound like it would work.

Then, miracles of miracles. Two days before the owner’s return, Russ was sitting there listening to the sound. He was used to it, it was the background to his day. He was even used to the anxiety that it produced. That worry too had faded into the background, even though it was always there. Russ knew he would have to live with that too, which was worse.

Suddenly, a second of silence. That silence, the lack of “Whump, Whump, Whump,” was the loudest thing Russ had ever heard. It was followed by a strident clattering as the machine began to print out on its paper tape.

Russ stared as it printed. Line after line of numbers. They looked random, but there it was, a long number that stretched almost to ninety digits. Finally, it stopped and the machine sat there silent and still, waiting for its next task.

Russ pulled out the tape and looked at it. Thinking, he figured the gears must have slipped a little bit with each Whump – and finally, after weeks, they slipped enough to add up to seven.

To this day, forty-four years later, on the wall of his office in the bowels of the University Mathematics Department, next to his PhD diploma, hangs an oddly shaped frame containing a long strip of aged yellowing paper. On that paper is a single, long number.

When asked, Professor Hathoway, Chairman of the math department, likes to answer with a wry smile, “That number is the answer to seven divided by zero.”

What I learned this week, June 19, 2020

This equation will change how you see the world (the logistic map)

I have always been facinated with the Mandelbrot set and fractal math in general – this is a particularly good example.




The ‘Untranslatable’ Emotions You Never Knew You Had

From gigil to wabi-sabi and tarab, there are many foreign emotion words with no English equivalent. Learning to identify and cultivate these experiences could give you a richer and more successful life.

Some of these are fascinating

  • Desbundar (Portuguese) – to shed one’s inhibitions in having fun
  • Tarab (Arabic) – a musically induced state of ecstasy or enchantment
  • Shinrin-yoku (Japanese) – the relaxation gained from bathing in the forest, figuratively or literally
  • ktsuarpok (Inuit) – the anticipation one feels when waiting for someone, whereby one keeps going outside to check if they have arrived
  • Natsukashii (Japanese) – a nostalgic longing for the past, with happiness for the fond memory, yet sadness that it is no longer
  • Wabi-sabi (Japanese) – a “dark, desolate sublimity” centered on transience and imperfection in beauty
  • Saudade (Portuguese) – a melancholic longing or nostalgia for a person, place or thing that is far away either spatially or in time – a vague, dreaming wistfulness for phenomena that may not even exist
  • Sehnsucht (German) – “life-longings”, an intense desire for alternative states and realizations of life, even if they are unattainable
  • Pihentagyú (Hungarian) – literally meaning “with a relaxed brain”, it describes quick-witted people who can come up with sophisticated jokes or solutions
  • Desenrascanço (Portuguese) – to artfully disentangle oneself from a troublesome situation

Read more here:

The ‘Untranslatable’ Emotions You Never Knew You Had


Bread and Butter Pickles

I have always loved these things – and never knew why they were called that. Apparently, during the depression people made sandwiches with bread, butter, and pickles. And it seems to have been delicious.

Read about it here:

The history and mystery of America’s long-lost pickle sandwich

The History of Popcorn

I always thought that popcorn was a modern invention. I was wrong.

Long before boxes of Pop Secret lined grocery store shelves, corn began as a wild grass called teosinte in southwestern Mexico, according to research compiled by Mexico’s National Institute of Anthropology and History. Corn was probably cultivated as a domesticated crop around 9,000 years ago, but it wasn’t until 2012 that archaeologists unearthed the first evidence of popcorn in Peru: 6,700-year-old corn cobs studded with puffed kernels.


Early popcorn probably resembled parched corn, which is made by cooking dried kernels, often in a frying pan. (Because parched corn typically uses kernels with lower water content, curbing its ability to pop, it’s considered a predecessor of CornNuts.) “Parched corn is much crunchier,” Frank says. “We know that in the early Southwest, there was popcorn—it just wasn’t a Jiffy Pop that you’d put in your microwave.”

The fluffy popcorn we know and love today is, in part, the result of thousands of years of careful cultivation of a few different strains of corn by those early tribes.

Read more here:

The History of Popcorn: How One Grain Became a Staple Snack


Corn in a Cup




Steadman and Thompson’s first meeting

The story of Hunter S. Thompson and Ralph Steadman covering the Kentucky derby.

Read it here:

Decadence and Depravity in Louisville, Kentucky





Information, Sunflowers, and Pinecones





“Information. What’s wrong with dope and women? Is it any wonder the world’s gone insane, with information come to be the only real medium of exchange?”
― Thomas Pynchon, Gravity’s Rainbow

Sunflower and fly

Wednesday evening, dark, cold, we were all sitting on the big wooden table for this week’s discussion of this week’s seventy page section of Gravity’s Rainbow. Somebody remarked on the relationship between nature and mathematics… “Mathematics is our way of describing nature,” and then brought up the Fibonacci sequence and the Golden Ration and the spirals in “Sunflowers and Pinecones.”

My ears perked up. Early that day I had stumbled across a YouTube video on the subject. Of course, everybody talks about those darned spirals and how they show up everywhere. This video was different, though. It talks about the Golden Ratio and then goes on to say why it shoes up on Sunflowers and Pinecones. It shows why it’s the only way to organize a Sunflower or a Pinecone.

Watch it or not.




What I learned this week, February 21, 2014

A skyscraper towers over the water feature in Beck Park

A skyscraper towers over the water feature in Beck Park

A Better Carpenter Plaza

The past and current green space plans for downtown Dallas aren’t thinking comprehensively about how development nor economics of urban spaces work. They’re band-aids to cover up mistakes rather than generate real value.

It’s not about the nail
“Don’t try to fix it. I just need you to listen.” Every man has heard these words. And they are the law of the land. No matter what.

The Wind Rises

If The Wind Rises is indeed the final film from Hayao Miyazaki—the animation master has both announced and rescinded his retirement—he leaves us with a moving, meaningful farewell. Based on Miyazaki’s own manga, this Oscar nominee for Animated Feature Film plays the gentle notes of a Japanese countryside against the impending horror of World War Two, Miyazaki seeing it all through the myopic eyes of a budding aeronautic engineer.

Examples of past Miyazaki genius:

Spirited Away trailer

Castle in the Sky trailer

Nausicaa trailer

For the last few decades one of the things I marked my life with was the release of each Hayao Miyazaki film… from Totoro to Mononoke, on to Spirited Away (a masterpice) with Nausica and Laputa and Howl’s Moving Castle and more and more thrown in for good measure. It gave me a feeling of periodic genius.

It looks like this has come to an end (really this time – he has threatened retirement before) and I will miss it – but the collection of work is stil out there.

Might be time to rewatch a few.

top ten underrated Studio Ghibli Films

The #1 movie on this list is Grave of the Fireflies – the most heartbreaking film I’ve ever seen.

I like some of the new Fat Bike designs - but this is a little much... maybe a lot much.

I like some of the new Fat Bike designs – but this is a little much… maybe a lot much.

Should You Buy a Fat Bike?

If you’re not familiar with fat bikes like the Salsa Mukluk or Surly Moonlander, think of a two-wheeled monster truck with you as the motor.

“Fat bikes allow people to ride bicycles in places that previously were simply not possible,” says Peter Koski, product development engineer at Salsa.


Math Explains Likely Long Shots, Miracles and Winning the Lottery [Excerpt]

Why you should not be surprised when long shots, miracles and other extraordinary events occur—even when the same six winning lottery numbers come up in two successive drawings

 10 Deliciously Complex TV Villians
I always say that in terms of entertainment, espectially visual, thriller-type entertainment, it’s not the hero that’s important… it’s the villian. Give me an interesting, complex villian over some goody-two-shoes anytime.

The fountain in back of the Richardson Library. (click to enlarge)

The fountain in back of the Richardson Library.
(click to enlarge)

These Are The 10 Happiest Mid-Sized Cities In America

I only live in one of these, but I do live in one… and I have spent significant time in four of them and been in eight.

top ten opera lyrics

It doesn’t get any better

Statistics Say We Should Take Friday Off From Work. All The Fridays, Forever And Ever.

Texan turning Japanese sake into a Lone Star tipple

What could be more Texas than this? Rice grown in Texas fields first planted by settlers more than a century ago, processed by a Texan in the heart of the capital, Austin, and sold under the product name “Rising Star.”

Welcome to the world of the Texas Sake Company, almost certainly the first – and most certainly the only – commercial brewer of the Japanese rice wine operating in the Lone Star State.