by Todd Borg
“Nice room,” I said.
“I suppose,” Giuseppe said, turning and looking at it as if he hadn’t really considered it. “I walk through it carrying my coffee up to my workshop, but that’s it. I hate the designer look. It’s like they set it up as a showroom for a magazine shoot. The house used to be owned by a movie producer. Maybe he thought he would entertain clients or something. But as far as I can tell, he never used the room, either.”
Giuseppe turned and walked through the living room toward a large kitchen. “The design of fancy living space,” he muttered as he moved away from me, “creates spaces that are less artfulness and more artifice. Places where one doesn’t really live.” He was shaking his head as he walked. “Humans must be the only species…,” he trailed off. He was still walking away from me, so I could barely hear him over the clicking of Spot’s nails on the stone floor. “Animals create housing that is all about function, not look. But their plumage… Now there’s something similar. I suppose a man’s living room could be like a peacock’s feathers, all part of the seduction routine.”
I couldn’t hear the rest of his words as he rounded a corner.
THIRTY-THREE
I followed Giuseppe as he walked through the kitchen and out a sliding door. Outside was a brick patio that was surrounded with bushes and trees. I followed him through an opening at the edge of the patio and stepped onto a brick path that curved through fir trees intermixed with clusters of aspen. The path went down a wide flight of steps made of the same brick, then traversed a short distance across the steep slope to another descent of stairs, and arrived at a wooden deck that was built out from the steep slope and overlooked the lake in the distance. The deck had a spectacular view. None of the neighboring houses was visible from the deck. To one side of the deck was a view of the steep, cliff-like bluff that was adjacent to Giuseppe’s house. The cliff was mostly a vertical pile of boulders interrupted with outcroppings of Manzanita.
On the deck were two lounge chairs facing the lake. In one corner was an umbrella in a heavy stand. Still holding his cat, Giuseppe struggled with it, trying to raise the umbrella sleeve and open it up. I reached out to help, and the umbrella opened, the catch clicking into place. The lounge chair cushions were brilliant red, as was the umbrella, dramatic against the deep blue of the lake. Or maybe, as Giuseppe had said, it was just artifice.
He walked over to one of the chaise lounges, leaned on his cane, then, with some struggle, got one leg lifted over a cushioned seat, and slowly lowered himself down. The cat rode in his other arm like royalty.
Spot trotted the perimeter of the deck, which projected out over the steep slope. He came back, reached his nose toward the cat but stopped 18 inches away, sniffing, still wary, doing the doggie calculation of risk and reward.
I sat next to Giuseppe, both of us facing the lake.
“When I was trying to find you, I discovered that you were lecturing on a cruise ship. So I called the company, and they said you’d just gotten off a fourteen-day cruise yesterday. Is that a rewarding project, teaching people about, what, physics?”
“Rewarding? I don’t know. It’s kind of fun. I do it as an exercise in staying engaged with people. Scientists are basically introverts. We’re happy to just be by ourselves, working on our projects.”
I nodded. “I know what you mean.”
“If we don’t want to become shut-ins, we have to force ourselves to go out and mix it up. I made a little study of it. I listed all the activities one could utilize to engage with people. Then I scored them in terms of the type of people you’d meet. I considered book clubs and churches and service clubs and travel groups and all manner of boating groups. I decided to become a speaker on cruise ships because I do better when I have a role to play. I wouldn’t be any good at standing around making small talk. The people running the lecture circuit told me that cruise passengers love learning about something new. So I decided that explaining about Lagrangian points might be fun. It’s worked out quite well. As a result, I’ve met a few people with whom I’ve kept in touch. I suppose it’s ego gratification. When you’re known for something, people flatter you. They want to have a drink with you. Or maybe they just want to be able to go home and tell their friends they had a drink with you.”
“It’s the Lagrangian points that I want to talk to you about,” I said.
“That’s what you said in your email. I was, of course, somewhat astonished, so I agreed to meet with you.”
“I’m a private investigator looking into the death of a woman named Dory Spatt. She ran a scam charity.”
“Do you mean, a charity that was a fraud?”
“Yes.”
“I’ve seen some charity marketing that looked suspicious. But I always hoped it was just my cynicism. I’m sorry to hear that charity fraud is real.”
“Me too,” I said. “My investigation took me to Dory’s Sausalito home where I saw a framed poster of the inner solar system with Lagrangian points marked on it. When I asked Dory’s brother about it, he said that her former charity partner believed that Lagrangian points are a good business model.”
“Goodness, what a concept. And an obscure clue,” Giuseppe said.
“I understand you’ve done a lot of work on Lagrangian points. Does the idea that they could serve as a business model make any sense to you?”
Giuseppe shook his head. His wild hair wobbled. “Not at all.”
“Maybe you could just tell me about your work on Lagrangian points,” I said.
“All I’m doing is developing some new ways of analyzing them.”
“What does that mean? Or is it too tedious to try to explain such things to a layman?”
“It’s not that tedious.”
“Just sort of tedious,” I said.
“Yes. Sort of. I’ll give you my lecture version. In seventeen seventy-two, my Italian namesake Giuseppe Lagrange, also known as Joseph Lagrange, discovered the solution to what was called the three-body problem for how objects move in space. That led to an understanding that there were various points of stability in space, what are now called Lagrangian points. They are parking places, if you will, where we can place satellites and have them stay put because there is an equilibrium of all of the forces acting on those points. In the case of Sun-Earth Lagrangian points, the gravity of the Sun and the Earth and the centrifugal force an object experiences as it goes around the Sun, all cancel each other out. In the case of Earth-Moon Lagrangian points, the same relationship exists but those would be for objects orbiting the Earth. Lagrange’s mathematics predicted this. Many years later, they were demonstrated to exist.”
“Parking places in space,” I repeated.
He nodded. “They exist for any large body that orbits another body, places where a third object can park.”
“You said seventeen seventy-two. So that was almost two hundred years before we were able to send up the first rocket ship into space.”
“Such is the power of math,” Giuseppe said. “Variational calculus, to be specific. Newton figured out the basic laws of motion. Then guys like Giuseppe Lagrange came along and fine-tuned it. His math innovation is now called Lagrangian Mechanics.”
“Does this high level math have any real-world applications?”
“Oh, yes, yes, yes!” Giuseppe said. “It is momentous. We now park multiple spacecraft at the Sun-Earth Lagrange points.”
“I notice that you seem to use the words Lagrange and Lagrangian interchangeably.”
“Yes. We use both words for the same concept.”
I nodded.
Giuseppe continued. “We’ve used the Earth-Moon Lagrange points as well. We also turned our telescopes toward the Sun-Jupiter Lagrange points because we knew that because of Jupiter’s large size, we would find natural objects suspended, so to speak, in space in those areas. It’s similar to the way floating debris gets caught in the eddies of a stream. And do you know what we found in the Jupiter Lagrange points? Thousands of asteroids! We call
them Jupiter Trojans.”
“So Lagrangian points are something special,” I said.
“Beyond special,” Giuseppe said. His enthusiasm for such an unusual subject was infectious. “An eighteenth century mathematician, using abstract symbols on a blackboard, figured out that for every two big objects in space, like the sun and a planet, or a planet and one of its moons, there are five special points – moving points – where there is stability in space. Two of the points are especially stable. What Lagrange did was simply amazing.”
“And so you’ve been figuring out something new about these parking places?”
“I have. Think of a merry-go-round. The different horses are the planets, orbiting around the sun at the center. If you set a marble on the floor of the merry-go-round, it flies off. But Lagrange points are like large, kidney bean-shaped bowls on a merry-go-round. Put a marble in one of the bowls, and it won’t escape. But it will wobble around, this way and that as the big merry-go-round turns. I’m working on a set of principles for regulating spacecraft that have been parked in what we call the L-Four and L-Five points.”
“Let me guess, your work would keep the spacecraft from wobbling around?”
“No. It’s merely a type of prescriptive orbital mechanics, which leads to adaptive technologies.”
Maybe Giuseppe could see my face go blank. He was so far over my head that I couldn’t process what he was saying.
“Imagine one of the marbles in the kidney bean bowl,” he said.
I nodded.
“Now imagine that it is a spacecraft with a powerful telescope trained on a distant galaxy.”
“Oh, I get it,” I interrupted. “If you know just how the spacecraft is wobbling around in the bowl, you can tell its computer how to adjust the telescope so the galaxy stays in focus.”
Giuseppe beamed at me, his eyes intense and his wild puff of hair vibrating. “You should have been a mathematician!”
“Thanks, Giuseppe. But trust me, no, I should not have been a mathematician. Visualizing marbles in a bowl that sits on a merry-go-round is kind of fun. But just thinking about those little abstract symbols that you use to figure out the laws of the universe makes me want to get a beer and a bowl of popcorn and escape into a Hollywood movie.”
Giuseppe seemed disappointed. He’d no doubt spent an entire life being entranced by higher math and its ability to discern the workings of the universe when other people were entranced by gossip magazines spewing the latest celebrity divorce scandal or cellulite reduction trick.
“This Lagrange math application,” I said.
He nodded.
“Will it produce other real world benefits?”
“Oh, you can’t imagine. As I said, we already use Lagrange points to park spacecraft for scientific study. But in the future, we’ll use these points to build space communities and refueling stations for spacecraft heading off to other planets and, one day, other solar systems.” Giuseppe’s eyes were wide with excitement.
I said, “Kind of like when Columbus set off from Spain and found islands that became outposts for future explorations.”
“Indeed.”
“I’m awed. I’m a nuts-and-bolts guy. If I wanted to be innovative and invent something, I’d try to dream up a new kind of widget, a more efficient device for doing a household task. You are using math to unlock the scope of the universe. The nature of your mind exploration is amazing. This big-picture math stuff makes what most of us do seem insignificant.”
Giuseppe reached out and put his hand on my forearm. “Mr. McKenna, in the big picture, we are all insignificant. Remember what Carl Sagan said when that spacecraft took the first picture looking back at us from far out in the Solar System? In the photograph, our planet was this unbelievably small blue dot of reflected light. Sagan described the Earth as a mote of dust suspended in a sunbeam. And the entire history of humanity has lived on that dust speck.” Giuseppe squeezed my arm. “We are all insignificant,” he said. “All I’m doing is trying to understand the nature of that insignificance. So I study these unusual places in space. Five special places for each pair of large bodies where one revolves around the other. Three of the five Lagrange points are somewhat unstable. The bowl on the merry-go-round is very flat, and sometimes the marble rolls out. But two of the five points are very stable, deeper bowls. I catalog how these places, each so simply numbered, climb toward instability. The math that describes these places helps NASA and its scientists plan their future space missions.”
We sat in silence. Bird songs floated on the air. Boats tracked across the water. When the breeze paused, the high-altitude sun was burning hot. Spot lay down at the far end of the deck, legs splayed, jawbone stretched out on the boards. A hummingbird buzzed, floating in the air above our heads. He was as brightly colored as Douglas Fairbanks in his bicycling spandex. The bird shot over to a planter where flowers waved, the yellow and purple and lavender mixing with his red body. A distant sailboat came into view, its white triangle of sail brilliant against the indigo water.
After a moment, I said, “If you had to imagine a reason why a charity scammer would see Lagrangian points as some kind of business model, what might it be?”
Giuseppe frowned. “I have no idea. I suppose it could be that if one could find places or concepts in the business world where the stresses and forces would cancel each other out, maybe such a businessman could make more money. Or, if a revenue source could be maneuvered into a stable place, the money would keep flowing? Does that sound crazy?”
I looked out at the lake as I pondered what he’d said. “You’re saying that Lagrange points might only serve as a vague metaphor.”
Giuseppe chuckled. “I don’t really have a clue about what I’m saying. I’m reaching. Reaching for metaphorical Lagrangian points.”
We sat for a bit, taking in the breeze and the view.
I gestured at the lake and the surrounding land. “An amazing place you have here.”
“Yes, I’ve been very fortunate.”
“Are you still working full time?”
“Of course. What else would I do? Oh, you’re wondering if I would retire,” he said as if surprised at the thought. “Perhaps if I were in a more ordinary line of work, I would. But what I do isn’t something you retire from. Although recently, I’ve wondered if I’m starting to get some premature dementia. I have a new neighbor named Aubrey Blackwood. She lives in the duplex near my barn, so I see her when I walk over there. She’s quite a good watercolorist. Anyway, she’s taken to calling me when I leave my car doors open and such. I never paid much attention before. I’d just go outside, see my door open, and hope the battery hasn’t run down too much. But now her concerned calls become a record of my lack of mindfulness, a catalog of my slow descent.”
“I met her when I came here. Seems like a nice lady. This barn of yours... Do you keep horses or something?”
“Goodness, no. It came with the house. But I like to walk there and ponder what kind of life the barn builder might have had. Anyway, I’ll keep working into the foreseeable future. Quitting would be like Aubrey giving up the easel and paints. For some, work is a means to an end. For others, it is the end. Our raison d’être.” He looked down at his cat, which was still balanced on his arm. “Quitting would be like Blofeld retiring from catching mice.”
“His name is Blofeld? How fun. I thought of the James Bond movies when I first saw your cat.”
“Yes, that’s why I gave him the name. Even as a six-week-old kitten, he acted like Blofeld’s cat.”
“I should get going. I really appreciate your time.”
Giuseppe nodded.
“If I have other questions, may I call?”
“Speaking of metaphors… Modern communication produces one of the great modern philosophical conundrums, very different from the days when we sent a letter by ship or train or Pony Express. Those letters were read and responded to at the recipient’s leisure.”
“I think I’m missing your meanin
g,” I said.
“You mentioned calling me. I gave you my number, after all. But phone calls are all about the caller’s convenience. The person generating the communication is, in effect, demanding to be attended to now. Email is all about the receiver’s convenience. The modern version of a letter. It should be obvious that convenience belongs with the person who is asked the favor of communication, not the person who is doing the asking.”
“Now I get it. So I won’t call you,” I said.
Giuseppe made a little grin. Maybe his whole statement was a bit of a joke.
“If I have a future question, I’ll email you,” I said.
The grin turned to a full smile. “I believe you have my email address as well.”
As I drove away, I thought of Blofeld and his evil owner in the James Bond movies. I wondered if Professor Calvarenna could be stringing people up by their ankles, and if so, why. But I remembered that he had been out doing his cruise ship routine when Dory was killed.
THIRTY-FOUR
M y phone rang at 6:30 a.m. the next morning.
“Owen McKenna,” I said.
“Ramos, here.”
“Wow, our tax dollars go to work early.”
“I learned of a death from hanging by the ankles,” he said, ignoring my comment. “Apparently, it was a house-painting accident. But I thought I should let you know.”
“I appreciate that.”
“The victim was an older gentleman, a retired doctor. He was up on an extension ladder painting the upper part of his house. He slipped and fell, and his foot caught in the rope that’s used to raise the extension part of the ladder. The rope wrapped around the man’s ankle, and he ended up hanging upside down, his head about five feet above the ground. The ME thought he’d probably hung for several hours before he suffered a hemorrhagic stroke and died. This happened in Ukiah. It’s a small town about one hundred miles north of the Bay Area on one-oh-one.”