CHAPTER SEVEN

The Investment Principle

I’m at Emily’s place, lounging on her couch and taking notes on the Wikipedia entry for “wave function.” Emily is telling me about one of her favorite poets, Mary Oliver, who died last year. Oliver, who spent much of her adult life in Cape Cod, celebrated nature. She liked to start her day by holding a notebook and pencil and looking out the front door of her house, waiting for a poem to come. Emily finds Oliver’s ritual inspiring. 

I tell Emily that I start my days that way too. I lie on the couch with my notebook in my lap and write down whatever comes into my head; this morning, for example, I’ve been riffing on wave functions, represented by that enigmatic symbol Ψ. I hold up my eight-by-eleven-inch notebook and show Emily a page of what she calls my Unabomber scribbles, which include many Ψs.

Emily looks at me and asks, Are you trying to ruin it for me? By “it” she means Mary Oliver’s sacred morning ritual. Emily is frowning, she’s not kidding. My feelings are hurt. Mary Oliver asks, at the end of “The Summer Day,” “Tell me, what is it you plan to do/with your one wild and precious life?” Well, Mary, right now I’m trying to learn quantum mechanics; this project is my way of paying attention to the mystery. Oliver ends her poem “Wild Geese” this way:

Whoever you are, no matter how lonely,

the world offers itself to your imagination,

calls to you like the wild geese, harsh and exciting—

over and over announcing your place

in the family of things.

“Wild Geese” is a little ruined for me by all the Canadian geese overrunning Hoboken. Last week, when I was reading about wave functions in a park along the river, a goose attacked a girl sitting near me for absolutely no reason, pecking her head and neck as the girl screamed. That wild goose was a jerk. But the next morning I’m lying on a pier, staring at the sky, and a squadron of geese hurtles past me, so close I hear the muffled thudding of their wings. As they rush away from me, southbound, they call to each other, and their honks are as harsh and exciting and inscrutable as wave functions.

Particle in a Box

I crave physics with metaphorical oomph, and PEP553 delivers. My favorite synecdoche so far is the infinite square well, more commonly known as the particle in a box. As usual, we read about the topic in Introduction to Quantum Mechanics by Griffiths, our textbook, then Ed goes over it in class to make sure we get it. The particle in a box is an unrealistic, idealized model of quantum behavior, Ed emphasizes, and yet it serves as a useful teaching tool. It also has practical value; it has inspired microdevices such as “quantum dots” and “quantum well lasers,” which are useful for sensing and communication.

The particle in a box is what physicists call a toy model. Toy models are grossly simplified, cartoon versions of reality, but good ones can be revealing. Griffiths puts it this way: “Despite its simplicity—or rather, precisely because of its simplicity—[the particle on a box] serves as a wonderfully accessible test case for all the fancy machinery that comes later.” The particle in a box shows how quantum mechanics diverges from classical mechanics and from common sense.

You place a generic, unspecified particle in a box with perfectly bouncy walls, so the particle doesn’t lose energy when it bounces. The particle can have any mass, and the box can be any size. Other than the particle, nothing is in the box; it’s a vacuum, free from gravity and other forces. Relativity doesn’t apply. According to classical physics, the particle can be anywhere in the box. It can move and bounce with any velocity and thus have any energy, kinetic or potential. It can sit still, with no energy at all.

Quantum physics, in contrast, dictates that the particle must behave in certain constrained ways. The particle can only inhabit specific energy levels, and it has a minimal energy that keeps it from sitting still. Yes, that was the theme of Quantum Physics for Babies. Unlike the classical equations of motion, which show exactly what the particle is doing, the wave function yields only the probability that it will be in certain locations.

In its entry on the particle in a box, Wikipedia presents videos that dramatize the gap between classical and quantum mechanics. In the classical-mechanics video, a red ball, the particle, bounces back and forth in the box along a straight line. Ho hum. In the quantum video, there is no ball; there are only red and blue waves sloshing back and forth in the box. The red and blue waves correspond to the imaginary and real components, respectively, of the particle’s wave function, which is made of complex numbers. Eerily, the video shows what we can never actually see: the wave function. As soon as we look in the box, the red and blue waves vanish, and we see only the particle, the red ball. Before we look in the box, the ball, you might say, is imaginary.

The Flaws of STEM Education

I hit the jackpot with Dean, my study buddy, with whom I Zoom Monday mornings. He’s modest, self-deprecating, 24 years old. After getting a computer science degree from Hunter College, Dean worked for a software company for four years. He quit that job to pursue a doctorate in computer science at Stevens. He’s interested in the philosophical implications of computer science, as well as quantum cryptography, brain-machines interfaces and quantum theories of consciousness. He hopes to get his Ph.D. in four years.

Dean rejects the shut-up-and-calculate mindset. He wants to understand, to get math and physics on a conceptual, intuitive level, so he can visualize, ideally, what’s going on. He reached out to a friend getting a Ph.D. in math for help with the homework on Gaussian distributions. My tutor has a tutor. I ask if it’s common for people in a class like PEP553 to get help, as I am with him. Absolutely, Dean says; many students in our class will struggle and look for help, although few would admit it.

Dean shows me how he solved the Gaussian problem with a program called Desmos, which turns equations into graphs. Dean shares his screen with me so I can see what he did. He plugs the equation into Desmos and gets a graphical readout, which changes as he shifts the variables with sliding bars. This program helps him guess the solution to the homework problem. Dean likes doing math in this way rather than cranking through calculations by hand. The Desmos graphics remind me of the Wikipedia videos of the particle in a box. 

We’re supposed to go over homework, but I’m curious about Dean’s attitudes toward STEM education: Does it do a good job, or does it need fixing? Dean lights up. “I’ve been waiting for someone to ask me this question,” he replies. STEM education is dysfunctional, he says; teachers cover material too quickly, and students just nod along, pretending to understand and doing whatever they can to pass the course.

Instead of helping confused students, teachers often compound their confusion. An episode in the autobiography of Roald Dahl, the children’s book author, provides a gruesome analogy. Dahl’s brother, as a boy, fell off a roof and broke his arm. A doctor, assuming the boy had dislocated his shoulder, tried to jam it back into place, splintering the bone further. The brother’s arm eventually had to be amputated. STEM teachers who jam information down students’ throats, Dean says, resemble that doctor.

Dean blames the STEM-education system rather than teachers, who are under tremendous pressure from their departments, schools and even students’ potential employers to cover certain material. Dean knows how hard it is to buck the system, because he has taught math and computer science. He wants to experiment as a teacher, to try new things, but he has a checklist of topics to get through by the end of each semester.

Not surprisingly, many students turn for help to each other and to online teaching resources. Dean, like me, loves 3Blue1Brown, which gives you an intuitive, visual understanding of calculus, linear algebra and other math. Dean’s impression is that humanities courses are not as dysfunctional as STEM courses. He has taken humanities courses and observed classes taught by his father, a professor of film at Brooklyn College. Humanities courses are looser, more conversational, more concerned with intuitive understanding.

Dean’s comments remind me of Scott Aaronson’s complaints about quantum-mechanics instruction. Aaronson, the quantum-computing whiz, says courses often laboriously retrace now-obsolete concepts that led to modern quantum theory. Aaronson compares conventional quantum instruction to the QWERTY keyboard, which is inferior to other key arrangements that allow for faster typing. QWERTY, which refers to the letters on the top row and left side of your keyboard, became the locked-in standard through an historical accident; the same is true of conventional quantum pedagogy. Bucking a locked-in system is hard, as Dean acknowledges. Professors teach the way they were taught, perpetuating the flawed system. Some professors might also want students to suffer as they, the professors, suffered.

My quantum project has drawn my attention to an unexpected topic: the flaws of physics education. I recall Dean’s complaints during our next PEP553 session. Ed Whittaker, our professor, returns to the mathematics of wave functions, those mysterious gadgets at the core of quantum mechanics. Ed is not like the doctor who maltreated Roald Dahls’ brother; Ed keeps asking us if we have any questions. Usually no one does, but still, Ed asks. 

Whittaker breaks us into groups to work on a problem involving complex conjugates. I’m stumped, and so are the three undergraduates in my breakout group. I ask the group if this course is hard. Yes, one classmate replies, because the material is so counterintuitive, totally unlike what’s in other physics classes. I say I’m glad I’m not the only one struggling. My young classmate responds, But Professor, you don’t have to worry about a grade. I’m chastened.

Any questions? Whittaker asks again toward the end of class. Since no one else pipes up, I ask Ed why, in Griffiths, the wave function symbol sometimes has a lower-case, italicized form, ψ, instead of Ψ. The upper-case version applies to quantum states that evolve in both time and space, Whittaker explains, and the lower-case version to “stationary states,” when time is not a factor. The latter are also called “time-independent states.”

I have more questions: What is a “stationary state”? How can time not be a factor? Is spin a stationary state? [1] But if I asked Whittaker about everything that confuses me, we’d never get anywhere; we’d be stuck in a Zeno-esque loop. And sometimes I’m so confused that I don’t even know what to ask, beyond, Huh? Demanding that the professor resolve my confusion before moving on would be unfair to my classmates. You can’t calibrate your class for the slowest students; that’s unfair to the others. 

The professor’s dilemma, with which I’ve often struggled, is this: How do you teach everyone in the class, when knowledge and aptitude vary? I try to bring all my students along with me, but I always fail; some students flounder. But I’m just a humanities professor. I’m not conveying the technical knowhow needed to make bridges and insulin pumps; if these applications don’t work, people die. Maybe STEM professors must set the bar high, so everyone struggles a little or, in my case, a lot.

After class, I find discussions of stationary states on Wikipedia, illustrated by more videos of waves sloshing around in boxes. A stationary state occurs when the wave function takes the form of a standing wave, which does not fluctuate as time passes. If the standing wave represents a particle in a box, then the probability of finding the particle in a certain place does not change; that is why the stationary state is called “time-independent.” But the terms stationary state, standing wave and time-independent are misleading. Like a mound of water downstream from a boulder in a fast-moving river, a quantum standing wave only appears to be at rest; energy surges beneath its surface. 

Stationary states provide a handy analogy to enlightenment, the goal of Buddhism and other mystical paths. Enlightenment is often described as a state of supreme stillness; your mind stops jumping around and comes to rest. You achieve a kind of time-independence, in which only this moment exists. Supposedly. But if enlightenment exists, it resembles a standing wave, like the one below the boulder in the stream. Like the particle in the box, our minds never really come to rest, unless we’re dead.

Minsky’s Restlessness

Mulling over how dysfunctional teaching methods get locked in, I remember a conversation I once had with Marvin Minsky. Here’s the back story: Minsky, who died in 2016, was a pioneer of artificial intelligence. I interviewed him in 1993 at MIT’s famed AI Lab, which he founded. Minsky looked like Buddha, chubby with a big, bald head and round belly and mischievous smile. But Minsky wasn’t serene, he was agitated, his mind kept darting this way and that.

Minsky’s restlessness was more than a personality trait; it was an ideology that guided him in science and in life. As soon as he mastered a technical skill or solved a problem, his curiosity compelled him to move on, to find a new problem to solve. “It's so thrilling not to be able to do something,” he told me. “It's such a rare experience to treasure.” This attitude had served Minsky well; he was a polymath, adept in mathematics, physics, electrical engineering, robotics, cognitive science and other fields. He was also an accomplished pianist.

Minsky feared what he called the “investment principle,” our tendency to keep doing something we have mastered after investing time and energy in it. The investment principle explains why science, including his own field of artificial intelligence, often bogs down after spurts of progress; scientists cling to their accomplishments instead of pushing ahead.

The investment principle also accounts for the more general human tendency to get locked into narrow ways of acting and thinking. Minsky had a remarkable way of expressing this idea. “If there's something you like very much,” he said, “then you should regard this not as you feeling good but as a kind of brain cancer, because it means that some small part of your mind has figured out how to turn off all the other things.”

The investment principle, I realize, has much in common with the principle of least action--or, as I prefer to call it, the law of laziness. These tendencies explain our all-too-human susceptibility to habituation; we end up sleepwalking through life, barely thinking about what we are doing. Yes, we have countertendencies, such as ambition and curiosity, which can send us careening in unexpected directions. But the investment principle/law of laziness, especially as we age, undermines our adventurousness and open-mindedness. We get locked in.

What about love? What about romantic relationships, like mine with Emily? Is that just another form of locked-in behavior, a manifestation of the investment principle/law of laziness? Love, especially when combined with the vector of sexual desire, can be a disruptive, even dangerous anti-habituation force, knocking us away from safer paths. Over time, yes, love can settle into a routine, a set of rituals that we reenact robotically, but isn’t that long-term equilibrium a good thing? 

I wish I’d asked Minsky, who was married for 64 years and had three kids, about how the investment principle applies to love; he would surely have had an interesting answer. Not that his judgement was infallible. His legacy is tainted by his association with Jeffrey Epstein, the financier and sexual predator. Minsky organized two conferences held on a Caribbean island owned by Epstein. The second meeting took place in 2011, after Epstein had been convicted of “procuring a child for prostitution.”

Is it fair for me to mention moral lapses on the part of men like Minsky, Schrodinger and Feynman? I’m not sure. But it’s better to mention the lapses than not, if only because they remind us of the limits of human reason. I should also mention that if I had been invited to one of those scientific shindigs on Jeffrey Epstein’s island, I probably would have gone. But only A-list people got invited.

Luis

At our next Zoom session, Dean has a surprise for me. Luis, one of our classmates, has joined our study group. Luis, like Dean, is one of the few students who shows his face in class. He looks tough, cool, a bit older than his classmates. He has a well-trimmed goatee, and he’s really smart. Last week, Ed posed a tricky technical question related to the particle in a box, and Luis deftly answered it. Luis is working toward a master’s in engineering physics, with a focus on applied optics. He already has a lot of quantum mechanics under his belt.

Prodded by Dean and me, Luis tells us about himself. His family is from Puerto Rico. He didn’t go to college right after high school, and he cultivated a bad-ass image, lifting weights and getting tattoos. He joined the Army like his father, who served for 20+ years. Luis served five years, four in Germany and one in Afghanistan, mostly as a military policeman. He was in Afghanistan when U.S. special forces killed Osama Bin Laden.

Luis was conflicted about his service. There are bad people in the world, he says, and we’ll always need soldiers to protect us, but he never understood what we were doing in Afghanistan. Luis went to college after he left the Army, and he discovered that he loves physics. After he got his undergraduate degree last year, he decided to go to graduate school. His dream is to get a master’s, maybe a Ph.D., and work for a tech company. Dean and I wish him luck in fulfilling his dream.

I like watching Dean and Luis interact. Luis clearly knows more about quantum mechanics and the underlying math than Dean does, but he never talks down to Dean or to me. Luis is modest and funny. I can’t follow much of what he and Dean say to each other, but I’m hoping some of their smarts will seep into me.

I ask Luis a question related to the particle in a box: The model assumes that the wave function of the particle does not extend beyond the box; that is, there is zero probability that the particle is outside of the box. But doesn’t the uncertainty principle, I ask, decree that there is always some probability that the particle will find its way outside the box? Isn’t that the basis of what is called quantum tunneling? Good question, Luis says. He’s not sure what the answer is, but he’ll look into it.

After our Zoom session, Luis sends me and Dean a video in which Jade Tan-Holmes, an Australian physicist, answers the question I posed. A particle can indeed escape the box, she explains, because of something called an evanescent wave. That term seems both evocative and redundant. Aren’t all waves evanescent? The video is titled, “What is quantum tunneling, exactly?” The answer of Tan-Holmes is too technical for me, but it gratifies me; my question wasn’t stupid.

I just thought of another application of the investment principle. It explains why string theory has endured for decades despite its failure to live up to its hype. Physicists who have labored for years to master the fantastically arcane mathematics of strings are loathe to admit they have wasted their wild and precious lives wandering down a dead end. 

Cheating and Brain Chips 

A colleague emails me and other humanities professors a memo on the cheating pandemic. Websites hook students up with experts who, for a fee, do homework, take exams and write papers for students. The shift to online learning during the Covid pandemic has made a bad problem worse. What should we professors at Stevens do about this problem? Companies have developed technologies that monitor students, to detect and deter cheating, but it’s not clear these methods are effective or legal.

The memo makes me reflect on whether I could cheat my way through PEP553 or my whole quantum experiment. Cheating would be silly, given that my goal is understanding. And anyone with genuine knowledge of physics could quickly expose my deception. A quiz like the one Ed gave us at the beginning of PEP553 would do the job. Plus, I’m too ignorant to cheat, as I learned when I looked up the answers to the first homework problems. 

In the future, brains chips might help us cheat. Your android professor asks you to solve the Schrodinger equation for a certain value of t. “You” can’t answer the question, but your brain chip can. It plugs the question into a cloud calculator, akin to Desmos, and feeds “you” the answer. How could such cheating be prevented? Bioethicists have actually fretted over this problem, which I find hilarious. Brain chips, if they work as well as the bioethicists fear, would radically alter us, exponentially boosting our IQs and linking us all via wi-fi-enabled telepathy. We might evolve into The Borg, the villainous hive mind of Star Trek: The Next Generation. And bioethicists are worried about chip-enhanced kids cheating on math quizzes?

Even in the hive mind, I’m guessing, brain chips won’t eliminate our tendency toward deception and self-deception. If we are still human, and even if we aren’t, we’ll still find ways to fool each other and ourselves. We’ll still be flailing in the dark, careening between certainty and doubt. Marvin Minsky said superintelligent machines will be as puzzled by free will and other mind-body problems as we are. My guess is that our cyborg descendants will still be baffled by quantum mechanics, too, even if their brains are quantum computers. 

The Quantum Vest

While eating lunch, I listen to a Radiolab episode starring David Eagleman, a neuroscientist with creative flair. He has invented a vest packed with buzzers. The vest can be attached to any data source: reports on stock prices, the weather, a Twitter feed. The data are fed through a filter that translates them into patterns of buzzes in the vest. After a while, Eagleman says, you learn to recognize the buzzes and extract a kind of intuitive meaning from them.

I say “you” learn, but it’s really your brain that does all the work, in ways that, as Eagleman emphasizes, resist scientific analysis. The brain is an exquisitely sensitive signal detector, which can make sense of even crude stimuli in ways we can’t understand. There’s something uncanny about this Radio Lab story. It sets up a dichotomy between “us” and our brains, which do things far beyond our conscious comprehension. Don’t I equal my brain? It’s as though you are inside the Chinese room and your brain is outside, sending you cryptic messages. Or vice versa.

Notwithstanding these qualms, I wish I had a vest, a quantum vest, that could translate my PEP553 textbook and lectures into patterns of buzzes. I would sit here in my collapsible chair on this lovely, breezy day, surrounded by happy people, dogs and nonviolent geese, absorbing the mathematics of non-commutation through my skin. Bioethicists would disapprove, but I wouldn’t care.

As I indulge in this fantasy, a cool wind comes off the river. It feels urgent, insistent, as though it’s trying to tell me something. My eyes, nose, ears and skin absorb the information, register it and secrete it somewhere in my brain and body. A clever part of me deep within my brain is translating the windy message, making sense of it, but my slow, stupid, conscious self remains oblivious. I’m left with a familiar feeling, excitement tinged with dread.  

Luis’s Test

In our next study session, Dean and Luis talk about Internet stars who have attracted huge audiences with tutorials on math and physics. Some of the best virtual teachers are female. Dean and Luis both like Jade Tan-Holmes, who has a show called “Up and Atom”; she is the physicist who answered my question about tunneling. They also admire Katie Bouman, who devised software for detecting and creating images of black holes. Dean and Luis are impressed when I brag that I know Sabine Hossenfelder; they like her videos too.

I bring up my fellow professors’ concerns about cheating. I ask Dean and Luis if cheating is widespread in STEM courses. I add awkwardly, I know you guys would never cheat, but… Dean says that, in his experience, many students in STEM classes cheat, because of their desperation for good grades and the sink-or-swim attitude of professors. Students look up answers online and hire tutors who do their work. This has happened in all of Dean’s classes since high school; he’s pretty sure it’s the norm.

Luis tells us a disturbing story about cheating. Last year, he was enrolled at another tech school, taking a class on electromagnetism. The course was a ballbuster; no one was doing well. But the professor graded on a sliding scale, so most of the class, including Luis, was passing. Then a classmate got the final-exam answers from someone who’d taken the class before and emailed them to everyone.

Luis didn’t want to cheat, so he didn’t look at the answers. He thought he did well enough to pass the exam. But the teacher failed him because his score was lower than the class average. Luis didn’t want to rat out his classmates. He hoped the professor would figure out that his classmates had cheated, since their exam answers were so similar, and those who had been struggling had aced the final. Luis pleaded with the professor for a passing grade, based on his overall record in the class, in vain. Luis was so disgusted that he transferred to Stevens. If he’d stayed at his previous school, he would have had to retake the same course with the same professor to get his degree.

Luis’s story appalls me. Punished for being honest--the injustice! Out of idle curiosity, I google “PEP553” and “Stevens Institute.” I find “Notes” and “Homework Help” for PEP553 on a site called Course Hero. A little black box says, “Stuck? We have tutors online 24/7 who can help you get unstuck.” For a fee. I wonder if any of my PEP553 classmates are taking advantage of this service. I don’t need it, I’ve got my study buddies. Dean and Luis are good guys in a fallen world; they give me hope.

Accept the Mystery

A Stevens colleague, after I tell him how PEP553 is busting my balls, asks if I have seen A Serious Man, the Coen brothers’ film, which has funny depictions of a physics class. I saw A Serious Man years ago but forgot the physics subplot, so I rewatch the film. Its hero, physics professor Larry Gopnik, struggles to be a good man in a chaotic, amoral world. The film is set in suburban Minneapolis, where the Coen brothers grew up.

In a classroom scene, Gopnik tells his sullen students that they cannot understand quantum mechanics without the math. Lecturing on Schrodinger’s cat and the uncertainty principle, he covers a blackboard with formulas. Staring at his scribbles, Gopnik mutters, more to himself than to the students, that he still doesn’t understand Schrodinger’s cat or uncertainty. As his students swarm out of the classroom, Gopnik yells that, although uncertainty rules in the quantum realm, they still need to know the answers on the exam.

Back in his office, Gopnik is confronted by a student who failed the last exam. After begging Gopnik to pass him, the student puts an envelope on Gopnik’s desk and leaves. Gopnik looks in the envelope and sees a wad of bills. Horrified by the bribe, Gopnik chases after the student but can’t find him. Later, the student’s father confronts Gopnik at his home. When Gopnik tries to return the bribe, the father threatens to sue Gopnik for claiming that his son tried to bribe him. The father also urges Gopnik to accept the bribe and give his son a good grade.

Gopnik, exasperated, says either the father and son are bribing him or they’re not; they can’t have it both ways. The father murmurs, “Accept the mystery.” Gopnik wants logic, order, clear-cut answers. But these answers are not forthcoming either in the quantum realm or in the human realm, where paradoxes and contradictions abound.

Gopnik is a good man in a universe where being good doesn’t do you any good. God keeps thrusting temptations at him, presumably testing him. Gopnik doesn’t know what God wants of him. After Gopnik decides to keep the bribe, he learns he might have cancer. Is God punishing him? If so, God must be cruel, or capricious. Or maybe there is no god, and life is just a sequence of random, meaningless events.

You can only understand quantum mechanics by understanding the math, but even then you can’t understand it. If anything, when you learn the math, quantum mechanics becomes weirder, more opaque, more seemingly arbitrary and ad hoc. Accept the mystery. Understand that you can’t understand. A Serious Man is ironic, it offers many superposed meanings. I find the film hilarious/terrifying, banal/profound, beautiful/ugly. Great works of art--poems, music, films like A Serious Man—resemble David Eagleman’s buzzing vest, evoking sensations in us that we can’t quite disentangle or articulate.

I keep returning to Wikipedia to look at the video of the particle, or rather the waves, one real and one imaginary, dancing in the box. The video evokes sensations in me that are hard to spell out. Looking at it feels illicit, as though I’m hearing one of the forbidden names of God. I can see why some sages suspect that the key to the mind-body problem lies within the wave function. The real and the imaginary collide not only in wave functions but also in the mind and in love, mind’s most sublime manifestation. 

The lowest possible energy level of a wave function is called its zero-point energy, which is never actually zero. Zero-point energy is the basis for wacky schemes, going back decades, for generating energy from nothing, that is, from a vacuum. Zero-point energy also underpins inflation, the theory of cosmic creation invented by Andrei Linde, the physicist who doesn’t want to die like a physicist. According to inflation, our universe sprang from a wave function sloshing around in the primordial void. From nothing, something: 0 = 1. But who looked in the primordial box to bring our cosmos into existence?

Other questions come to mind as I look at the video of the particle in a box: Is each of us a particle in our own individual box, or are we all in the same box? Is there, perhaps, only one box, and one particle, pretending to be many particles? As I consider these questions, I feel my real and imaginary selves sloshing back and forth, amplifying and interfering with each other as they bounce off the walls of my box.

I can’t accept the mystery. 

The Debate

Polls show Biden ahead of Trump, just as they showed Hillary Clinton ahead four years ago. My trouble-making friend Robert says if Trump wins, we should meet in Washington again to protest his inauguration, as we did in 2017. You’re on, I say. Robert adds that Namibia’s Covid-19 numbers have been improving; he’s hoping we can trek through the Fish River Canyon next spring. Robert’s plans for the future hearten me; the new experimental treatment of his liver cancer must be going well.

Emily and I decide to check out the first debate between Trump and Biden. We worry that the debate will upset us, but it’s our duty as citizens to stay informed. Isn’t it? The debate is much worse than we expected. Trump keeps yelling at Biden, interrupting and insulting him. Biden looks startled, almost frightened; he seems too frail to stand up to this bully. Emily and I share murmurs of dismay and try to sleep.

Like a smack in the face, the debate reminds me of all the things I’ve been avoiding during my quantum experiment. I want to believe that humanity is basically decent and rational, and becoming more so over time. I want to believe that things are getting better. But one of the most powerful men on the planet is a cruel, vain thug. Millions of my fellow citizens admire him. They might re-elect him.

The next morning, I walk to the Hudson River to catch the ferry to Hoboken. I stop to read a poem affixed to a railing along the river. The poem, by Rita Dove, is almost too dead-on, given all the shit happening lately. It reads:

Let it be said

while in the midst of horror

we fed on beauty, and that,

my love, is what sustained us.

It’s getting harder to see the beauty. As I exit the Hoboken ferry terminal, I pass a man I’ve seen many times. He’s tall, burly, black, mid-50s-ish, weirdly handsome. He’s sitting on a stone bench, surrounded by bundles. He’s tending with a stoic expression to a cracked, swollen foot, deformed, probably, by diabetes. I turn away to give him privacy, and because I am disgusted. Then I’m disgusted by my disgust. What is real? This homeless man is real. Trump and his minions are real. As the horror grows, so does our duty to pay attention and our temptation to turn away.

Notes

1. Is spin a stationary state? I email Prof. Whittaker this question after class. He replies: “Spin states are eigenstates of the angular momentum operator, actually the square of angular momentum and one component. So if the Hamiltonian of a system was for example just the square of the angular momentum, then the spin eigenstate would be a stationary state. Stationary state is reserved for the eigenstates of energy.” If I asked my question in class, and got this response, I would have had to nod sagely, as if I understood.

Table of Contents

ABOUT MY QUANTUM EXPERIMENT

INTRODUCTION
Old Man Gets More Befuddled

CHAPTER ONE
The Strange Theory of
You and Me

CHAPTER TWO
Laziness

CHAPTER THREE
The Minus First Law

CHAPTER FOUR
I Understand That
I Can’t Understand

CHAPTER FIVE
Competence Without Comprehension

CHAPTER SIX
Reality Check

CHAPTER SEVEN
The Investment Principle

CHAPTER EIGHT
Order Matters

CHAPTER NINE
The Two-Body Problem

CHAPTER TEN
Entropy

CHAPTER ELEVEN
The Mist

CHAPTER TWELVE
Thin Ice

CHAPTER THIRTEEN
Irony

EPILOGUE
Thanksgiving

THANKS

DISCUSSION