- #1
DavidTheNERD
Hi guys! This is the third (and in my opinion, the most whimsical) chapter in a series of short stories I wrote about mathematics and physics; I hope you guys like it. Helpful comments or suggestions are welcome. Thanks!
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Chapter 3: Particles and Waves
A surly teenager stood in the doorway of an engineering laboratory. A single nerd, possibly in his mid-thirties, stood inside the laboratory as he worked with various breadboards, transistors, microcontrollers and soldering irons while writing his observations in a notebook. An easy target.
“Who would have thought that a bunch of pencil-necked number heads would have the balls to order a crap-load of cheap-*** paper?” challenged the youth.
Linus cut the power to his electrical equipment and met the teenager’s gaze.
“Whoever you are, you have got to be kidding me.”
The teenager squinted at Linus and quizzically cocked his head to one side.
“Why?”
“Because no person in his right mind would simply walk into an engineering laboratory while pushing a shopping cart and proceed to trash-talk its employees.”
“Well, I don’t know about you, bro, but my name’s Paul Olum. And in case you’re wondering, I brought a shopping cart here to hold the crap-load of paper you ordered. Ten copies of Scientific American, five copies of Chemical and Engineering News, five copies of Physical Review D, five copies of Nature, and five copies of Science, all for General Dynamics Laboratories, 16706 Carmel Valley Road, San Diego, CA, 92130. Is that correct?”
“Yes, that is correct,” said Linus. He looked around the laboratory. Utterly empty, save for Linus and Paul. Then he looked at the heaping pile of magazines in Paul’s shopping cart. “Since I’m the only person crazy enough to even bother staying here past five, I’ll gladly take them now.”
“Then sign here.”
Paul held out a yellow pad and a pen. Linus took the pen and signed his name. He was just about to unload the magazines from the cart when Paul interrupted him.
“Linus?”
“How the heck do you know my name? Oh yeah, I signed my name just seconds ago. At any rate, continue with your question.”
“I’ve delivered mail for quite a few math types lately, and I’ve been seeing that the math types typically read things like The American Mathematical Monthly or The Journal of Recreational Mathematics while everyone else reads Cosmopolitan or People. I just don’t get why some people would rather read about numbers when they can get the latest gossip about the hottest celebrities. To people like you, are numbers really all that interesting?”
“Mathematics is okay, but what really gets me going is physics. From automobiles and gas engines to smartphones and computers, every one of our technological innovations can be explained by a set of simple and beautiful physical principles. For example, the workings of the internal combustion engine are described by the laws of thermodynamics while semiconductor devices such as transistors, integrated circuits, microcontrollers and computers are nicely explained by the principles of quantum mechanics.”
“What’s physics?” mumbled Paul.
“Physics is simply the love story between matter and energy,” said Linus. “Scientifically speaking, it studies the properties of matter and those of energy and its transformations, but on a more personal level, it reminds me of my childhood sweetheart and our many thought-provoking conversations, which often lasted for hours at a time.”
Almost instantly, Paul was paying attention, and his eyes opened wide with curiosity. “You’re telling me you had a girlfriend before?! Now you’re talking!”
“Miss Christina was very curious about physics,” said Linus, “and I would often try to explain things to her. Most of the time, I did quite well, but it always seemed that no matter where we started or how we approached the subject, mathematically or otherwise, our hopes would always be dashed on the crazy cliffs of quantum mechanics.”
“Wait, I’m confused,” said Paul, “Which one am I supposed to pay attention to–the childhood sweetheart or the quantum mechanics?”
Linus drew a photograph from his pocket, making sure to gently hold it by the edges. In the static world of the picture, a boy and a girl were falling through space but suspended in time, intoxicated by the simple, wonderful act of drinking soda, of sharing in one of the simple pleasures of life. Linus pointed to the girl.
“That lovely young lady was the home of a brilliant mind, and that was the day she taught me about group theory. Miss Christina had an enormous helping of patience and loved to captivate the minds of other people, and often, she would try to teach me mathematics. At the same time, though, I was desperately trying to teach her physics, and whenever we reached the crazy cliffs of quantum mechanics, it always seemed that she was about to fall off. I told her that I couldn’t explain those ideas in an hour, a day, or even a week, but I promised her that over the course of months and years, I would try my best to ease her into the subject and hopefully answer her questions.”
“I don’t get it,” said Paul. “If your ‘childhood sweetheart’ was as smart as you claim she was, then how come she didn’t understand anything you were talking about? Quantum mechanics. It’s easy enough to pronounce.”
“To begin with,” said Linus, “one of the very first problems we encountered was the so-called ‘wave-particle duality.’ Prior to the development of quantum mechanics, it was commonly accepted that light was waves. But then instruments sensitive enough to detect a single photon were developed, and these instruments, called photomultipliers, would click every time a photon was detected. The wave theory predicted that the clicks would get softer as the light source got dimmer, but in reality, the clicks stayed at full volume but just occurred further apart, implying that light behaved like particles. Electrons, on the other hand, were thought of as particles at first, but then C.J. Davisson and L.H. Germer of Bell Labs bombarded a nickel crystal with electrons and found that the angles at which the electrons bounced off could be predicted from the wave theory. Finally in 1925, Louis de Broglie showed that the two theories were in fact interrelated: the momentum of a particle is related to its corresponding wavelength by the equation λ=h/p , where λ is the de-Broglie wavelength, p is the momentum of the particle and h is Planck’s constant, roughly 6.626×10-34 joule-seconds.”
“It sounds like trying to order tacos when your friends want burgers, and trying to order burgers when your friends want tacos,” said Paul. “But I still don’t believe for a second that you actually tried that hard to explain physics to this girl, or that you actually loved her as much as you say you did. To be honest, I don’t even know why I’m spending my Friday afternoon talking to a 30-year-old nerd in a dark green shirt, a light green tie, and dark green khaki pants. Your body looks like a giant green pencil and your head looks like a hard-boiled egg.”
“I am 24, not 30, and would have stopped talking to you long ago if I didn’t somehow believe that you would actually appreciate my time.”
“Sorry, dude. But I just found it strange how the two craziest people on the planet are not together anymore.”
“Well, eventually, the time came for Miss Christina to leave our small, cozy town in Southern California for bigger and better places in her homeland of China, and the day before she left, she wrote down her contact information on a slip of paper and put it in my pocket.
At the same time, though, I was struggling with an immensely difficult problem in quantum electrodynamics. It was getting to be too much for my poor four-year-old mind to handle, and I had filled my entire notebook with Feynman diagrams and path integrals. Having no other paper on which to write, I began to scribble on the back of the extra sheet of paper in my pocket, having temporarily forgotten that it contained Miss Christina’s contact information. My writing eventually reached the bottom of the sheet, but the solution still eluded me.
An image of my mother materialized before me.
She said, ‘Linus, put away your science-y stuff and get the hell back to bed!’
I said, ‘I don’t need an editorial, Ma, I need a freakin’ solution!’
‘Well, if you spent as much time sleeping as you do arguing with me, then maybe the solution would show itself more often.’
‘Your rationale is valid to a certain extent, but I really don’t see the point of going to bed at three in the afternoon.’
‘I really don’t see the point of even bothering with quantum electrodynamics. Beneath the high-class mathematical appearances of those path integrals in your notebook, all you’re doing is drawing little arrows on a piece of paper and adding them together. And what do you get at the end of it? The probability for a series of ridiculously simple events. A photon goes from point to point. An electron goes from point to point. An electron emits or absorbs a photon. Feynman said it himself in the book QED: The Strange Theory of Light and Matter.’
‘Blasphemy! You don’t distort the beautiful words of Richard Feynman, use them to insult the crown jewel of physics, and still expect to have my cooperation, Ma!’
‘The more you cooperate with me, the better off you’ll be. I’m trimming your crooked branches so that you might grow into a sturdy oak tree instead of a small, frail thorn bush.’
‘Don’t give me another second of that crap! You’ve never supported me in anything I’ve done! What makes you think I’d believe a single word that comes out of your mouth?’
Then I got so frustrated that I...that I...”
It was getting noticeably difficult for Linus to continue his story. He choked for a bit, his body stiffened, and he began to rub his eyes.
“My guess is that everyone has a song inside that’s waiting to be free,” said Paul. “Even the math types.”
“Well, then I got so frustrated that I crumpled up the piece of paper I had been writing on and threw it at the image of my mother. Then she simply vanished from my sight, just as she always did when she was angry with me. Only this time, she never appeared before me again. Not once more. The crumpled ball of paper simply passed through the empty space where my mother had been and into the trash can. And the next morning, after the can had been emptied, I realized what a fool I had been. Right there, in the crumpled ball of paper, was Miss Christina’s contact information.”
Linus sighed. “In retrospect, I should have treated that lady with a measure of courtesy before she got so fed up with me that she vanished from my sight. After all, she is my mother, and only God knows where I would be if she hadn’t taken the time to nurse me to health with vitamin supplements or cook chicken soup for me every time I was sick. She deserves the highest thanks, or at least a peaceful life without my enormous tantrums.”
“I lost my two closest friends that fateful day,” said Linus. “One was the only fair maiden I ever loved, and the other was the only mother I ever had. I hadn’t the slightest clue where either of them were. All of this happened 20 years ago, before the era of Google and Facebook, and it was much, much harder to find people back then.”
“I think I know who you’re talking about,” said Paul. “There’s a crazy chick named Christina in our apartment complex who looks exactly like an older version of the girl in that picture. She’s one of those people who subscribes to The American Mathematical Monthly, and she tells me that ever since she lost her job teaching math to college kids, she’s devoted her life to solving the 36-Cube. She says that some guy named Leonhard Euler once told her that the puzzle had no solution, and that she’s set out to prove him wrong, to ‘do what he never had the brains to do.’ And that’s not even the start of it. She drinks nearly half a gallon of lemon-lime soda every day, and when people ask her why she drinks that much, she says, ‘I like the way it tickles my throat.’”
“Someday,” continued Paul, “I’d like to talk to this Euler guy, whoever he is, and tell him that he’s taken his biggest rival and made her completely crazy. To be honest, I liked her better when she was hanging out with those college kids.”
“Then I’m afraid my dear Miss Christina is horribly mistaken,” said Linus. “First of all, Leonhard Euler is not just ‘some guy.’ He is one of the greatest mathematicians in the history of mankind, and I’m afraid you can’t talk to him because he’s long since passed away. Second, the 36-Cube was invented not by Euler, but by Dr. Leon Niederman of MIT, who designed the 36-Cube on the basis of Euler’s 36-Officer Problem. Euler correctly conjectured that there was no solution to the 36-Officer Problem, but the 36-Cube was specifically designed to have a solution, albeit an extremely difficult one.”
“You math types never cease to amaze me,” said Paul. “You can be so picky about all sorts of minor details, but when the big solution is sitting right in front of you, you barely even notice it! Only God knows how many great opportunities you’ve missed this way.”
“You’re talking about big solutions and missed opportunities, but I don’t get it at all. There is no solution to the 36-Officer Problem, and the solution to the 36-Cube is extremely hard to come by.”
Paul simply looked away and shook his head in disappointment.
Linus paused for a minute as his thought processes gradually connected the various pieces of information he had gained. At first, there was nothing. Then something clicked within the depths of his mind.
“Call me Archimedes of Syracuse!” cried Linus. “For I have found it!”
“No, dude. I’m pretty sure your name is Linus.”
“Oh, of all the engineers in this laboratory and all the paper boys that have delivered mail for us, you know where Miss Christina is!” he said as he grasped Paul’s shoulders in frenzied excitement. “The great man of Syracuse wept for joy when he discovered the principle of water displacement, and the entire world was covered in smiles as Neil Armstrong took our first steps on the moon. I have floated upon the lofty clouds of the sprightly universities, and I have slogged through the murky depths of the working world, but only now have I realized how fortunate I have been! Oh, a most gracious thanks to you, oh, noble paper boy!”
Paul didn’t say a word, but simply drew a pair of sunglasses from his pocket and calmly handed them to Linus.
“What’s this?” asked a puzzled Linus.
“If you’re going to see your crazy girlfriend, you might as well look good.”
“Paul, she’s not my–”
“Whatever. Let’s go.”
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All copies and transfers, text-based, electronic or otherwise, must be approved with permission from the author. Ask before using my content–I might say yes! :)
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Chapter 3: Particles and Waves
A surly teenager stood in the doorway of an engineering laboratory. A single nerd, possibly in his mid-thirties, stood inside the laboratory as he worked with various breadboards, transistors, microcontrollers and soldering irons while writing his observations in a notebook. An easy target.
“Who would have thought that a bunch of pencil-necked number heads would have the balls to order a crap-load of cheap-*** paper?” challenged the youth.
Linus cut the power to his electrical equipment and met the teenager’s gaze.
“Whoever you are, you have got to be kidding me.”
The teenager squinted at Linus and quizzically cocked his head to one side.
“Why?”
“Because no person in his right mind would simply walk into an engineering laboratory while pushing a shopping cart and proceed to trash-talk its employees.”
“Well, I don’t know about you, bro, but my name’s Paul Olum. And in case you’re wondering, I brought a shopping cart here to hold the crap-load of paper you ordered. Ten copies of Scientific American, five copies of Chemical and Engineering News, five copies of Physical Review D, five copies of Nature, and five copies of Science, all for General Dynamics Laboratories, 16706 Carmel Valley Road, San Diego, CA, 92130. Is that correct?”
“Yes, that is correct,” said Linus. He looked around the laboratory. Utterly empty, save for Linus and Paul. Then he looked at the heaping pile of magazines in Paul’s shopping cart. “Since I’m the only person crazy enough to even bother staying here past five, I’ll gladly take them now.”
“Then sign here.”
Paul held out a yellow pad and a pen. Linus took the pen and signed his name. He was just about to unload the magazines from the cart when Paul interrupted him.
“Linus?”
“How the heck do you know my name? Oh yeah, I signed my name just seconds ago. At any rate, continue with your question.”
“I’ve delivered mail for quite a few math types lately, and I’ve been seeing that the math types typically read things like The American Mathematical Monthly or The Journal of Recreational Mathematics while everyone else reads Cosmopolitan or People. I just don’t get why some people would rather read about numbers when they can get the latest gossip about the hottest celebrities. To people like you, are numbers really all that interesting?”
“Mathematics is okay, but what really gets me going is physics. From automobiles and gas engines to smartphones and computers, every one of our technological innovations can be explained by a set of simple and beautiful physical principles. For example, the workings of the internal combustion engine are described by the laws of thermodynamics while semiconductor devices such as transistors, integrated circuits, microcontrollers and computers are nicely explained by the principles of quantum mechanics.”
“What’s physics?” mumbled Paul.
“Physics is simply the love story between matter and energy,” said Linus. “Scientifically speaking, it studies the properties of matter and those of energy and its transformations, but on a more personal level, it reminds me of my childhood sweetheart and our many thought-provoking conversations, which often lasted for hours at a time.”
Almost instantly, Paul was paying attention, and his eyes opened wide with curiosity. “You’re telling me you had a girlfriend before?! Now you’re talking!”
“Miss Christina was very curious about physics,” said Linus, “and I would often try to explain things to her. Most of the time, I did quite well, but it always seemed that no matter where we started or how we approached the subject, mathematically or otherwise, our hopes would always be dashed on the crazy cliffs of quantum mechanics.”
“Wait, I’m confused,” said Paul, “Which one am I supposed to pay attention to–the childhood sweetheart or the quantum mechanics?”
Linus drew a photograph from his pocket, making sure to gently hold it by the edges. In the static world of the picture, a boy and a girl were falling through space but suspended in time, intoxicated by the simple, wonderful act of drinking soda, of sharing in one of the simple pleasures of life. Linus pointed to the girl.
“That lovely young lady was the home of a brilliant mind, and that was the day she taught me about group theory. Miss Christina had an enormous helping of patience and loved to captivate the minds of other people, and often, she would try to teach me mathematics. At the same time, though, I was desperately trying to teach her physics, and whenever we reached the crazy cliffs of quantum mechanics, it always seemed that she was about to fall off. I told her that I couldn’t explain those ideas in an hour, a day, or even a week, but I promised her that over the course of months and years, I would try my best to ease her into the subject and hopefully answer her questions.”
“I don’t get it,” said Paul. “If your ‘childhood sweetheart’ was as smart as you claim she was, then how come she didn’t understand anything you were talking about? Quantum mechanics. It’s easy enough to pronounce.”
“To begin with,” said Linus, “one of the very first problems we encountered was the so-called ‘wave-particle duality.’ Prior to the development of quantum mechanics, it was commonly accepted that light was waves. But then instruments sensitive enough to detect a single photon were developed, and these instruments, called photomultipliers, would click every time a photon was detected. The wave theory predicted that the clicks would get softer as the light source got dimmer, but in reality, the clicks stayed at full volume but just occurred further apart, implying that light behaved like particles. Electrons, on the other hand, were thought of as particles at first, but then C.J. Davisson and L.H. Germer of Bell Labs bombarded a nickel crystal with electrons and found that the angles at which the electrons bounced off could be predicted from the wave theory. Finally in 1925, Louis de Broglie showed that the two theories were in fact interrelated: the momentum of a particle is related to its corresponding wavelength by the equation λ=h/p , where λ is the de-Broglie wavelength, p is the momentum of the particle and h is Planck’s constant, roughly 6.626×10-34 joule-seconds.”
“It sounds like trying to order tacos when your friends want burgers, and trying to order burgers when your friends want tacos,” said Paul. “But I still don’t believe for a second that you actually tried that hard to explain physics to this girl, or that you actually loved her as much as you say you did. To be honest, I don’t even know why I’m spending my Friday afternoon talking to a 30-year-old nerd in a dark green shirt, a light green tie, and dark green khaki pants. Your body looks like a giant green pencil and your head looks like a hard-boiled egg.”
“I am 24, not 30, and would have stopped talking to you long ago if I didn’t somehow believe that you would actually appreciate my time.”
“Sorry, dude. But I just found it strange how the two craziest people on the planet are not together anymore.”
“Well, eventually, the time came for Miss Christina to leave our small, cozy town in Southern California for bigger and better places in her homeland of China, and the day before she left, she wrote down her contact information on a slip of paper and put it in my pocket.
At the same time, though, I was struggling with an immensely difficult problem in quantum electrodynamics. It was getting to be too much for my poor four-year-old mind to handle, and I had filled my entire notebook with Feynman diagrams and path integrals. Having no other paper on which to write, I began to scribble on the back of the extra sheet of paper in my pocket, having temporarily forgotten that it contained Miss Christina’s contact information. My writing eventually reached the bottom of the sheet, but the solution still eluded me.
An image of my mother materialized before me.
She said, ‘Linus, put away your science-y stuff and get the hell back to bed!’
I said, ‘I don’t need an editorial, Ma, I need a freakin’ solution!’
‘Well, if you spent as much time sleeping as you do arguing with me, then maybe the solution would show itself more often.’
‘Your rationale is valid to a certain extent, but I really don’t see the point of going to bed at three in the afternoon.’
‘I really don’t see the point of even bothering with quantum electrodynamics. Beneath the high-class mathematical appearances of those path integrals in your notebook, all you’re doing is drawing little arrows on a piece of paper and adding them together. And what do you get at the end of it? The probability for a series of ridiculously simple events. A photon goes from point to point. An electron goes from point to point. An electron emits or absorbs a photon. Feynman said it himself in the book QED: The Strange Theory of Light and Matter.’
‘Blasphemy! You don’t distort the beautiful words of Richard Feynman, use them to insult the crown jewel of physics, and still expect to have my cooperation, Ma!’
‘The more you cooperate with me, the better off you’ll be. I’m trimming your crooked branches so that you might grow into a sturdy oak tree instead of a small, frail thorn bush.’
‘Don’t give me another second of that crap! You’ve never supported me in anything I’ve done! What makes you think I’d believe a single word that comes out of your mouth?’
Then I got so frustrated that I...that I...”
It was getting noticeably difficult for Linus to continue his story. He choked for a bit, his body stiffened, and he began to rub his eyes.
“My guess is that everyone has a song inside that’s waiting to be free,” said Paul. “Even the math types.”
“Well, then I got so frustrated that I crumpled up the piece of paper I had been writing on and threw it at the image of my mother. Then she simply vanished from my sight, just as she always did when she was angry with me. Only this time, she never appeared before me again. Not once more. The crumpled ball of paper simply passed through the empty space where my mother had been and into the trash can. And the next morning, after the can had been emptied, I realized what a fool I had been. Right there, in the crumpled ball of paper, was Miss Christina’s contact information.”
Linus sighed. “In retrospect, I should have treated that lady with a measure of courtesy before she got so fed up with me that she vanished from my sight. After all, she is my mother, and only God knows where I would be if she hadn’t taken the time to nurse me to health with vitamin supplements or cook chicken soup for me every time I was sick. She deserves the highest thanks, or at least a peaceful life without my enormous tantrums.”
“I lost my two closest friends that fateful day,” said Linus. “One was the only fair maiden I ever loved, and the other was the only mother I ever had. I hadn’t the slightest clue where either of them were. All of this happened 20 years ago, before the era of Google and Facebook, and it was much, much harder to find people back then.”
“I think I know who you’re talking about,” said Paul. “There’s a crazy chick named Christina in our apartment complex who looks exactly like an older version of the girl in that picture. She’s one of those people who subscribes to The American Mathematical Monthly, and she tells me that ever since she lost her job teaching math to college kids, she’s devoted her life to solving the 36-Cube. She says that some guy named Leonhard Euler once told her that the puzzle had no solution, and that she’s set out to prove him wrong, to ‘do what he never had the brains to do.’ And that’s not even the start of it. She drinks nearly half a gallon of lemon-lime soda every day, and when people ask her why she drinks that much, she says, ‘I like the way it tickles my throat.’”
“Someday,” continued Paul, “I’d like to talk to this Euler guy, whoever he is, and tell him that he’s taken his biggest rival and made her completely crazy. To be honest, I liked her better when she was hanging out with those college kids.”
“Then I’m afraid my dear Miss Christina is horribly mistaken,” said Linus. “First of all, Leonhard Euler is not just ‘some guy.’ He is one of the greatest mathematicians in the history of mankind, and I’m afraid you can’t talk to him because he’s long since passed away. Second, the 36-Cube was invented not by Euler, but by Dr. Leon Niederman of MIT, who designed the 36-Cube on the basis of Euler’s 36-Officer Problem. Euler correctly conjectured that there was no solution to the 36-Officer Problem, but the 36-Cube was specifically designed to have a solution, albeit an extremely difficult one.”
“You math types never cease to amaze me,” said Paul. “You can be so picky about all sorts of minor details, but when the big solution is sitting right in front of you, you barely even notice it! Only God knows how many great opportunities you’ve missed this way.”
“You’re talking about big solutions and missed opportunities, but I don’t get it at all. There is no solution to the 36-Officer Problem, and the solution to the 36-Cube is extremely hard to come by.”
Paul simply looked away and shook his head in disappointment.
Linus paused for a minute as his thought processes gradually connected the various pieces of information he had gained. At first, there was nothing. Then something clicked within the depths of his mind.
“Call me Archimedes of Syracuse!” cried Linus. “For I have found it!”
“No, dude. I’m pretty sure your name is Linus.”
“Oh, of all the engineers in this laboratory and all the paper boys that have delivered mail for us, you know where Miss Christina is!” he said as he grasped Paul’s shoulders in frenzied excitement. “The great man of Syracuse wept for joy when he discovered the principle of water displacement, and the entire world was covered in smiles as Neil Armstrong took our first steps on the moon. I have floated upon the lofty clouds of the sprightly universities, and I have slogged through the murky depths of the working world, but only now have I realized how fortunate I have been! Oh, a most gracious thanks to you, oh, noble paper boy!”
Paul didn’t say a word, but simply drew a pair of sunglasses from his pocket and calmly handed them to Linus.
“What’s this?” asked a puzzled Linus.
“If you’re going to see your crazy girlfriend, you might as well look good.”
“Paul, she’s not my–”
“Whatever. Let’s go.”
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All copies and transfers, text-based, electronic or otherwise, must be approved with permission from the author. Ask before using my content–I might say yes! :)