I think he would have gone on with this declamation if I hadn't butted in sarcastically with, “What? Did Isaac Newton do quantum chemistry?"
"In fact, he did. Yes, Isaac Newton invented quantum chemistry as far as I'm concerned. Of course, he would not have called it that."
I waited for him to continue, but apparently it was my turn to say something. So, after a reasonable silence, I went ahead and set him up as he wanted. With obvious skepticism, I asked, “All right, you win: What would Newton have called it?"
"Alchemy!"
* * * *
It was quite rude of me to just walk out on Dr. Stein without saying a word, but I needed some time to think about this.
Alchemy, huh? That's what we're doing at the institute: turning lead into gold! I would have been seriously embarrassed to tell my friends at the University about that, and I suspected that it would not look good on a CV. Could I get hired, I wondered, at a real math department after spending a year doing witchcraft with a loon?
Consequently, I was mad and worried, and I just turned around and walked out of there. But I guess I had grown to trust Stein at least a little bit, and to like him as well. So I wanted to at least consider the possibility that he knew what he was doing.
That's why I didn't just get back on a train home, but instead went to the grad library and did some reading about alchemy.
There were some things I learned that I had not known. For instance, Isaac Newton really did work on alchemy! (One point for Stein.) I had too much respect for Newton's mathematical discoveries to discount him as another complete wacko. On the other hand, everything else I read just reinforced my impression of alchemy as an early pseudo-science based more on wishful thinking than scientific rigor. The experts agree that people who believed in alchemy back in the seventeenth century were basically crackpots, and anyone who still believes it today is just plain nuts. (By my reckoning that made it two to one against poor Dr. Stein.)
I should definitely have gone back to the institute at this point, packed my bags, and headed for home. That was certainly my plan, but I saw the light on in Dr. Stein's room and knocked lightly on the door.
He seemed to know that I was planning to leave, and I was starting to feel guilty.
"Don't go now, Igor. I'm ... we're so close!” he pleaded.
"You can do it without me, Dr. Stein. You wouldn't want me around anyway if I don't believe, would you?” I thought that perhaps, like psychic powers and homeopathy, alchemy could be something that never seems to work when a skeptic is around.
"I can do almost all of it without you, and have been for years. But I never could understand that non-standard analysis that you do."
People are always saying that to me, and I don't understand why. “It's easy,” I assured him. “Just pretend that there are real numbers that are infinitely big or infinitely small and do what you always do in a calculation."
"It is easy for you, and that is a gift. I would be ever so grateful if you would share that gift with me just one more time. I really think I've got it now. Solve this problem for me and tomorrow I can show you that I really do know what I'm doing."
Pity is not one of my favorite emotions, and I resented him for playing on it. But his ploy worked. I stayed awake that night deriving complex functions with prescribed jumps for my boss one last time.
I probably was not looking my best when I wandered into the kitchen at 6:30 in the morning, where I found Stein waiting for me with a fresh pot of coffee. As I struggled to stay awake and dunked my donut, he tried to explain the whole idea to me.
"What did Newton do, before he turned to alchemy?” he asked rhetorically. “He wrote down formulas for matter moving under gravity, and he came to understand the wave nature of light. Then, he took a leap that was too big for any of his contemporaries to follow: he put them together."
"So, you're saying he discovered a theory of quantum gravity,” I said between sips, “just like all of the physicists are trying to do today."
"Yes, but he had quite an advantage because he didn't spend hundreds of years believing in nonsense first."
"What nonsense would that be?” I inquired, thinking that for the first time, Dr. Stein was beginning to look as unhinged as all of my friends said he was.
"Particles, my boy! The idea that matter is made up of particles is a terrible mistake our physicists made early on and we've been paying a price for it ever since."
"Of course matter is made of particles,” I said patronizingly, though I was well aware that my limited background in college physics was nothing compared to his years of experience at the forefront of mathematical physics. “I think we're pretty sure of that. Molecules, atoms, electrons, and protons. I learned all about that in school and I've heard friends talking about things like quarks and moo-ons. Particles are an established fact, not nonsense."
"You mean muons. Yes, of course. I learned about all that, too. I learned the standard model. I even proved a theorem about super-symmetry that particle physicists are always making use of, but that doesn't mean it is an accurate description of the real world. I also learned that Columbus discovered America, but by the time you went to school, they knew that it was not quite true. Here, let's try this. You say you took a course in quantum mechanics, right? What did they tell you about the speed and position of a particle?"
"That you can't measure them both at the same time."
"Yes, but there is more to it than that. Even physicists will tell you it is not only that the particle has a speed and a position that you do not know, the particle does not even have a position or a speed until you measure it."
"Yeah, I suppose I've heard that,” I said, beginning to wonder whether all physicists are nuts. “That never quite made sense to me."
"And I'll tell you a simple way to solve the dilemma: get rid of the particles. There are no particles after all, only waves. The particle is just a figment of our imagination, and that is why it only has the properties we know it to have. This is what Isaac Newton realized when he combined his understanding of gravity with his experiments on light: all of this around us is just a big wave, rippling and moving under the force of gravity. The gravitational effect may make it look like there are particles, but looks can be deceiving, no?"
To demonstrate this last remark, he held the eraser of his pencil loosely between his fingers and shook it up and down quickly. It sure looked like it was flopping around like a rubber tube instead of a wooden pencil, and I just had to laugh.
"But,” I said, almost starting to believe him, “if Newton knew all of this, why didn't he tell anyone?"
"He tried! That's what his fluxions were, a new mathematical notation for the wave nature of reality itself. If only he'd had your non-standard analysis to make it rigorous, people might have seen what he was getting at. But, as it was, they thought it was just an inferior attempt at defining derivatives and chose to go with Leibniz instead. But he wasn't just talking about functions and calculus; he was talking about the ultimate description of reality. That's what his alchemy was about."
"Okay, so now we get to it! What does it have to do with alchemy?"
"That's what alchemy is! Look, today's scientists with their belief in particles wouldn't try to turn lead into gold. How could they? Particles are particles, unchanging by their very nature. But suppose instead that lead and gold are just different ripple patterns in a wave. With the right sort of nudging, you can change one into the other. I'm not just talking about a theoretical possibility. I know exactly what I need to do now, and I'm about to do it!"
"You mean you're really trying to turn lead into gold? Come on, even if I believed you could do it, isn't there something more useful you could be doing with this new science of yours?"
"Sure, sure. If today's experiment works, I'll move on to something bigger: producing the philosopher's stone. The ultimate, universal substance, entirely unknown to modern science, a quantum superposition of the resonance patterns of all of the oth
er elements. Newton proved its existence mathematically, but was never able to work out how to make any. All of the alchemists of his day set creating some as their highest goal. The associated Riemann-Hilbert problem might be so hard that even you would have trouble solving it ... but that's for another day. Today, we need to turn lead into gold because that is what it takes to get the attention of the media."
"Well, there I guess I can agree with you, Professor Stein. If today's experiment works and you really turn lead into gold, then you could have a TV news crew here tomorrow and..."
"But they are already here! And, today's experiment will work. How can you have any doubt? You solved the latest jump problem, no? Well, then we're ready to go!"
It was only then that I noticed how much light was coming from the living room. I had mistakenly believed that it was sunlight, but this time of year it is not so bright so early in the morning. When I followed the professor through the doorway and my eyes became accustomed to the light, I saw that there were several reporters and camera crews set up there. Dr. Stein went over to a computer terminal in the corner and began typing in the results of my night's computations.
A tall man with a huge pile of light brown hair and unbearably white teeth started talking as soon as we entered. “This is Tom Cannon reporting from the home of Dr. Franklin Stein, a U. of M. mathematics professor who is either a genius or a certifiable kook depending on who you want to believe. We are here today because Dr. Stein claims to be able to turn lead into gold using an old science called ‘alchemy'...."
Meanwhile, an Asian woman in a short skirt was saying, “The mathematics department has refused to comment, but Peter Watkins, author of last year's best selling The Alien Abduction Diet Plan, insists that Stein's approach is well grounded and sure to produce spectacular results...."
And, most distressingly, the local access channel's young volunteer reporters were doing a terrible job of discussing me and my role in today's spectacular demonstration: “According to Stein, Igor Stravinsky—no relation to the famous violinist—played a key role in his research by solving Rhymon-Dilbert problems, math questions about integrals like those you might have seen in your calculus class...."
While I tried to hide in the corner, all eyes (and cameras) were on Dr. Stein as he began his big show.
"Thank you all for coming here today to witness a tremendous advance in the human understanding of the universe.” At this point, he switched on one of those hokey electric spark machines that you see in old horror movies. It was sitting on the coffee table and began buzzing and zapping as the spark climbed higher and higher before returning suddenly to the bottom. “This journey was begun long, long ago. Al chemie, like al gebra, and even—ironically—al cohol, all owe their origins to that period in the history of Arabia when their scientists were at the forefront of discovery. However, they did not know enough about waves to take it through to its conclusion. This, like so many of their great discoveries, was lost to time. Similarly, Isaac Newton, who finally knew enough to put together the main ideas, did not know enough about his own invention, the infinitesimal calculus, to..."
"Hey Doc,” called out one of the cameramen, demonstrating that despite their mock sincerity, the news crews did not have any respect for Stein as a man of science. “We've only got a little bit of tape left here. Can you get on with it and turn the lead into gold already so we can get out of here?"
A few others snickered, either at the idea that we might actually see lead turned into gold or at the cameraman's rude behavior, but Stein complied politely and dramatically. He picked up a gray, metallic bar from the coffee table and dropped it. It actually shattered the tabletop and fell to the floor with a loud thunk. “This is a lead bar,” he said matter-of-factly. “This is a generator of vibrations in the electro-magnetic field,” he continued, indicating the spark-making thing. “I place the lead bar on this vibrating platform which, like the field generator, is controlled by a digital computer."
"What kind of computer is it, doc?"
"Well, it is a Dell running Linux. But the point is that it vibrates the bar and the electromagnetic field according to the real and imaginary parts of Igor's solution of the Riemann-Hilbert problem respectively so that..."
Though I was already in the corner, behind the recliner, I tried even harder to hide at the mention of my name and hoped that Becka was not watching TV this morning. But then, something began to happen. The bar began to shake very quickly, and the pattern of sparks became much more erratic. Then, space itself seemed to bend visibly. This ripple of space began at the bar, but seemed to spread out in all directions, even passing through me—a very strange sensation—before disappearing through the walls.
I was impressed! Dr. Stein really seemed to know what he was doing after all. Or so I thought until I looked at him. He looked quite puzzled and concerned. Soon, however, he looked up again at the camera crews and smiled, proudly displaying a shining gold bar where the dull lead had been previously.
The reporters were temporarily speechless. This was not going to be the humorous “human interest” story they had originally expected it would be. Everyone in the room, even Stein, was only starting to realize the implications of what we had seen. But this sense of triumph did not last long.
Beginning with just a few drops, soon a steady stream of water was dripping down on us from the chandelier. We all looked up at it, still and silent, noticing the cracks forming in the ceiling, before taking the necessary action. Everyone ran out onto the street as fast as we could. And we were just in time too, as we heard the ceiling crash in and saw the living room flooding through the windows very shortly thereafter.
Up and down the street, every house was going through the same strange set of circumstances. Wet people running out into the street as their homes and possessions were soaked in a flood of water. (Of course, ours was the only house that had camera crews.)
"I don't understand...” Stein whimpered, not really to me but within earshot. He looked miserable, but I was in a pretty good mood as it looked as if I was actually part of something noteworthy.
"The pipes, Dr. Stein. These old buildings still had lead pipes,” I explained. “You've turned them all to gold, which may earn the homeowners a nice profit in the long run, but for now the problem is that gold is not strong enough to..."
"Of course, I know that!" he snapped. “But only the bar in our experiment should have been affected. The wave should have dissipated before ever reaching ... unless..."
His expression vacillated between horror and anger as he grabbed me by the shoulders and asked, “The solution, wasn't it compactly supported?"
"Oh, well ... that didn't seem to be working out nicely,” I admitted, “so I used periodic boundary conditions this time. Was that, um, bad?"
Behind him I could see an angry mob heading in our direction, accompanied by the local access film crew. So far, they did not seem to be too grateful for our gift of golden plumbing.
"It depends,” he asked, with a broad smile but wrinkles appearing only around his left eye. “What do you think the effect will be on the world, on technology, on the economy now that every atom of lead on the planet has suddenly become gold?"
Copyright (c) 2007 Alex Kasman
* * * *
"It's incredible how much intelligence is used in this world to prove nonsense."—Friedrich Hebbel
[Back to Table of Contents]
EL DORADO by TOM LIGON
* * * *
Illustration by Vincent Di Fate
* * * *
Heroes don't always fit the expected image....
Victor Gendeg let his eyes adjust as he studied the jumbled ball of dirty ice before him. It was illuminated only by starlight, especially by one bright star about 3.3 light-days away, and his eyes strained to make out any detail. He leaned so close to the window that his breath frosted it. He wiped the white deposit away and held his breath to gaze at it again.
"Computer, voice log on."
>
"That must be it. Classic exit jumble. Definitely had a collision with a smaller, denser object."
He checked the magnetometer. Was it just beginning to show a trace of a magnetic field as he approached it?
"Yes! Magnetic. This has to be it!” He glanced at the monitors, which showed the object so much clearer than naked human eyes could, then turned back to the window to gain a more personal connection with the planetesimal. “Eureka! Right freakin’ where you're supposed to be! Sumbitch thought you were pretty sneaky, hiding out in the Oort Cloud, didn't ya? Well, Victor Gendeg tracked your banged-up ass down! Four billion years of ducking and hiding, but your ass is mine now, baby. I am so freakin’ rich the damn Astrofellers are gonna envy me. I have found El Dorado!"
* * * *
The solar system was young when Jupiter and Saturn migrated into a 2:1 orbital resonance. It was an interesting time for all of the other bodies there. Chaos reigned until the two giants moved beyond that dance. The two largest bodies in the system other than the Sun played tug of war in a game Jupiter won and all of the small bystanders lost.
Two of the worst losers were minor rocky planets, each with a small core of iron and other metals, and mantles that had already turned to solid stone. They were set on a collision course. It would not happen for hundreds of millions of years, but it was inevitable.
When it happened, both bodies shattered their rocky outer layers, exposing their metal cores. Pieces showered away from the impact in many directions, some into the depths of space, some into the inner system, where they would eventually meet a dramatic end. Some pelted the third planet and its moon, part of what its later inhabitants would call the “late heavy bombardment.” Many simply formed a belt, shepherded into shape by resonance with Jupiter and a few other significant orbs. One of the cores stayed safely in the belt, covered in a thick layer of rubble from the collision, some its own, and some from the other unfortunate body. The other was in an elliptical orbit that flirted dangerously with the dominant gas giant. It was similarly covered with debris, and had an entourage of orbiting fragments of the same sort.
Analog SFF, October 2007 Page 14
