"Mike."
Whose voice is that?
"Hey, Mike."
Is he talking to me?
"Mike, buddy. I know you're awake."
Man, it's bright in here. I blink slowly and the world starts to resolve itself.
"There he is," the voice by the bed says encouragingly.
"Hello?" I ask dumbly, not recognizing the face that enters my vision.
"Mike, it's Tom."
I blink a few more times. Now that he mentions it, he does look like Tom...I think. I smile at him. "Yeah, hey Tom. Don't mind me. I'm just a little..." I sit up look around in confusion. "Am I in a hospital?"
Tom nods. "Yeah. Listen, Mike, don't worry. The doctors say you'll be fine. You just had a minor heart attack. If you just take it-"
"Heart attack?" I ask, bewildered.
"Yeah," Tom says calmly, "if you just take it easy, you're gonna be alright."
I lay back against the pillow. I can feel my heart pumping. It makes me feel a little light headed.
"Now look, Mike. I need to ask you something pretty important. I need you to relax and try to remember," he says to me in a very serious tone.
I look at him. "What is it?"
Tom sighs. "You remember the new girl at the office?" he asks.
My heart beats a little faster for some reason. "Uh, yeah. Lori, er, uh...Loretta?"
"Loretta, that's right," Tom nods. "Well, she's missing."
"Ok," I say hesitantly. While I'm sure I don't know what he's talking about, my chest seems to be pounding an answer. This can't be good for someone who recently had a heart attack.
"Well, Mike, the last time anyone saw her was with you," Tom says pointedly.
I shake my head. "What are you asking?"
He gives me a long hard look, then sighs again. "Mike, it's hard for me to say this because I know things have been difficult for you, but everyone knows about you two."
"Knows about...about what?" I ask, my nervousness matched only by my confusion.
Tom shrugs. "That you've been...y'know seeing each other," he answers, looking away.
I stare in disbelief, my head shaking of its own accord. "Tom, I...Linda..." is all I can manage to stutter.
"Linda's gone, Mike," he says sympathetically. "It's ok to move on."
It all rushes back to me. The bank. Linda's blood. Her lips moving. "No!" I shout, curling over onto my side and shielding my head.
"Mike, it's ok. Calm down," Tom tells me.
My sleeve is quickly soaked with tears. "Linda..." I whisper between sobs.
"Mike, we just need to know where Loretta is," he says with a hint of urgency.
Something about that tone tears me from my self pity. I look up at Tom. His eyes are quietly demanding. "Who's 'we'?" I ask suspiciously.
Tom leans back and looks up in thought. "Look, I didn't want to tell you this, but the police think..." he trails off.
"What?" I urge him on.
He looks at me with a pained expression. "Mike, they think you may have had something to do with it," he explains. "I'm here to help you before they get their hands on you."
"Tom," I begin, but I'm not really sure what to follow it up with.
"Is there anything you can tell me?" he asks, looking sympathetic again. "Is there some place where you guys usually meet?"
The memory of a church flashes through my mind. A small room. A syringe. Someone injecting me with something. I look up at Tom and shake my head.
He sighs. "Ok, you obviously need some time to rest. I'm going to be in the lobby. Call for me if you can remember anything."
Without pausing for my reaction, he walks out of the room.
I take a moment to look around the room. It's pretty sparse. There's no window. Not even a TV. Seems more like a prison cell than a hospital room. I sit up and swing my legs over the edge of the bed. Man, I feel really weak. I wonder if this is what it feels like after a heart attack.
Taking a breath, I slide myself onto my feet and stand. This is a very shaky process. My legs feel like they haven't worked in weeks, maybe more. I step carefully over to the door and turn the handle. At least, I try to turn the handle. It's locked. Why am I locked in my room?
Something definitely doesn't feel right about this. What's really going on here? I try to think back to where I was before I woke up here. I was at work. The day was pretty normal. I went home and fell asleep. But if I went home and fell asleep, where did I have the heart attack? How did anyone find me? Think!
I was home asleep and then... Oh yeah, there was that crazy dream about Linda. She was on the table. She turned to look at me. She said something that freaked me out. What was it? I close my eyes and concentrate.
"Richard..."
My eyes snap open. I shudder at the memory of Linda's lifeless corpse looking up at me. Why did she call me Richard? Does it have anything to do with my heart attack? She said that; then I woke up. I got some water. Then I got into the car and went...
Went where? Where would I have gone? Dammit, think, Rick!
Rick. Why did I just call myself Rick? What the hell is wrong with me?
"...we erased your memory..." a female voice echoes from the recesses of my mind. I close my eyes and try to remember more.
"...most of the subjects reported a surrealism to their memories. Some even had odd things go on, like what you might expect in a dream," the woman's voice explains to me from some time in the recent past.
When did that happen? It seems so familiar, but I don't know why.
"...come to this address: 1420 Mission Avenue. It's an abandoned church near the city limits..."
The image of a run down building with a steeple stretching into the night sky fades into view behind my eyelids.
"If you manage to get out, don't wait for me. We'll meet here."
Loretta. It must be. So, Tom was right; we were meeting somewhere, but it wasn't for the reason he thought. She was saying something about...erasing my memory? But she had said 'we'. What did she have to do with it and why did she tell me? I didn't actually do something to her, did I?
Again, I briefly recall someone injecting something into my forearm. Was that her? Maybe she did something to me...aside from erasing my memory. Maybe she's the reason I had a heart attack. I wish I could remember all of it!
The sound of someone turning the door handle catches my attention. I back away from the door to avoid being hit as it swings open. Someone outside says something I can't hear, then steps into the room.
"Mr. Menda, you really should be resting," the nurse says to me as she walks in.
I look out into the hallway before the door closes. It seems empty. "Yeah. I, uh, was just wondering why the door was locked," I say to her.
She smiles and says, "I'm sorry about that. Must've been locked by accident."
"Ok," I say hesitantly. "Does that mean I can leave whenever I want?"
"Well, Mr. Menda," she begins, "you've just undergone treatment for a heart attack. You've only been here for a day. We'd like to observe you for at least two more days before we start talking about whether it's ok for you to go home."
"Of course," I say, not bothering to keep the sarcasm from my voice.
"Now, come back to your bed and I'll go get you some lunch," the nurse promises. She adds, after looking around the room, "Let's get you a TV too, so you're not bored to death."
Eyeing her warily, I make my way back to the bed. If I weren't suddenly so hungry, I'd keep pressing her for more answers. Really, though, just her presence and the promise of lunch and a TV makes this seem more like a hospital than I thought it did a few minutes ago. Maybe that's just a justification for the other reasons I don't want to leave just yet. I definitely don't feel 100%. It won't do me any good to get out of here and have another heart attack in the parking lot. I'll wait another two days, but that's it. If they don't let me out, I'm leaving of my own accord.
Time passes interminably slowly. If it weren't for the clock on the wall, I'd swear they were lying about the passage of days. I try to distract myself with TV. When that doesn't work, I try sleep, but I'm just not tired. I feel like I've slept for months and just don't need to anymore.
On the second day, Tom comes to talk to me again. He pries pretty insistently about Loretta, but I still don't remember everything, so I let on nothing. He leaves, seemingly a little more frustrated than I might have expected. On the third day, a couple of cops show up.
"Good morning, Mr. Menda," on of them greets me. "If you have a minute, we'd like to ask you some questions."
I look around the hospital room and say in a sardonic tone, "I think I could free up a few seconds."
He smiles tightly. "I'm Detective Haskell with the Madison PD, and this is my partner, Detective Allen."
Detective Allen nods, looking stern.
I reach up and shake Det. Haskell's hand. "How can I help you, gentlemen?" I ask.
"Mr. Menda, we were wondering if you knew the whereabouts of a Miss Loretta Vine. She was reported missing three days ago and you were the last person seen with her," Haskell explains.
"Really?" I ask. "Where were we seen together?"
The detectives exchange a glance. This time, Allen is the one who speaks. "It was reported to us that the two of you are involved in a relationship. The last time Miss Vine was seen, she was getting into your car as you were leaving your mutual workplace. No one has seen her since."
I shake my head slowly. "I'm sorry, gentlemen. I have no recollection of any of this. I mean, I spoke to her a few times at the office, but that's it."
"I understand," Det. Haskell says with a furrowed brow. "We know you recently lost your wife. It's hard. You have feelings for someone and you're afraid it might be too soon. You're worried that you're dishonoring your wife's memory."
I look away, but say nothing.
"Did something happen?" Det. Allen asks, trying on the same reassuring voice his partner just used. "Maybe you got into an argument over your doubts about the relationship and things got out of hand."
I turn my gaze back toward them, narrowing my eyes. "What, so I just lost my wife and then turned around and kidnapped this woman?"
Det. Allen jumps at the opening. "Nobody said anything about kidnapping. Did you kidnap her?"
"No!" I snap, rolling my eyes.
"Where is she?" he shouts back.
Haskell puts his hands up and gives his partner a calming look. "Mr. Menda," he says, turning back to me, "no one is suggesting you did anything to her...yet. We have to investigate all leads. If someone says they saw you together, we have to check it out."
"So, I'm a suspect," I growl accusingly.
"You're a person of interest," he corrects me, "but if you have some idea of where Miss Vine might be, you would do well to tell us. People who care are worried about her. They just want to know where she is. If there's anything...anything at all you can tell us..."
"I'm sorry," I insist. "I don't know where she is."
Haskell sighs and reaches into his jacket. "Very well. Thank you for your time. If you think of anything, please give me a call," he says, handing me a business card.
I take the card, but offer no response. The two men leave me alone, once again, with my thoughts. My confusion remains, but above that is a resolve to find out exactly what's going on. It will be interesting to see if I am actually released today. Either way, I'm leaving this hospital tonight, come hell or high water.
"Good Morning, Mr. Menda," a chipper voice interrupts my thoughts.
I look up at the nurse who just stepped in. "Oh, uh, morning," I reply.
"Ready to go home today?" she asks me.
My surprise renders me momentarily speechless.
"We're going to get the doctor in here to check on you one more time. If he says you're ok, we'll send you on your way!" she explains with way more excitement than I'm sure she actually feels.
"Oh. That's great," I manage to say.
"Uh-huh," she says absently as she comes over and starts checking my vitals. She sticks my finger in a clip hooked up to a machine and also takes my blood pressure.
After writing a few things down, she smiles at me. "Ok, he should just be a few minutes," she reassures me before hurrying back out the door.
Well, that's interesting. I'm not going to get my hopes up, though. Just watch, there will be some kind of heart murmur or my blood pressure will be too high or something. They'll figure out something to keep me here for 'a few more days'.
About 15 minutes later, a young guy in a lab coat walks in with a stethoscope across his shoulders and a clipboard in his hand. He looks like he's fresh out of med school.
"Good morning, Mr..." He flips to the front of the file. "Ah, Mr. Menda. I'm Doctor Fulton."
I nod to him.
"Doctor Patel is on call today, so I'm going to be checking you out before you go home."
"Ok," I say.
He looks at the stuff the nurse wrote on my file. "Ok, that looks ok," he mutters. "Let's take a listen," he says, grabbing his stethoscope.
I pull off my shirt and sit up straight.
He listens to my chest for a few seconds, then tells me to take a deep breath. He repeats this in a few places on my chest and back. When he's done, he nods and slings the stethoscope back over his shoulders.
"Ok, Mr. Menda," he says, "you're heart sounds okay, breathing sounds normal. You're blood pressure's ok and everything else checks out."
While I find it hard to believe that my blood pressure is ok, given my brief grilling by the detectives, I'm greatly relieved.
"The nurse will stop by in a few minutes to give you some literature," he tells me. "You've just had a heart attack, so you should take it easy. I'd recommend maybe taking a few more days off from work. The stuff the nurse will bring will give you some info on how to proceed from here, foods you should avoid, exercise regimens, that kind of thing."
"Ok," I nod.
"Ok?" the doctor repeats, heading toward the door. "Great, you take care." With that, he quickly exits.
So...how about that? It seems like I actually will be leaving today. The nurse pops in just a few minutes later to give me the aforementioned 'literature', then wishes me well. Everybody seems to be in a hurry today, which suits me just fine.
I get up and put on my clothes. After making sure I have everything, I take one last look at the room and step out into the hallway. I half expect to see armed guards, or at least the two detectives hovering around, but there's no one. I look down the hall and see a green exit sign. I head toward it.
With every step that brings me closer to that sign, my belief that I'm actually getting out of here increases. By the end of the hallway, I feel better than I can remember feeling in quite a while. It's so strange. I've only been here for three days. Still, my excitement continues to mount as I follow the next exit sign, and then the next.
My heart skips a beat when, as I'm walking toward a set of doors through which I can see the parking lot outside, someone calls my name.
"Mike!" the voice repeats.
I look around. Tom comes jogging up to me. "Hey, buddy!" he says jovially.
Glancing back toward the doors, I return the greeting. "Hey, Tom. You still here?"
"Yeah, I stopped by to see if they were releasing you today," he says. "I guess they are."
I nod, "Yep."
"Well, good thing I got here when I did," he chuckles.
"Oh yeah?" I ask absently, eyeing the doors again.
"Well, yeah!" he says incredulously. "Otherwise you'd be walking home."
"Oh."
"What, did you think you drove yourself here in the throes of a heart attack?" he laughs.
"Hey, thanks for picking me up," I tell him sincerely.
Tom nods. "No problem, buddy. Now, let's get you out of here."
"Yeah," I agree enthusiastically.
Tom is pretty talkative as we make our way to my house. I have a hard time paying attention. The warmth of the sun on my face and the spectacle of the city distract me. I don't get it. I wasn't even in the hospital for a week. I apologize to Tom several times for spacing out on him. He just shrugs it off and continues talking. Oddly, he doesn't mention Loretta at all.
When Tom's car rolls to a stop in front of a vaguely familiar house, I look around in confusion. "Are we here already?" I ask.
"Yeah," he answers with a hint of concern. "You feeling ok?"
I take a long look at my house. I guess it's how I remember it. Something just seems...out of place.
"Listen, you want me to hang out for a while?" Tom asks.
I blink away my distracted expression and look over at him. "Thanks, Tom, but I think I'd just like to relax by myself for a while."
He nods. "Ok," he says, "but you call me if you need anything."
"I will," I assure him.
"Ok, buddy. Take care," he calls as I exit the vehicle.
"Yep, you too," I reply, pushing the passenger door closed.
I watch him drive off until he turns the corner at the end of the street, then turn to look again at my house. Everything feels a bit surreal. My house seems like something out of a distant memory, but I know I was here four days ago. Taking a deep breath, I walk up the driveway and step over to the front door. I easily extract my keys from my pocket and pick the right one with barely a glance. In a motion that definitely feels automatic, I unlock the door and walk in.
This place is empty. It's nice enough. I can see hints of my tastes here and there. I recognize everything and know my way around, and yet it feels like something's missing or maybe like it doesn't quite look like I remember it. It all serves to make me feel like I need to find out what's going on...now.
I lock the front door behind me and cross the living room, walk through the kitchen and out the side door to the garage. My awkward feelings persist as I quickly hop into my car and hit the button for the automatic garage door opener. As I back down the driveway and into the road, I look around to make sure no one's watching me. Guided by only the vaguest sense that I know where I'm going, I put the car in drive and proceed down the road.
I find myself wondering, oddly enough, if I'll ever make it back.
* * * * *
Entropic Meditations is a forum for the writings and random thoughts of an author and lover of linguistics.
Friday, May 22, 2009
Wednesday, May 13, 2009
More on Determinism...
So, I recently read A Brief History of Time by Stephen Hawking. Given my interests, it's surprising it's taken me this long to get around to reading it. I have to say that I'm sorry I didn't read it sooner. It's quite fascinating, if a bit over my head at times. It's amazing to me how counter-intuitive physics becomes when you break it down to the quantum level or try to stretch it back to the beginning of time. It's even more amazing that we've managed to figure out any of the parts beyond Newtonian physics, which is, relatively speaking, pretty easy to observe.
I can't imagine the internal conflict for the first physicists to investigate these advanced concepts. Bohr, Schrödinger, Einstein, just to name a few, must have been stunned by the things they discovered. Indeed, Einstein's objections to some of the conclusions he and his colleagues were coming to are well documented. I'm reminded somewhat of Darwin's inner struggle with the reality he observed with evolution and natural selection versus what his lifelong faith told him about the origin of species.
Most interesting, though, is what these researches discovered about what we don't know and, indeed, perhaps can never know. The most significant of these, in my opinion, is Werner Heisenberg’s formulation of the uncertainty principle. I have to admit, this is one of those things that kind of goes over my head. I'm sure if I were a better mathematician, I might "get it" a bit more, but I'm not, so I don't.
I understand only the most basic concepts that come from uncertainty. Let me sum it up in my own words. Uncertainty basically tells us that there are certain variables that cannot be known to the same level of precision simultaneously. These variables seem to be somehow complementary to one another, or at least, the possible methods of measuring them seem to be complementary in such a fashion that the more precisely you know one, the less precisely you can know the other. For example, if you measure the position of some particle with high degree of precision, you will be unable to measure its momentum with much precision at all. Conversely, if you've measured its exact momentum, its position will be a mystery.
I've actually known this specific example of the uncertainty principle for quite some time, but I always thought that it was merely a matter of weakness in our measuring capabilities. According to Heisenberg's work, however, uncertainty is actually a feature of the universe. It wouldn't matter how advanced our instruments were, we could never measure these things simultaneously to the same level of precision.
I was thinking about this the other day, trying to figure out if I could come up with a macroscopic example that would demonstrate how this could possibly be true, and I think I came up with one. Please bear with me as I try to set it up...
Have you ever played Outburst? How about Password? In these games, and a few others, you have a card with some words written on them in light blue ink. Then, over the entire surface of the card, there are a bunch of small, randomly-shaped, and transparent red splotches. The purpose of this red pattern is to obscure the words written in blue so that they cannot be read at a glance. The only way to read them clearly is to insert the card into this little red plastic window that comes with the game. The clear red window cancels out the red on the card and the light blue ink of the words stand out as a dark purple.
Another example of this same concept is those old red and blue 3-D glasses. When I was a kid, I had this book with a bunch of drawings of dinosaurs in this blue and red ink. When you looked at it through the 3-D glasses, the dinosaurs seemed to jump off the page. I noticed that when I put the red eye of the glasses over a part of the drawing, the red lines would disappear. Similarly, when I put the blue eye of the glasses over the drawing, the blue lines would disappear.
Ok, going back to the Outburst example, say you wanted to read the words on the card as clearly as you possibly could. The best way to do that would be to slip the card into the red window. Now, say you wanted to see the random red splotches as clearly as you could. To do that, you'd put the card into a blue window. Now, it is true that green would contrast best with the red splotches, but you would still barely be able to see the word in blue ink, which might interfere with how well you were able to see the detailed shape of the red splotches over that word.
So, what if you wanted to be able to see both the words and the red splotches in the best detail possible simultaneously? One might suppose that a purple window might work, but probably not very well. I doubt you could see either the blue or the red ink any better than you could in regular light. Even if it was better, it still wouldn't be as good as seeing either one color or the other in the windows specifically designed to cancel out the color you wanted it to.
Wow, are you still with me?
So, translating this example to uncertainty, the words in blue ink represent a particle's position and the red splotches represent its momentum. To know its position with a high degree of precision, you have to put it in the red window. For its momentum, the blue window is best. There exists no window, however, that would reveal both simultaneously as nicely as the red and blue windows reveal the blue and red ink respectively.
Well, how do you like that? I've just reduced one of the most puzzling (to me) aspects of quantum physics to the simple pieces of a family game. Though I admit, this may just as well describe a lack of understanding as it does the basic concept of uncertainty. I'd be curious to know what a physicist thinks of it.
Ok, so what the hell does this have to do with determinism? Well, when I first read that uncertainty was "built in" to the universe and is something we are not likely to be able to overcome, my whole idea of a deterministic universe started crashing around me. Now, keep in mind that I was sleepily reading this on a flight to L.A., so my brain wasn't at its peak. What I later realized was that it still doesn't necessarily rule out determinism. All it does is solidify the idea that the universe is ultimately unpredictable. Uncertainty assures that we will never have all the information necessary to propagate the laws of physics out theoretically to some future moment.
In my last post about determinism, I hypothesized about a computer that was powerful enough to hold all the information and perform all the calculations necessary to predict the future. I reasoned that such a computer could not be built because it would require infinite resources. Thinking about it now, I realize I may have been wrong about not only the reason it was impossible, but also its requirements. The reason it would be impossible is because uncertainty guarantees that we will never have all the information necessary to load into the computer. So, even if we had infinite memory, we wouldn't be able to fill it with the necessary information to perform our calculations.
Which brings me to its requirements. Would it really need infinite memory? My reasoning was that such a computer would have to include a simulation of itself resident in memory, which would set up an infinitely recursive situation. If we're talking about building a computer in the sense of a modern-day computer, that might not be far off. In A Brief History of Time, Hawking talks about the laws of thermodynamics and entropy. He says that in the process of storing data in memory or processing that data, a computer generates heat, which increases the overall entropy in the universe by a much higher degree than the order that is created by the memory storage or processing. So, my future-gazing computer would have to at least include in its simulation the amount of heat it outputs into the universe, which would require more memory and processing, which would increase the heat further...etc.
But, let's say we don't build the computer like a modern-day computer. Instead, we'll let the universe run the simulation itself. Or, at least, we'll have half the universe run the simulation. So, let's ignore uncertainty for a moment. All we have to do is freeze time and build a huge partition that splits the universe exactly in half and prevents any energy transfer between the two. Then, we arrange every particle in one half in exactly the same position as the particles in the other half. Once that's done, we use the laws of physics to manipulate one half as it will appear at some arbitrary point in the future. Now the only thing left is to start up time again. If you want to know what's going to happen in the future of the one half, you just have to look at the other half. Simple, no?
Actually, it's not simple. In fact, it's ridiculous. You have to throw out so many physical laws to accomplish this, in the end you're just dealing with fantasy. Ignore uncertainty? Freeze time? Build a perfect barrier between two halves of the universe? Even if you could do these things, what do you then do to calculate out the future of each particle in the half that's going to be your future universe? You can't use a computer, because that's what you're building. It's the whole reason for this insane project! The only option that leaves is to do it by hand or incrementally using weaker computers. Even so, if you could freeze time, you could take the preposterously ponderous amount of time required to calculate the future incrementally using your weaker computers.
I could go on, but it doesn't serve my point, which is that even if the universe is deterministic, which I believe it to be, it may as well not be. Daunting does not even begin to describe the most trivial of steps in calculating the exact future of the universe, and that's even ignoring uncertainty. Throw uncertainty into the picture and your nearly infinitely difficult task literally becomes impossible.
Now, let me propose a thought experiment to you. I'm not sure what conclusions you might draw from it, but I think its purpose is more to evaluate how you think about time (and time travel) than to determine whether or not the universe is deterministic. However, if any definite conclusions could be reached with this experiment, they might have some interesting implications about determinism. So, here goes:
Suppose I approached you and asked you at some specific moment to choose a random number between 1 and 100. If there are truly random events in the universe and human free will is a consequence of that randomness, then there is a 1 in 100 chance that you will pick a particular number within that range, regardless of any events that occurred in all of the universe's history before I asked you to choose.
Now, suppose at some arbitrary point in the future I traveled back in time to a point before I asked you to choose a number and, taking the place of my past self, I approach you at the same moment I did previously and ask you in exactly the same way to choose a random number between 1 and 100. Again, we are assuming that there are truly random events and our free will is a consequence of them. It shouldn't matter, then, that this already happened in the past I know. There should still be a 1 in 100 chance that you will pick a specific number in that range, which means that the number you choose this time might not be the same as the number you chose last time.
Think about how time travel is represented in science fiction. Does this thought experiment agree with that representation? Consider the hypothetical "what if you could go back and kill Hitler?" question. Well, what if you went back far enough that enough events that depended upon the random elements of a non-deterministic universe played out differently and maybe Hitler wasn't even born, or maybe he made different decisions that led to a different history than the one we know? In this hypothetical universe where random events truly happen and have noticeable effects, you wouldn't necessarily have to do anything to stop Hitler. It might just work out that Hitler never ends up doing what he did in our history, if he even exists at all.
There is, of course, one minor kink in this experiment. If the universe is deterministic, then the amount of entropy you inject into the past universe by arriving there via time travel might have a significant effect on future events as well. Just by being there, the energy your body gives off as it metabolizes calories might change how history plays out. Unless you can figure out how to travel to the past without adding more entropy to the past universe, you'd never be able to completely rely upon your observations to prove randomness. But to talk about figuring out how to prevent contamination of your experiment while traveling to the past, you have to figure out how to travel to the past in the first place.
Ultimately, we're no further along in figuring out whether or not the universe is deterministic. I still believe that it is, but I also still believe that it doesn't matter. And it seems like the more we know, the more we're starting to understand that we'll never know it all. We may end up knowing a lot of it, but some things in the universe will still remain a mystery. I'm ok with that.
* * * * *
I can't imagine the internal conflict for the first physicists to investigate these advanced concepts. Bohr, Schrödinger, Einstein, just to name a few, must have been stunned by the things they discovered. Indeed, Einstein's objections to some of the conclusions he and his colleagues were coming to are well documented. I'm reminded somewhat of Darwin's inner struggle with the reality he observed with evolution and natural selection versus what his lifelong faith told him about the origin of species.
Most interesting, though, is what these researches discovered about what we don't know and, indeed, perhaps can never know. The most significant of these, in my opinion, is Werner Heisenberg’s formulation of the uncertainty principle. I have to admit, this is one of those things that kind of goes over my head. I'm sure if I were a better mathematician, I might "get it" a bit more, but I'm not, so I don't.
I understand only the most basic concepts that come from uncertainty. Let me sum it up in my own words. Uncertainty basically tells us that there are certain variables that cannot be known to the same level of precision simultaneously. These variables seem to be somehow complementary to one another, or at least, the possible methods of measuring them seem to be complementary in such a fashion that the more precisely you know one, the less precisely you can know the other. For example, if you measure the position of some particle with high degree of precision, you will be unable to measure its momentum with much precision at all. Conversely, if you've measured its exact momentum, its position will be a mystery.
I've actually known this specific example of the uncertainty principle for quite some time, but I always thought that it was merely a matter of weakness in our measuring capabilities. According to Heisenberg's work, however, uncertainty is actually a feature of the universe. It wouldn't matter how advanced our instruments were, we could never measure these things simultaneously to the same level of precision.
I was thinking about this the other day, trying to figure out if I could come up with a macroscopic example that would demonstrate how this could possibly be true, and I think I came up with one. Please bear with me as I try to set it up...
Have you ever played Outburst? How about Password? In these games, and a few others, you have a card with some words written on them in light blue ink. Then, over the entire surface of the card, there are a bunch of small, randomly-shaped, and transparent red splotches. The purpose of this red pattern is to obscure the words written in blue so that they cannot be read at a glance. The only way to read them clearly is to insert the card into this little red plastic window that comes with the game. The clear red window cancels out the red on the card and the light blue ink of the words stand out as a dark purple.
Another example of this same concept is those old red and blue 3-D glasses. When I was a kid, I had this book with a bunch of drawings of dinosaurs in this blue and red ink. When you looked at it through the 3-D glasses, the dinosaurs seemed to jump off the page. I noticed that when I put the red eye of the glasses over a part of the drawing, the red lines would disappear. Similarly, when I put the blue eye of the glasses over the drawing, the blue lines would disappear.
Ok, going back to the Outburst example, say you wanted to read the words on the card as clearly as you possibly could. The best way to do that would be to slip the card into the red window. Now, say you wanted to see the random red splotches as clearly as you could. To do that, you'd put the card into a blue window. Now, it is true that green would contrast best with the red splotches, but you would still barely be able to see the word in blue ink, which might interfere with how well you were able to see the detailed shape of the red splotches over that word.
So, what if you wanted to be able to see both the words and the red splotches in the best detail possible simultaneously? One might suppose that a purple window might work, but probably not very well. I doubt you could see either the blue or the red ink any better than you could in regular light. Even if it was better, it still wouldn't be as good as seeing either one color or the other in the windows specifically designed to cancel out the color you wanted it to.
Wow, are you still with me?
So, translating this example to uncertainty, the words in blue ink represent a particle's position and the red splotches represent its momentum. To know its position with a high degree of precision, you have to put it in the red window. For its momentum, the blue window is best. There exists no window, however, that would reveal both simultaneously as nicely as the red and blue windows reveal the blue and red ink respectively.
Well, how do you like that? I've just reduced one of the most puzzling (to me) aspects of quantum physics to the simple pieces of a family game. Though I admit, this may just as well describe a lack of understanding as it does the basic concept of uncertainty. I'd be curious to know what a physicist thinks of it.
Ok, so what the hell does this have to do with determinism? Well, when I first read that uncertainty was "built in" to the universe and is something we are not likely to be able to overcome, my whole idea of a deterministic universe started crashing around me. Now, keep in mind that I was sleepily reading this on a flight to L.A., so my brain wasn't at its peak. What I later realized was that it still doesn't necessarily rule out determinism. All it does is solidify the idea that the universe is ultimately unpredictable. Uncertainty assures that we will never have all the information necessary to propagate the laws of physics out theoretically to some future moment.
In my last post about determinism, I hypothesized about a computer that was powerful enough to hold all the information and perform all the calculations necessary to predict the future. I reasoned that such a computer could not be built because it would require infinite resources. Thinking about it now, I realize I may have been wrong about not only the reason it was impossible, but also its requirements. The reason it would be impossible is because uncertainty guarantees that we will never have all the information necessary to load into the computer. So, even if we had infinite memory, we wouldn't be able to fill it with the necessary information to perform our calculations.
Which brings me to its requirements. Would it really need infinite memory? My reasoning was that such a computer would have to include a simulation of itself resident in memory, which would set up an infinitely recursive situation. If we're talking about building a computer in the sense of a modern-day computer, that might not be far off. In A Brief History of Time, Hawking talks about the laws of thermodynamics and entropy. He says that in the process of storing data in memory or processing that data, a computer generates heat, which increases the overall entropy in the universe by a much higher degree than the order that is created by the memory storage or processing. So, my future-gazing computer would have to at least include in its simulation the amount of heat it outputs into the universe, which would require more memory and processing, which would increase the heat further...etc.
But, let's say we don't build the computer like a modern-day computer. Instead, we'll let the universe run the simulation itself. Or, at least, we'll have half the universe run the simulation. So, let's ignore uncertainty for a moment. All we have to do is freeze time and build a huge partition that splits the universe exactly in half and prevents any energy transfer between the two. Then, we arrange every particle in one half in exactly the same position as the particles in the other half. Once that's done, we use the laws of physics to manipulate one half as it will appear at some arbitrary point in the future. Now the only thing left is to start up time again. If you want to know what's going to happen in the future of the one half, you just have to look at the other half. Simple, no?
Actually, it's not simple. In fact, it's ridiculous. You have to throw out so many physical laws to accomplish this, in the end you're just dealing with fantasy. Ignore uncertainty? Freeze time? Build a perfect barrier between two halves of the universe? Even if you could do these things, what do you then do to calculate out the future of each particle in the half that's going to be your future universe? You can't use a computer, because that's what you're building. It's the whole reason for this insane project! The only option that leaves is to do it by hand or incrementally using weaker computers. Even so, if you could freeze time, you could take the preposterously ponderous amount of time required to calculate the future incrementally using your weaker computers.
I could go on, but it doesn't serve my point, which is that even if the universe is deterministic, which I believe it to be, it may as well not be. Daunting does not even begin to describe the most trivial of steps in calculating the exact future of the universe, and that's even ignoring uncertainty. Throw uncertainty into the picture and your nearly infinitely difficult task literally becomes impossible.
Now, let me propose a thought experiment to you. I'm not sure what conclusions you might draw from it, but I think its purpose is more to evaluate how you think about time (and time travel) than to determine whether or not the universe is deterministic. However, if any definite conclusions could be reached with this experiment, they might have some interesting implications about determinism. So, here goes:
Suppose I approached you and asked you at some specific moment to choose a random number between 1 and 100. If there are truly random events in the universe and human free will is a consequence of that randomness, then there is a 1 in 100 chance that you will pick a particular number within that range, regardless of any events that occurred in all of the universe's history before I asked you to choose.
Now, suppose at some arbitrary point in the future I traveled back in time to a point before I asked you to choose a number and, taking the place of my past self, I approach you at the same moment I did previously and ask you in exactly the same way to choose a random number between 1 and 100. Again, we are assuming that there are truly random events and our free will is a consequence of them. It shouldn't matter, then, that this already happened in the past I know. There should still be a 1 in 100 chance that you will pick a specific number in that range, which means that the number you choose this time might not be the same as the number you chose last time.
Think about how time travel is represented in science fiction. Does this thought experiment agree with that representation? Consider the hypothetical "what if you could go back and kill Hitler?" question. Well, what if you went back far enough that enough events that depended upon the random elements of a non-deterministic universe played out differently and maybe Hitler wasn't even born, or maybe he made different decisions that led to a different history than the one we know? In this hypothetical universe where random events truly happen and have noticeable effects, you wouldn't necessarily have to do anything to stop Hitler. It might just work out that Hitler never ends up doing what he did in our history, if he even exists at all.
There is, of course, one minor kink in this experiment. If the universe is deterministic, then the amount of entropy you inject into the past universe by arriving there via time travel might have a significant effect on future events as well. Just by being there, the energy your body gives off as it metabolizes calories might change how history plays out. Unless you can figure out how to travel to the past without adding more entropy to the past universe, you'd never be able to completely rely upon your observations to prove randomness. But to talk about figuring out how to prevent contamination of your experiment while traveling to the past, you have to figure out how to travel to the past in the first place.
Ultimately, we're no further along in figuring out whether or not the universe is deterministic. I still believe that it is, but I also still believe that it doesn't matter. And it seems like the more we know, the more we're starting to understand that we'll never know it all. We may end up knowing a lot of it, but some things in the universe will still remain a mystery. I'm ok with that.
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