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.

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Determinism in a Chaotic Universe

Lately, I find myself frequently thinking of determinism. I'd like to put down some of my thoughts, though I doubt I have anything new to say on the matter. It's one of those things, like so many, that we probably can't really know the answer to, but that's one of the reasons these kinds questions are so intriguing. It's only when our questions are finally fully answered that we will stop asking them. So, let's hope for the sake of human intellectual development that some of these questions never get answered, or that, if they do, others take their place.

Anyhow, on to determinism. The question in most people's minds, I think, when they think about determinism is whether a deterministic universe can allow free will. Also, many proponents of free will often wonder how a belief in determinism does not result in fatalism or defeatism. Ostensibly, it does seem rather contradictory to believe in both determinism and free will. It's a complicated question, and not one that I'm all that sure I can even begin to answer. I don't think my purpose is really to answer any questions, rather to hypothesize, or at least to ramble thoughtfully. What I'm trying to say is, don't take me too seriously.

Okay, so as a basic definition, determinism is the belief that every event, from the most trivial to the most significant, has a cause or set of causes. Physics suggests that the universe is at least partially deterministic. Psychology tells us that human behavior is deterministic to some degree. Causality is a deterministic concept and popular fodder for time-travel-loving sci-fi writers.

For society in general, feelings about determinism are complicated. Some say there's a reason for everything. Concepts of fate and destiny are romanticized in popular culture. When we see someone we pity doing something horrible, we say he can't help it. It's just the way he was raised, or he doesn't know any better. If some tragedy befalls us, it's not our fault. There were events beyond your control. Suggest to the average person, however, that every decision she makes or feeling she has is the end result of a sequence of events that chains back to the beginning of existence, and she will likely feel insulted, or at least be a little indignant at the suggestion that her thoughts are not completely her choice.

That is not to say that all determinists believe that our actions are predetermined. There are those who also believe in free will and even those who say that, despite the deterministic nature of the universe and its influence on our thoughts and feelings, we are still ultimately in control. As I've already said, I don't think I can answer the obvious questions that spring from this stance. All I can do is discuss my thoughts.

So, do I think our thoughts and feelings are predetermined? Well, as uncomfortable as the idea makes me, I'm kind of leaning towards yes. To me, thoughts and feelings are simply a sequence of complex chemical and electrical interactions. It might seem cold to reduce them to that, and I confess it is rather an oversimplification, but it's difficult for me to think otherwise, given my interpretation of what science has to say on the matter. If it can really be reduced to simply a sequence of chemical and electrical interactions, which by their nature are governed by the laws of physics, then how they could possibly be non-deterministic is beyond me.

Then what's the point of doing anything? Or deciding anything? If everything is predetermined, then what is the point of anything? Well, that attitude is fatalist, and I think you'll find that there are few determinists who are fatalists. Why? Well, to put it obviously, events that depend upon you doing them to get done won't get done if you decide not to do them. Of course, if that decision is not really in your control, that is to say, if whether or not you make that decision is based on every event in history since the beginning of time, then, again I ask, what is the point of "deciding" anything? Enough commas in that sentence for you?

Here's the problem with thinking of the universe in deterministic terms. It always leads to cyclic or self referential arguments. Whether it's about whether our decisions are our own or about the origin of a deterministic universe, we find ourselves getting caught up in the pointless infinite loop of logic that our limited brains must do when we try to reason about the unknowable.

The thing is, nothing is gained from the knowledge of whether or not the universe is deterministic. Even if we knew for certain that it was, it still wouldn't make the universe predictable. If the universe is truly deterministic, that would mean that if we knew every governing rule of existence and every single state of every infinitesimal piece therein, we could extrapolate future events with 100% accuracy. The problem is, that is not possible for us. No human brain, no matter how evolved, could hold that much information and process it fast enough to glean any useful information from it. Similarly, we could never build a computer that could do it either. In order to hold the state of every infinitesimal piece of existence, first of all, we would have to have discovered them all first, and second of all, we would have to be able to hold an infinite amount of stuff in memory. Even if there is only a finite amount of information in a single slice of time in existence, the computer would also have to have a simulation of itself in its simulation of the universe. And we're back to the self-referencing problem we had earlier. Even the finite information would become infinite because the simulation of the computer simulating the universe would have the same simulation of the universe running inside it, which would contain the same simulated computer running a simulation...ad infinitum.

Let me explain why it doesn't matter in simpler terms. Pick a random number between 1 and 100. Ok, now I'm going to guess what it is. Are you thinking of it? Good.

It's 68.

Was I right? According to probability, I'm not likely to be. According to probability, on the average I would guess correctly for 1 out of every 100 people who read this post. I would guess that, given a large enough sample, it probably works out that way too. Does that mean people are actually capable of choosing random numbers? Would I be able to guess any better if I knew every experience you had ever had since birth? Probably not, but that doesn't mean that your choice wasn't influenced by those experiences.

Now take this little JavaScript I wrote to generate a random Sudoku puzzle. It generates a bunch of random numbers to fill in a grid, then randomly deletes pairs of cells such that it doesn't end up in multiple solutions. Now, is it truly random? No. I know for sure that it isn't. I know that when the script requests a random number, it looks at the system time, does some kind of math with it and returns the result. If I knew the exact system times when each random request was made and the math that was used to generate the number, I could calculate by hand the solution to the Sudoku puzzle the same way the computer did.

Ah, now we're getting to the heart of my point. Here's the thing, even if I could know all of the starting information and solve it by doing exactly what the computer did by hand, why the hell would I want to do that? What's the point? Is it faster that way? Not with my math skills. Is it more fun? I daresay it isn't. Similarly, even if I could somehow calculate "by hand" which random number you would have chosen, is it worth our time? Is nearly as amazing as my simply guessing it "at random" (assuming either one of those is amazing to any degree)?

See, the thing is, JavaScript’s random number generator is "good enough", as it serves our purposes for such a trivial task. Just like the number I asked you to choose randomly. Even if it wasn't random, it might as well be. It works the same for the universe. It might be deterministic, but it may as well be at least a little random because we can't ever know every state in one timeslice of existence and thus the starting conditions for it all.

I don't know that this argues that we should be mindful of our decisions and keep trying to improve our lives, but the possibility that it doesn't matter isn't going to stop me. If the universe IS deterministic, then things aren't going to just get better randomly. It's going to require the initial condition of effort on my part. My decision to make that effort might be predetermined, but I'm grateful that it is if that's the case. I also take comfort, like many people, in the fact that, whether the universe is random or deterministic, some events (most of them, in fact) really are beyond our control. It might not be the highest note to end on, but it serves its purpose.