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30 Nov 2007

Random thoughts – Today’s entry ranges far and wide, but it begins with my iPod. I got it as a birthday present earlier this year, and since then I have grown quite fond of it. I particularly enjoy the fact that I can play videos on it—subway rides are much more pleasant now that I can sit there and stare at a screen rather than pretending to be asleep. Most of the time, though, I use it to listen to music (who would have thought that watching a tiny video screen on a bus could make me sick?). While I will occasionally get a hankering for a specific album, most of the time I will just put it on shuffle and let randomness take its course. Half the fun is wondering what the iPod will come up with next. Will it go from Barry White to Mozart? Maybe it will follow up U2 with Erasure, or some of my K-Pop with my brother’s music. It’s a way of listening to music that simply was not possible before I could fit my entire collection of CDs onto a single portable device.

“This has gotten me thinking about the concept of randomness. What exactly does it mean for something to be random?”

If there is one thing I could change about the way the iPod (and iTunes) works, though, it would be to add a “continuous shuffle” function. Every time I hit “Shuffle Songs” on my iPod, it starts from scratch. There is a “Now Playing” option that allows you to pick up where you left off, but if you tend to alternate between music and video (like I do), that doesn’t work. So I end up starting a new random sequence of songs every time I shuffle.

iTunes can be configured to show more information than iPod, including the number of times that a song has been played. One thing I have noticed as I look through my music library is that certain songs seem to be played far more often than other songs. For example, of the eight tracks on Erasure’s Breath of Life maxi-single, one of them has been played ten times, while another song has not been played even once. I have never played any of these tracks separately, so all of those plays come from shuffling, and it just seems odd to me that one song could be played ten times and another song could never come up at all.

If I were to keep iTunes open (and leave my computer on) and just play music for five days straight (which is how long it would take to get through my library), it would eventually play every song once. In that respect, it’s not really a completely random selection of songs, but it is—or at least it’s supposed to be—a random ordering of songs. And yet some songs come up a lot while other songs never come up at all, meaning that the “popular” songs are getting placed toward the front of the queue while the “outcast” songs are getting placed toward the back of the queue. I suppose it’s kind of like high school, if you think about it.

This has gotten me thinking about the concept of randomness. What exactly does it mean for something to be random? The first definition in the OED is somewhat archaic, defining the word as “impetuosity, great speed, force, or violence” and saying that it is used in the phrase “with great random”—a phrase that I don’t ever remember hearing. It also has a number of greatly varying meanings in different fields: in gunnery it refers to the range of a piece of artillery, in mining it refers to the direction of a vein, in dyeing it refers to clouded yarn, and in printing it refers to a frame used by compositors. As a word geek, I find all of these definitions fascinating, but none of them help us here. This is what we’re looking for:

Governed by or involving equal chances for each of the actual or hypothetical members of a population; also, produced or obtained by a random process (and therefore completely unpredictable in detail)

This is how the term is defined in the field of statistics. I think the important part here is that a random sequence is completely unpredictable. A good example of a truly random number generator is a die (i.e., the singular form of “dice”), as long as we assume that it is perfectly balanced and not weighted or tampered with in some way. You can roll a die until the day you die (heh) and you will never be able to predict the next roll. You might be able to guess, but you’ll never be able to truly predict.

It may seem counterintuitive, but computers have a really hard time generating truly random numbers. You might think that, since a computer is far more complex than a simple die, it should be able to generate truly random numbers just as well as a die, if not better, but this is not the case. The problem is that computers can only follow instructions—so unless the process that the computer is relying on is completely random, the output is not going to be truly random. If you could attach sensors to each face of a die being tossed around in a chamber and then feed that information into a computer, you would get true randomness.

Most computers (especially something like my iPod) are not capable of doing this, so they have to rely on a work-around. Basically, they take a “seed” number (for example, the current time, going down to fractions of a second—which I’m guessing is what the iPod uses) and generate a sequence of pseudo-random numbers from that seed. These numbers are called pseudo-random because they look unpredictable, and they are in fact unpredictable—as long as you don’t have the seed. Once you have the seed, though, you can predict the entire sequence. This can be useful if you want to generate a basically random sequence but you also want to be able to repeat that sequence in the future for testing purposes. But it’s not true randomness. If you want true randomness from a computer, you need to go to, which generates random numbers based on atmospheric noise (and also has an excellent article on the concept of randomness that goes into more detail than I do here).

The reason that a die roll can be truly random is because of all the variables that go into determining the result. When you toss the die in the air, it spins on one, two, or three axes, and even the slightest change in the toss can drastically change this spin. Each time the die hits or bounces off of a surface the speed and angle of that spin will be changed again until it finally comes to rest. What we are seeing is the chaos theory in action—the idea that minute changes in the initial conditions of a system can drastically influence how that system develops. You know, how a moth farting in Brazil can cause a Swiss banker to choke on a piece of lettuce a hundred years later, that sort of thing. The interplay of all variables and the environment explodes into so many possibilities that the outcome could never be predicted.

This is where we get into what I’ve really been thinking about all this time. No doubt some of my readers are a step ahead of me and have figured out where I’m going with this—namely, that randomness is subjective. That is, to someone who has no knowledge of how a sequence is produced, that sequence is, for all intents and purposes, random. But once we come to understand the calculations behind the sequence, we can predict how it will develop and it is no longer random. But isn’t this just semantics? After all, who could possibly understand all the minute calculations that go into determining the result of a die roll, let alone the calculations that would be required to figure out atmospheric noise? Even with the most advanced technology available today, predicting the weather is still mostly guesswork once you get past a certain point (as is quick to point out).

But what if the human race advances enough to create computers that can make all of these calculations in a reasonable period of time? Or what if the human race develops into a higher level of consciousness, a level where we can do all these calculations ourselves? All of these sequences that we might consider random today would no longer be random. Randomness, like beauty, is in the eye of the beholder.

Maybe ultra-supercomputers and ascended human beings seem like the stuff of science fiction and fantasy. There is another possibility, one that is embraced by a large percent of the world’s population: an omniscient being, namely God. If God is all-knowing, then he has the necessary knowledge (and presumably the necessary intellect) to predict the outcome of every sequence, every process, and every system. And it this is so, then there can be no true randomness from God’s point of view. Continuing down this path, we come to determinism, which is the idea that everything that happens is the inevitable consequence of what has happened beforehand. When you bring the idea of an omniscient God (whose omniscience extends to future knowledge) into the picture, you come to the conclusion that the entire course of history is following a path that has already been set.

Nimbler minds than my own have tackled the ramifications of these ideas, so I’m not going to go into them here. Instead, I will point you to some of those nimbler minds. The article at I mentioned above discusses the matter briefly as it relates to randomness, and links to Wikipedia’s discussion of determinism, which is a pretty good distillation of the idea. It also links to a page entitled “Can You Behave Randomly? ” (spoiler: probably not), which links randomness to free will. But before I got interested in randomness and started poking around, it was Kevin Kim who had me scratching my head the most over questions of determinism, free will, and God’s omnipotence/omniscience. His book, Water From a Skull, deals with the subject, as does his website (Blogger’s site search seems to be borked at the moment, so I shall direct you to a simple Google search of his site, from which you can pick and choose).

And that’s all I’m going to say about that subject for now, because, to be honest, it makes my head hurt. Sometimes I don’t really know what to think. Rather than rehash the issue here, I’d rather change the focus of the discussion a bit. I’m going to set aside for the moment whether or not Christian theology logically allows for true free will. Instead, I’d like to look at the question from the inside out—what does the Bible say about free will? I can’t, of course, promise an exhaustive discussion, but I would like to at least make a start.

The term “free will” does not actually appear in the Bible, but there are a number of instances that illustrate the concept. Actually, it would be more correct to say that there are a number of instances that seem to negate the idea, especially in the Old Testament. It would be hard to prove whether many of the choices in the Bible were made out of free will or if they were predetermined, but there a number of places where free will is expressly denied. Even if it might not be the earliest instance, the most striking example I can think of is the story of the Israelites in Egypt, told in the book of Exodus. When God tells Moses that he is going to free the Israelites, he adds, “But I will harden Pharaoh’s heart, and though I multiply miraculous signs and wonders in Egypt, he will not listen to you” (Exodus 7:3-4). The following chapters describe the plagues of Egypt, and after each plague the hardness of Pharaoh’s heart prevents him from letting the children of Israel go. The wording changes, and at times it seems that Pharaoh himself is doing the heart-hardening, but the truth is clear: “Then the LORD said to Moses, ‘Go to Pharaoh, for I have hardened his heart and the hearts of his officials so that I may perform these miraculous signs of mine among them that you may tell your children and grandchildren how I dealt harshly with the Egyptians and how I performed my signs among them, and that you may know that I am the LORD’” (Exodus 10:2-3).

Even with a charitable reading of the passage, it is hard to deny that Pharaoh was a puppet whose sole purpose was to fulfill the role that God had planned for him. The implication is that, had God not hardened Pharaoh’s heart, he might have let the Israelites go after the early signs and plagues and the impression made by these signs and plagues might not have been as lasting as all of the plagues together, including the one that claimed Pharaoh’s firstborn son. And yet, this was not the end of Pharaoh’s woes. After Pharaoh finally ordered the Israelites to leave Egypt, God then hardened his heart again so that he would pursue them in the wilderness: “And I will harden Pharaoh’s heart, and he will pursue them. But I will gain glory for myself through Pharaoh and all his army” (Exodus 14:4). The result was that the Israelites passed through the parted seas on dry land, but Pharaoh and all his army drowned when the seas came together again. The Egyptian threat was removed, and the Israelites came to fear and trust God (at least until the next time they got hungry or thirsty).

I will admit that this passage has bothered me since the first time I read it as a young boy. It didn’t seem fair to me then, and it’s still hard to swallow now. Yeah, it might have been great for the Israelites, seeing as how they escaped from slavery and saw their enemies destroyed before their eyes (which didn’t have quite the effect God had intended, seeing how they all ended up wandering around in the wilderness for forty years until the rebellious generation, including Moses, had died), but boy did it suck for Pharaoh and the Egyptians. If there is a lesson in the Old Testament, it has to be: do not get on Yahweh’s bad side.

I speak partly in jest, of course—I do realize that there is a lot more to the Old Testament than that. But the fact remains that things went rather poorly for those who got on God’s bad side, including his chosen people themselves. The idea of free will is a foreign one before the coming of Christ. Things happen according to God’s plan, and no one and nothing is going to stand in the way of that. History still develops according to God’s plan in the New Testament, but these later writings seem more amenable to the idea of free will. There is no talk of God hardening anyone’s heart in the New Testament—although there is talk of Satan poisoning hearts (the tale of Ananias and Sapphira, for example, in Acts 5:1-11), which may ultimately be the same thing in terms of free will. Still, though, the New Testament is more the story of people surrendering their own free will to the will of God. Christ’s prayer in Gethsemane is a perfect example of this: “My Father, if it is possible, may this cup be taken from me. Yet not as I will, but as you will” (Matthew 26:39). And Paul is constantly talking about being a “slave of Christ,” referring to the paradox of gaining freedom by surrendering to the will of God. The denizen of the New Testament has free will, but unless he surrenders that free will he becomes a slave to his own passions and open to manipulation by the evil one.

It’s hard to tie together these two vastly differing theologies into one neat package, but I’m going to give it a shot. If I had to sum up the Bible’s depiction of free will, I would say that it does exist, at least in the New Testament, but “free will” and “freedom” are not the same thing. If you choose to exercise your free will in defiance of God’s will, you are ultimately enslaved by sin and passion, but if you surrender your free will to the will of God, you become free to experience his blessings. To the non-believer, of course, this sounds like being stuck between a rock and a hard place, but if you believe the Bible, the choice is clear.

So the question for me as a Christian is not, “Do I have free will or not?” Instead, I think the question is, “Am I OK with not having free will? Am I OK with God being in complete control?” I don’t think you can truly believe the Bible and at the same time believe that you have free will, if we understand “free will” to be the ability to be in complete charge of one’s destiny (like I said above, I realize that this is a complicated issue, and that not all thinkers define free will this way, but this is what most people think of when they consider the idea). So it comes down to either being OK with that or not being OK with that.

There is a specific verse in Proverbs in which I have found comfort over the years: “In his heart a man plans his course, but the Lord determines his steps” (Proverbs 16:9). This is, of course, yet another piece of evidence to support the notion of no free will in the Bible, or at least in the Old Testament. At the same time, though, it can be very comforting to know that someone has a plan, that things don’t just happen at random, that everything that happens in my life happens for a reason. I have gone through some depressing times in my life, and this verse has been a ray of hope in those dark times. I can look back at the events in my life and see how they have led me to this point, and in that I see God’s plan for me.

(There is another way of looking at things, of course. It’s quite easy to look back at a sequence of events and see how they have led to a certain conclusion simply because that’s the way things have worked out. To put it another way, while some may marvel at how conditions on this planet just happened to lead to our coming into existence, others see it as only natural—after all, if the conditions had been slightly different, we probably wouldn’t be around to marvel at anything. We’re here because that’s the just the way things happened to turn out. There is no “divine plan” for life, things happen at random, and there is no greater, underlying meaning to events. Some people find this view just as comforting as I find the view I described in the previous paragraph. But I’m not going to debate the existence of God or the functioning of the universe right now.)

Ultimately, being OK with relinquishing free will comes down to a matter of trust. Do I trust God to do what is best for me? I’ve been thinking about this a lot lately. My prayer and meditation sessions have become times of soul searching. What do I really believe? Where do I place my trust? I will readily admit that there are many things I do not understand. My head starts to spin when I get into philosophical discussions, and the non-theists make very logical and persuasive arguments about the nature of the universe. But I cannot just relinquish my beliefs. Some may see this as holding on to the remnants of an outmoded and inconsistent ancient religion. I would like to think that it is something more fundamentally important to my life than just religion, though. It is faith, it is hope, and it is love. Though I may struggle at times, when my spirit feels as dry as a valley of bones, there is something inside me that gives me the strength to keep this faith.

I didn’t really have a good idea of where all this was going when I started writing. It is not a scholarly piece on randomness, or determinism, or the Bible, or any of the other subjects I may have touched on in the course of the entry. It’s just a flow of thought from one point to another. It has no real beginning and no real end; it’s just another musing in a long string of musings that will continue until I leave this earth. I cannot lay claim to anything more than a layman’s general knowledge of the subjects discussed, and I would be glad to hear corrections or contributions from more knowledgeable minds.

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