Please bear with me for the next 20 seconds or so while I recite the numerical value Pi as well as I can.
Okay, that's Pi to 55 digits. I memorized that about 40 years ago and on a good day I can still remember it. I'm pretty sure that with so many digits I could calculate the circumference of the galaxy and be accurate to less than the width of an atom. So it seems like a pretty useless thing to remember.
I'm not the only person to have memorized Pi to absurd levels of accuracy. According to a list I have from 2007, a Chinese guy named Lu Chao memorized it to over 67,000 digits! The list mentions 54 more people who have memorized 1000 or more digits.
What is it about Pi that is so fascinating? I can't speak for Lu Chao or the others, but to me it's the fact that a seemingly random infinite number is right under my nose every time I look at a circle. Because if you remember your high school math class, Pi is the number you get when you divide a circle's length around the outside edge by its width across. That is to say, you're dividing its circumference by its diameter. And you end up with a weird series of digits that go on forever without repeating.
You might think that surely the numbers repeat at some point. I can't personally prove to you that that's wrong, but I've read several proofs, by actual mathematicians, that clearly showed me that the digits never, ever repeat. So I'm convinced that the digits continue forever and ever, always presenting something new.
So what does Pi have to do with the sort of things I usually talk about? Well, when I look at the number Pi I am reminded of the apparent unpredictability of my own life.
Now, I say that there is no Free Will — that everything I do could, in theory, be predicted if there was enough information about what makes me choose one action over another. I also say that, under everyday circumstances, nobody will ever be able to predict what I'll do next because it's impossible for any human to get enough information.
Please note that qualification I used: “under everyday circumstances.” If I'm wired up to a bunch of machines that are monitoring my brain it is possible to predict what I will do if the prediction is about something trivial, like whether or not I'll push a button. In such cases my actions can be predicted, but in a standard day, when I'm not hooked up to machines, and my decisions involve things like what to have for lunch, there is usually no way to predict what I'll do next.
Think about what I'm saying for a moment. Think about it skeptically and suspiciously. Suspect that I've made a mistake, or that I might be lying to myself. Do you see something wrong in what I've been saying?
Well, doesn't it sound like I've come up with the idea that there's no Free Will, then came up with a reason (“You can't get enough information!”) why you can't prove me wrong?
That's the kind of convenient cop-out you usually hear from religions, who say that God exists, but here are two dozen reasons why nobody can prove that. How convenient!
Nonetheless, I think that Pi demonstrates that my hypothesis about Free Will is at least reasonable. Because even though I know the first 55 digits — far more than anybody actually needs — having only that knowledge in no way helps me predict the 56th digit. I simply don't have enough information to figure it out. And this, to me, is exactly what my life is like: I seem to know everything that has happened up until this moment, but I can't predict what I'll do next.
That lack of predictability sure seems like Free Will, doesn't it? But nobody claims that Pi has Free Will, even though it seems to act as unpredictably as I do.
Let me tell you a story that might at first seem unrelated to what I've written above.
Once upon a time there was a pair of conjoined twins. They were what people sometimes call “Siamese Twins.” In fact, these two people were the original Siamese Twins. Their names were Chang and Eng, and they were originally from Siam (now known as Thailand).
Most of us are fascinated by their story: how they made a life for themselves, married two sisters, and sired 21 children. These are all impressive accomplishments for people in difficult circumstances. But what fascinates me just as much is the fact that Chang was a heavy drinker, while Eng was not.
You might think that this disproves my entire hypothesis about Free Will. After all, Chang and Eng had identical DNA and nearly identical life experiences. So if my hypothesis is correct, you'd expect them to behave exactly alike, wouldn't you? Either they'd both drink heavily or neither would. Right?
Well, no. There were some significant differences that would affect their lives and subsequent actions. In my mind, one of the most obvious differences is that Chang was on the left-hand side, while Eng was on the right-hand side. Thus, Eng had convenient use of a right hand, which makes a big difference in this right-hand-oriented world.
There must have been other major differences, too. But even small differences can make a huge difference in how we develop. For example, imagine you're at a party and somebody looks at you in a strange way. This might affect your enjoyment for the rest of the evening. If, on the other hand, you hadn't noticed that odd look, your experience of the party would be completely different. That's two possible versions of the same party, and the only thing that distinguishes one from the other is a momentary difference in what you were paying attention to.
It takes very little difference to make a big difference in the long run. In mathematics and elsewhere this sensitivity to small differences has been called “The Butterfly Effect.” And since it affects our imaginings about Free Will, I'm tempted to also call it “The Free Will Effect.”
If you really think you've got Free Will, I'm guessing you've never been addicted to anything. I stopped smoking 2 years ago and I still want a cigarette. (Young readers, if any, take note! You really don't want this kind of problem. You won't become addicted if you don't start.)
Also, like Chang, there was a time when I was a heavy drinker. I don't know why that happened. Well, I can list some reasons but that would just be rationalization. The fact is, I can't possibly know all the reasons that go into why I do something. I cannot get enough information. To know for sure why somebody does something I'd need to know the trajectory of every atom going back to the time of the Big Bang.
Science Note: More accurately, to predict something N seconds into the future all I probably need to know is the states of all particles within N times 299,792,458 meters. It that all? Gee, how hard could that be?
Mind you, people can (and do) make generalizations, many of which are accurate, using incomplete information. So I'm not utterly unpredictable. My wife, for example, could predict that I'd tend to turn down a ham sandwich because for the past 6 years I've declared myself a strict vegetarian.
Let's get back to the drinking example, though. It took me several attempts to quit drinking. I thought it would simply be an informed choice. It seemed clear that drinking was a poor solution to whatever problems it was supposed to address. Since I'm a reasonably intelligent person it should have been easy to stop. But it wasn't.
No matter how much one part of my brain would scream that having another drink was stupid, I'd see myself — no, watch myself — marching to the liquor store to buy another bottle. I daresay that anybody who has ever experienced that sort of thing will be pretty sure that there's no such thing as Free Will.
How did I stop drinking? Well, it took me several tries, and I had help from a lot of fine people, both on the internet and off. Eventually the right circumstances arose and the right choices were made. But it would be silly for me to say that I “chose” to stop. It makes more sense to say stopping happened for some reason I do not have sufficient information to explain.
If you think you have Free Will and are afraid to consider that perhaps you don't, I heartily recommend that you either get addicted to something and then try to stop, or memorize Pi to a few dozen digits. Of those two options, the second one is far, far less damaging to your health. To the extent that you can choose, I'd recommend the second choice.
Of course, you may choose neither option. But nobody has enough information to know far in advance which choice you'll make or not make. Not even you can know that.
One thing I will predict, though: when you finally make your choice it will feel like Free Will.