The Bounded Infinite and Free Will

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.


  1. cont.
    Under these conditions, output should only be based on previous input conditions responding to contextual programming. Thus, free will can only occur with the constraints of previous experience. In relation to addiction, the brain pathways have obsessed = practiced, fantasized, and been rewarded for the addictive behavior such that they behave similar to dissociative personality states and would have access to the motor and decision making output neurons independant of other areas of brain activity. Thus, the free will of drinking has been translated into a well defined neural pathway of activity which acts now on a separat programming loop. The more frequently that loop is allowed to operate without any interference by the inhibitory mechanisms of self control, the fewer of those inhibitory neurons will have access to that loop and so the loop will have more 'fire power' to overide any signal from self control neurons. Only with continued practice do those self control neurons have physical connection to send enough signal to create a functional override. This can be experienced as bringing the act into more concious awareness rather than watching oneself perform acts one wishes they weren't. Our brains are not one object, merely billions of cooperating cells with their own connections whose sole purpose is to receive feedback, and work towards that goal, for to stop receiving feedback that their signal was sent is for that cell to wither and ultimately be pruned back, and die. Dopamine is the ultimate 'got it!' feedback neurotransmitter, even bacteria use it at part of feedback loops that their goal has been accomplished and seeking behaviors can be shut down, thus its primary role in reward, pleasure (which is what reward is), and addiction. Once the choice has been brought back into a more conscious awareness process, it will feel like free will, however it was our choices that trained our brain in the first place.

  2. cont.
    Now, if free will is in regards to no part in a divine plan, that is a very different matter. That would require that 1. there is a divine plan, 2. we have a specific part to play in that divine plan, 3. that the plan is set in stone. As a writer of fiction, I know full well that if I write character based, the characters can end up doing things differently than I had envisioned. They are acting in the context in which I created their characteristics, rather than in the plot I had desired. I can force them back into the plot (a bit of deus ex machina?) , or I can let the story unfold based on who they are. Sometimes something will happen that even I find suprising, and both the story and the characters will have to adapt due to that change. In our own cosmic space, there is the waveform of energy, matter, thought, etc which can behave like a giant contextual frame. To know the exact action of a particle in this waveform totality might be possible, but only beyond the system as it functions. There is always the random probablity of quantum mechanics which can alter events in unforseen ways. And some contexts bring our choices down to minimal events, all of which may be unpleasant. To determine we have the free will to overcome all obstances despite another persons exercise of their will denies the aspect of chance. Even most of evolution owes it current state to huge elements of chance.

    Free will, however, how we respond to events, is so tied to the character of our contextual experience that to be outside of it is virtually impossible. To have a choice which hurts others, is mostly neutral to others, or benefits others is really as far as free will goes. What one chooses is able to be chosen. Yet, contextual experience determines which pattern of choices one will ultimately make.

  3. Sweet, the first part ends up being the last part. I do so love technology. So, this was meant to be at the beginning:

    It sounds like free will as described here requires making a choice out of context. Or to create a choice where the choice was not part of the offered possibilities, although that level of creative adaptability would also be part of the personal context.

    Biologically, 'will' is tied to specific neurons which evolutionarily were responsible for transforming the monitored internal input, i.e. associations based on learned memory, emotional content, the knowledge base of previously rewarded behavior pathways, etc, those neurons will then activate(d) external output such as muscle movement, which with higher thinking also correlates with planning, fantasizing (mental practicing), etc., but at their most basic these neurons are output initiation loci.

  4. Phoenix11331: “Dopamine is the ultimate 'got it!' feedback neurotransmitter, even bacteria use it ...”

    I didn't know that about bacteria. Thanks.